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More integrals tested.

======================================================================
diff --git a/changelog b/changelog
index 6b98774..a9a8d1b 100644
--- a/changelog
+++ b/changelog
@@ -1,3 +1,5 @@
+20080331 tpd src/input/Makefile add integration regression testing
+20080331 tpd src/input/schaum12.input integrals of ax^2+bx+c
 20080330 tpd src/input/Makefile add integration regression testing
 20080330 tpd src/input/schaum11.input integrals of sqrt(a^2-x^2)
 20080330 tpd src/input/schaum10.input integrals of sqrt(x^2-a^2)
diff --git a/src/input/Makefile.pamphlet b/src/input/Makefile.pamphlet
index a1382e4..e42c5c0 100644
--- a/src/input/Makefile.pamphlet
+++ b/src/input/Makefile.pamphlet
@@ -357,7 +357,7 @@ REGRES= algaggr.regress algbrbf.regress  algfacob.regress alist.regress  \
     roman.regress     roots.regress    ruleset.regress  rules.regress \
     schaum1.regress   schaum2.regress  schaum3.regress  schaum4.regress \
     schaum5.regress   schaum6.regress  schaum7.regress  schaum8.regress \
-    schaum9.regress   schaum10.regress schaum11.regress \
+    schaum9.regress   schaum10.regress schaum11.regress schaum12.regress \
     scherk.regress    scope.regress    seccsc.regress \
     segbind.regress   seg.regress \
     series2.regress   series.regress   sersolve.regress set.regress \
@@ -633,7 +633,7 @@ FILES= ${OUT}/algaggr.input  ${OUT}/algbrbf.input    ${OUT}/algfacob.input \
        ${OUT}/schaum2.input  ${OUT}/schaum3.input    ${OUT}/schaum4.input \
        ${OUT}/schaum5.input  ${OUT}/schaum6.input    ${OUT}/schaum7.input \
        ${OUT}/schaum8.input  ${OUT}/schaum9.input    ${OUT}/schaum10.input \
-       ${OUT}/schaum11.input \
+       ${OUT}/schaum11.input ${OUT}/schaum12.input \
        ${OUT}/saddle.input \
        ${OUT}/scherk.input   ${OUT}/scope.input      ${OUT}/seccsc.input \
        ${OUT}/segbind.input  ${OUT}/seg.input        ${OUT}/series2.input \
@@ -937,7 +937,7 @@ DOCFILES= \
   ${DOC}/schaum5.input.dvi     ${DOC}/schaum6.input.dvi \
   ${DOC}/schaum7.input.dvi     ${DOC}/schaum8.input.dvi \
   ${DOC}/schaum9.input.dvi     ${DOC}/schaum10.input.dvi \
-  ${DOC}/schaum11.input.dvi \
+  ${DOC}/schaum11.input.dvi    ${DOC}/schaum12.input.dvi \
   ${DOC}/s01eaf.input.dvi      ${DOC}/s13aaf.input.dvi     \
   ${DOC}/s13acf.input.dvi      ${DOC}/s13adf.input.dvi     \
   ${DOC}/s14aaf.input.dvi      ${DOC}/s14abf.input.dvi     \
diff --git a/src/input/schaum12.input.pamphlet b/src/input/schaum12.input.pamphlet
new file mode 100644
index 0000000..6027801
--- /dev/null
+++ b/src/input/schaum12.input.pamphlet
@@ -0,0 +1,780 @@
+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/input schaum12.input}
+\author{Timothy Daly}
+\maketitle
+\eject
+\tableofcontents
+\eject
+\section{\cite{1}:14.265~~~~~$\displaystyle
+\int{\frac{dx}{ax^2+bx+c}}$}
+$$\int{\frac{1}{ax^2+bx+c}}=
+\left\{
+\begin{array}{l}
+\displaystyle\frac{2}{\sqrt{4ac-b^2}}\tan^{-1}\frac{2ax+b}{\sqrt{4ac-b^2}}\\
+\displaystyle\frac{1}{\sqrt{b^2-4ac}}\ln\left(
+\frac{2ax+b-\sqrt{b^2-4ac}}{2ax+b+\sqrt{b^2-4ac}}\right)
+\end{array}
+\right.
+$$
+<<*>>=
+)spool schaum12.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1 of 15
+aa:=integrate(1/sqrt(a*x^2+b*x+c),x)
+--R 
+--R
+--R   (1)
+--R   [
+--R       log
+--R                                 +--------------+
+--R                 +-+ +-+         |   2                   +-+
+--R              (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
+--R            + 
+--R                     2             +-+
+--R              (- 2a x  - b x - 2c)\|a
+--R         /
+--R                  +--------------+
+--R              +-+ |   2
+--R            2\|c \|a x  + b x + c  - b x - 2c
+--R    /
+--R        +-+
+--R       \|a
+--R     ,
+--R                 +--------------+
+--R           +---+ |   2               +---+ +-+
+--R          \|- a \|a x  + b x + c  - \|- a \|c
+--R    2atan(------------------------------------)
+--R                           a x
+--R    -------------------------------------------]
+--R                        +---+
+--R                       \|- a
+--R                                     Type: Union(List Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.266~~~~~$\displaystyle
+\int{\frac{x~dx}{ax^2+bx+c}}$}
+$$\int{\frac{x}{ax^2+bx+c}}=
+\frac{1}{2a}\ln(ax^2+bx+c)-\frac{b}{2a}\int{\frac{1}{ax^2+bx+c}}
+$$
+<<*>>=
+)clear all
+
+--S 2 of 15
+aa:=integrate(x/sqrt(a*x^2+b*x+c),x)
+--R 
+--R
+--R   (1)
+--R   [
+--R                   +--------------+
+--R               +-+ |   2               2
+--R           (2b\|c \|a x  + b x + c  - b x - 2b c)
+--R        *
+--R           log
+--R                                     +--------------+
+--R                     +-+ +-+         |   2                   +-+
+--R                  (2\|a \|c  + 2a x)\|a x  + b x + c  - 2a x\|c
+--R                + 
+--R                         2             +-+
+--R                  (- 2a x  - b x - 2c)\|a
+--R             /
+--R                      +--------------+
+--R                  +-+ |   2
+--R                2\|c \|a x  + b x + c  - b x - 2c
+--R       + 
+--R                    +--------------+
+--R                +-+ |   2                   2         +-+ +-+
+--R         - 2b x\|a \|a x  + b x + c  + (4a x  + 2b x)\|a \|c
+--R    /
+--R                  +--------------+
+--R          +-+ +-+ |   2                                +-+
+--R       4a\|a \|c \|a x  + b x + c  + (- 2a b x - 4a c)\|a
+--R     ,
+--R
+--R                     +--------------+
+--R                 +-+ |   2               2
+--R           (- 2b\|c \|a x  + b x + c  + b x + 2b c)
+--R        *
+--R                       +--------------+
+--R                 +---+ |   2               +---+ +-+
+--R                \|- a \|a x  + b x + c  - \|- a \|c
+--R           atan(------------------------------------)
+--R                                 a x
+--R       + 
+--R                     +--------------+
+--R               +---+ |   2                   2        +---+ +-+
+--R         - b x\|- a \|a x  + b x + c  + (2a x  + b x)\|- a \|c
+--R    /
+--R                    +--------------+
+--R          +---+ +-+ |   2                               +---+
+--R       2a\|- a \|c \|a x  + b x + c  + (- a b x - 2a c)\|- a
+--R     ]
+--R                                     Type: Union(List Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.267~~~~~$\displaystyle
+\int{\frac{x^2dx}{ax^2+bx+c}}$}
+$$\int{\frac{x^2}{ax^2+bx+c}}=
+\frac{x}{a}-\frac{b}{2a^2}\ln(ax^2+bx+c)+\frac{b^2-2ac}{2a^2}
+\int{\frac{1}{ax^2+bx+c}}
+$$
+<<*>>=
+)clear all
+
+--S 3 of 15
+aa:=integrate(x^2/(a*x^2+b*x+c),x)
+--R 
+--R
+--R   (1)
+--R   [
+--R                    2
+--R           (2a c - b )
+--R        *
+--R           log
+--R                                               +-----------+
+--R                     2 2                    2  |          2         2        2
+--R                  (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
+--R                + 
+--R                              3
+--R                  - 4a b c + b
+--R             /
+--R                   2
+--R                a x  + b x + c
+--R       + 
+--R                                          +-----------+
+--R                     2                    |          2
+--R         (- b log(a x  + b x + c) + 2a x)\|- 4a c + b
+--R    /
+--R           +-----------+
+--R         2 |          2
+--R       2a \|- 4a c + b
+--R     ,
+--R
+--R                                       +---------+
+--R                                       |        2
+--R                     2      (2a x + b)\|4a c - b
+--R         (- 4a c + 2b )atan(----------------------)
+--R                                           2
+--R                                   4a c - b
+--R       + 
+--R                                          +---------+
+--R                     2                    |        2
+--R         (- b log(a x  + b x + c) + 2a x)\|4a c - b
+--R    /
+--R           +---------+
+--R         2 |        2
+--R       2a \|4a c - b
+--R     ]
+--R                                     Type: Union(List Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.268~~~~~$\displaystyle
+\int{\frac{x^m~dx}{ax^2+bx+c}}$}
+$$\int{\frac{x^m}{ax^2+bx+c}}=
+\frac{x^{m-1}}{(m-1)a}-\frac{c}{a}\int{\frac{x^{m-2}}{ax^2+bx+c}}-
+\frac{b}{a}\int{\frac{x^{m-1}}{ax^2+bx+c}}
+$$
+<<*>>=
+)clear all
+
+--S 4 of 15
+aa:=integrate(x^m/(a*x^2+b*x+c),x)
+--R 
+--R
+--R           x         m
+--R         ++        %N
+--R   (1)   |   --------------- d%N
+--R        ++                2
+--R             c + %N b + %N a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.269~~~~~$\displaystyle
+\int{\frac{dx}{x(ax^2+bx+c)}}$}
+$$\int{\frac{1}{x(ax^2+bx+c)}}=
+\frac{1}{2c}\ln\left(\frac{x^2}{ax^2+bx+c}\right)-
+\frac{b}{2c}\int{\frac{1}{ax^2+bx+c}}
+$$
+<<*>>=
+)clear all
+
+--S 5 of 15
+aa:=integrate(1/(x*(a*x^2+b*x+c)),x)
+--R 
+--R
+--R   (1)
+--R   [
+--R           b
+--R        *
+--R           log
+--R                                               +-----------+
+--R                     2 2                    2  |          2         2        2
+--R                  (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
+--R                + 
+--R                              3
+--R                  - 4a b c + b
+--R             /
+--R                   2
+--R                a x  + b x + c
+--R       + 
+--R                                           +-----------+
+--R                   2                       |          2
+--R         (- log(a x  + b x + c) + 2log(x))\|- 4a c + b
+--R    /
+--R          +-----------+
+--R          |          2
+--R       2c\|- 4a c + b
+--R     ,
+--R
+--R                              +---------+
+--R                              |        2
+--R                   (2a x + b)\|4a c - b
+--R         - 2b atan(----------------------)
+--R                                  2
+--R                          4a c - b
+--R       + 
+--R                                           +---------+
+--R                   2                       |        2
+--R         (- log(a x  + b x + c) + 2log(x))\|4a c - b
+--R    /
+--R          +---------+
+--R          |        2
+--R       2c\|4a c - b
+--R     ]
+--R                                     Type: Union(List Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.270~~~~~$\displaystyle
+\int{\frac{dx}{x^2(ax^2+bx+c)}}$}
+$$\int{\frac{1}{x^2(ax^2+bx+c)}}=
+\frac{b}{2c^2}\ln\left(\frac{ax^2+bx+c}{x^2}\right)-\frac{1}{cx}+
+\frac{b^2-2ac}{2c^2}\int{\frac{1}{ax^2+bx+c}}
+$$
+<<*>>=
+)clear all
+
+--S 6 of 15
+aa:=integrate(1/(x^2*(a*x^2+b*x+c)),x)
+--R 
+--R
+--R   (1)
+--R   [
+--R                    2
+--R           (2a c - b )x
+--R        *
+--R           log
+--R                                               +-----------+
+--R                     2 2                    2  |          2         2        2
+--R                  (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
+--R                + 
+--R                              3
+--R                  - 4a b c + b
+--R             /
+--R                   2
+--R                a x  + b x + c
+--R       + 
+--R                                                      +-----------+
+--R                     2                                |          2
+--R         (b x log(a x  + b x + c) - 2b x log(x) - 2c)\|- 4a c + b
+--R    /
+--R            +-----------+
+--R         2  |          2
+--R       2c x\|- 4a c + b
+--R     ,
+--R
+--R                                         +---------+
+--R                                         |        2
+--R                     2        (2a x + b)\|4a c - b
+--R         (- 4a c + 2b )x atan(----------------------)
+--R                                             2
+--R                                     4a c - b
+--R       + 
+--R                                                      +---------+
+--R                     2                                |        2
+--R         (b x log(a x  + b x + c) - 2b x log(x) - 2c)\|4a c - b
+--R    /
+--R            +---------+
+--R         2  |        2
+--R       2c x\|4a c - b
+--R     ]
+--R                                     Type: Union(List Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.271~~~~~$\displaystyle
+\int{\frac{dx}{x^n(ax^2+bx+c)}}$}
+$$\int{\frac{1}{x^n(ax^2+bx+c)}}=
+-\frac{1}{(n-1)cx^{n-1}}-
+\frac{b}{c}\int{\frac{1}{x^{n-1}(ax^2+bx+c)}}-
+\frac{a}{c}\int{\frac{1}{x^{x-2}(ax^2+bx+c)}}
+$$
+<<*>>=
+)clear all
+
+--S 7 of 15
+aa:=integrate(1/(x^n*(ax^2+bx+c)),x)
+--R 
+--R
+--R                               x
+--R   (1)  - ------------------------------------------
+--R                       2                2   n log(x)
+--R          ((c + bx + ax )n - c - bx - ax )%e
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.272~~~~~$\displaystyle
+\int{\frac{dx}{(ax^2+bx+c)^2}}$}
+$$\int{\frac{1}{(ax^2+bx+c)^2}}=
+\frac{2xa+b}{(4ac-b^2)(ax^2+bx+c)}+
+\frac{2a}{4ac-b^2}\int{\frac{1}{ax^2+bx+c}}
+$$
+<<*>>=
+)clear all
+
+--S 8 of 15
+aa:=integrate(1/(a*x^2+b*x+c)^2,x)
+--R 
+--R
+--R   (1)
+--R   [
+--R              2 2
+--R           (2a x  + 2a b x + 2a c)
+--R        *
+--R           log
+--R                                               +-----------+
+--R                     2 2                    2  |          2       2        2
+--R                  (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
+--R                + 
+--R                            3
+--R                  4a b c - b
+--R             /
+--R                   2
+--R                a x  + b x + c
+--R       + 
+--R                    +-----------+
+--R                    |          2
+--R         (2a x + b)\|- 4a c + b
+--R    /
+--R                                                        +-----------+
+--R           2       2  2              3         2    2   |          2
+--R       ((4a c - a b )x  + (4a b c - b )x + 4a c  - b c)\|- 4a c + b
+--R     ,
+--R                                           +---------+
+--R                                           |        2                +---------+
+--R       2 2                      (2a x + b)\|4a c - b                 |        2
+--R    (4a x  + 4a b x + 4a c)atan(----------------------) + (2a x + b)\|4a c - b
+--R                                               2
+--R                                       4a c - b
+--R    ----------------------------------------------------------------------------
+--R                                                             +---------+
+--R                2       2  2              3         2    2   |        2
+--R            ((4a c - a b )x  + (4a b c - b )x + 4a c  - b c)\|4a c - b
+--R     ]
+--R                                     Type: Union(List Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.273~~~~~$\displaystyle
+\int{\frac{x~dx}{(ax^2+bx+c)^2}}$}
+$$\int{\frac{x}{(ax^2+bx+c)^2}}=
+-\frac{bx+2c}{(4ac-b^2)(ax^2+bx+c)}-
+\frac{b}{4ac-b^2}\int{\frac{1}{ax^2+bx+c}}
+$$
+<<*>>=
+)clear all
+
+--S 9 of 15
+aa:=integrate(x/(a*x^2+b*x+c)^2,x)
+--R 
+--R
+--R   (1)
+--R   [
+--R                 2    2
+--R           (a b x  + b x + b c)
+--R        *
+--R           log
+--R                                               +-----------+
+--R                     2 2                    2  |          2         2        2
+--R                  (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
+--R                + 
+--R                              3
+--R                  - 4a b c + b
+--R             /
+--R                   2
+--R                a x  + b x + c
+--R       + 
+--R                      +-----------+
+--R                      |          2
+--R         (- b x - 2c)\|- 4a c + b
+--R    /
+--R                                                        +-----------+
+--R           2       2  2              3         2    2   |          2
+--R       ((4a c - a b )x  + (4a b c - b )x + 4a c  - b c)\|- 4a c + b
+--R     ,
+--R
+--R                                                  +---------+
+--R                                                  |        2
+--R                  2     2              (2a x + b)\|4a c - b
+--R         (- 2a b x  - 2b x - 2b c)atan(----------------------)
+--R                                                      2
+--R                                              4a c - b
+--R       + 
+--R                      +---------+
+--R                      |        2
+--R         (- b x - 2c)\|4a c - b
+--R    /
+--R                                                        +---------+
+--R           2       2  2              3         2    2   |        2
+--R       ((4a c - a b )x  + (4a b c - b )x + 4a c  - b c)\|4a c - b
+--R     ]
+--R                                     Type: Union(List Expression Integer,...)
+--E
+@
+
+\section{\cite{1}:14.274~~~~~$\displaystyle
+\int{\frac{x^2~dx}{(ax^2+bx+c)^2}}$}
+$$\int{\frac{x^2}{(ax^2+bx+c)^2}}=
+\frac{(b^2-2ac)x+bc}{a(4ac-b^2)(ax^2+bx+c)}+
+\frac{2c}{4ac-b^2}\int{\frac{1}{ax^2+bx+c}}
+$$
+<<*>>=
+)clear all
+
+--S 10 of 15
+aa:=integrate(x^2/(a*x^2+b*x+c)^2,x)
+--R 
+--R
+--R   (1)
+--R   [
+--R              2   2                  2
+--R           (2a c x  + 2a b c x + 2a c )
+--R        *
+--R           log
+--R                                               +-----------+
+--R                     2 2                    2  |          2       2        2
+--R                  (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
+--R                + 
+--R                            3
+--R                  4a b c - b
+--R             /
+--R                   2
+--R                a x  + b x + c
+--R       + 
+--R                                +-----------+
+--R                     2          |          2
+--R         ((- 2a c + b )x + b c)\|- 4a c + b
+--R    /
+--R                                                            +-----------+
+--R           3     2 2  2      2         3       2 2      2   |          2
+--R       ((4a c - a b )x  + (4a b c - a b )x + 4a c  - a b c)\|- 4a c + b
+--R     ,
+--R
+--R                                                     +---------+
+--R                                                     |        2
+--R            2   2                  2      (2a x + b)\|4a c - b
+--R         (4a c x  + 4a b c x + 4a c )atan(----------------------)
+--R                                                         2
+--R                                                 4a c - b
+--R       + 
+--R                                +---------+
+--R                     2          |        2
+--R         ((- 2a c + b )x + b c)\|4a c - b
+--R    /
+--R                                                            +---------+
+--R           3     2 2  2      2         3       2 2      2   |        2
+--R       ((4a c - a b )x  + (4a b c - a b )x + 4a c  - a b c)\|4a c - b
+--R     ]
+--R                                     Type: Union(List Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.275~~~~~$\displaystyle
+\int{\frac{x^m~dx}{(ax^2+bx+c)^n}}$}
+$$
+\begin{array}{lr}
+\displaystyle\int{\frac{x^m}{(ax^2+bx+c)^n}}=
+&\displaystyle-\frac{x^{m-1}}{(2n-m-1)a(ax^2+bx+c)^{n-1}}\\
+&\\
+&\displaystyle+\frac{(m-1)c}{(2n-m-1)a}\int{\frac{x^{m-2}}{(ax^2+bx+2)^n}}\\
+&\\
+&\displaystyle-\frac{(n-m)b}{(2n-m-1)a}\int{\frac{x^{m-1}}{(ax^2+bx+c)^n}}
+\end{array}
+$$
+<<*>>=
+)clear all
+
+--S 11 of 15
+aa:=integrate(x^m/(a*x^2+b*x+c)^n,x)
+--R 
+--R
+--R           x           m
+--R         ++          %N
+--R   (1)   |   ------------------ d%N
+--R        ++                 2  n
+--R             (c + %N b + %N a)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.276~~~~~$\displaystyle
+\int{\frac{x^{2n-1}~dx}{(ax^2+bx+c)^n}}$}
+$$\begin{array}{lr}
+\displaystyle\int{\frac{x^{2n-1}}{(ax^2+bx+c)^n}}=
+&\displaystyle\frac{1}{a}\int{\frac{x^{2n-3}}{(ax^2+bx+c)^{n-1}}}\\
+&\\
+&\displaystyle-\frac{c}{a}\int{\frac{x^{2n-3}}{(ax^2+bx+c)^n}}\\
+&\\
+&\displaystyle-\frac{b}{a}\int{\frac{x^{2n-2}}{(ax^2+bx+c)^n}}
+\end{array}
+$$
+<<*>>=
+)clear all
+
+--S 12 of 15
+aa:=integrate(x^(2*n-1)/(a*x^2+b*x+c)^n,x)
+--R 
+--R
+--R           x        2n - 1
+--R         ++       %N
+--R   (1)   |   ------------------ d%N
+--R        ++                 2  n
+--R             (c + %N b + %N a)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.277~~~~~$\displaystyle
+\int{\frac{dx}{x(ax^2+bx+c)^2}}$}
+$$\begin{array}{lr}
+\displaystyle\int{\frac{1}{x(ax^2+bx+c)^2}}=
+&\displaystyle\frac{1}{2c(ax^2+bx+2)}\\
+&\\
+&\displaystyle-\frac{b}{2c}\int{\frac{1}{(ax^2+bx+c)^2}}\\
+&\\
+&\displaystyle+\frac{1}{c}\int{\frac{1}{x(ax^2+bx+c)}}
+\end{array}
+$$
+<<*>>=
+)clear all
+
+--S 13 of 15
+aa:=integrate(1/(x*(a*x^2+b*x+c)^2),x)
+--R 
+--R
+--R   (1)
+--R   [
+--R               2         3  2        2     4           2    3
+--R           ((6a b c - a b )x  + (6a b c - b )x + 6a b c  - b c)
+--R        *
+--R           log
+--R                                               +-----------+
+--R                     2 2                    2  |          2         2        2
+--R                  (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
+--R                + 
+--R                              3
+--R                  - 4a b c + b
+--R             /
+--R                   2
+--R                a x  + b x + c
+--R       + 
+--R                     2       2  2                3         2    2
+--R               ((- 4a c + a b )x  + (- 4a b c + b )x - 4a c  + b c)
+--R            *
+--R                      2
+--R               log(a x  + b x + c)
+--R           + 
+--R                 2        2  2               3         2     2
+--R             ((8a c - 2a b )x  + (8a b c - 2b )x + 8a c  - 2b c)log(x)
+--R           + 
+--R                              2     2
+--R             - 2a b c x + 4a c  - 2b c
+--R        *
+--R            +-----------+
+--R            |          2
+--R           \|- 4a c + b
+--R    /
+--R                                                                  +-----------+
+--R           2 3       2 2  2          3     3 2         4     2 3  |          2
+--R       ((8a c  - 2a b c )x  + (8a b c  - 2b c )x + 8a c  - 2b c )\|- 4a c + b
+--R     ,
+--R
+--R                  2          3  2           2      4            2     3
+--R           ((- 12a b c + 2a b )x  + (- 12a b c + 2b )x - 12a b c  + 2b c)
+--R        *
+--R                           +---------+
+--R                           |        2
+--R                (2a x + b)\|4a c - b
+--R           atan(----------------------)
+--R                               2
+--R                       4a c - b
+--R       + 
+--R                     2       2  2                3         2    2
+--R               ((- 4a c + a b )x  + (- 4a b c + b )x - 4a c  + b c)
+--R            *
+--R                      2
+--R               log(a x  + b x + c)
+--R           + 
+--R                 2        2  2               3         2     2
+--R             ((8a c - 2a b )x  + (8a b c - 2b )x + 8a c  - 2b c)log(x)
+--R           + 
+--R                              2     2
+--R             - 2a b c x + 4a c  - 2b c
+--R        *
+--R            +---------+
+--R            |        2
+--R           \|4a c - b
+--R    /
+--R                                                                  +---------+
+--R           2 3       2 2  2          3     3 2         4     2 3  |        2
+--R       ((8a c  - 2a b c )x  + (8a b c  - 2b c )x + 8a c  - 2b c )\|4a c - b
+--R     ]
+--R                                     Type: Union(List Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.278~~~~~$\displaystyle
+\int{\frac{dx}{x^2(ax^2+bx+c)^2}}$}
+$$\begin{array}{lr}
+\displaystyle\int{\frac{1}{x^2(ax^2+bx+c)^2}}=
+&\displaystyle-\frac{1}{cx(ax^2+bx+c)}\\
+&\\
+&\displaystyle-\frac{3a}{c}\int{\frac{1}{(ax^2+bx+c)^2}}\\
+&\\
+&\displaystyle-\frac{2b}{c}\int{\frac{1}{x(ax^2+bx+c)^2}}
+\end{array}
+$$
+<<*>>=
+)clear all
+
+--S 14 of 15
+aa:=integrate(1/(x^2*(a*x^2+b*x+c)^2),x)
+--R 
+--R
+--R   (1)
+--R   [
+--R                3 2     2 2       4  3      2   2       3     5  2
+--R             (6a c  - 6a b c + a b )x  + (6a b c  - 6a b c + b )x
+--R           + 
+--R                2 3       2 2    4
+--R             (6a c  - 6a b c  + b c)x
+--R        *
+--R           log
+--R                                               +-----------+
+--R                     2 2                    2  |          2         2        2
+--R                  (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
+--R                + 
+--R                              3
+--R                  - 4a b c + b
+--R             /
+--R                   2
+--R                a x  + b x + c
+--R       + 
+--R                   2         3  3        2     4  2          2    3
+--R               ((4a b c - a b )x  + (4a b c - b )x  + (4a b c  - b c)x)
+--R            *
+--R                      2
+--R               log(a x  + b x + c)
+--R           + 
+--R                     2          3  3          2      4  2            2     3
+--R               ((- 8a b c + 2a b )x  + (- 8a b c + 2b )x  + (- 8a b c  + 2b c)x)
+--R            *
+--R               log(x)
+--R           + 
+--R                  2 2       2   2            2     3          3    2 2
+--R             (- 6a c  + 2a b c)x  + (- 7a b c  + 2b c)x - 4a c  + b c
+--R        *
+--R            +-----------+
+--R            |          2
+--R           \|- 4a c + b
+--R    /
+--R                                                                   +-----------+
+--R           2 4      2 3  3          4    3 3  2        5    2 4    |          2
+--R       ((4a c  - a b c )x  + (4a b c  - b c )x  + (4a c  - b c )x)\|- 4a c + b
+--R     ,
+--R
+--R                   3 2      2 2        4  3         2   2        3      5  2
+--R             (- 12a c  + 12a b c - 2a b )x  + (- 12a b c  + 12a b c - 2b )x
+--R           + 
+--R                   2 3        2 2     4
+--R             (- 12a c  + 12a b c  - 2b c)x
+--R        *
+--R                           +---------+
+--R                           |        2
+--R                (2a x + b)\|4a c - b
+--R           atan(----------------------)
+--R                               2
+--R                       4a c - b
+--R       + 
+--R                   2         3  3        2     4  2          2    3
+--R               ((4a b c - a b )x  + (4a b c - b )x  + (4a b c  - b c)x)
+--R            *
+--R                      2
+--R               log(a x  + b x + c)
+--R           + 
+--R                     2          3  3          2      4  2            2     3
+--R               ((- 8a b c + 2a b )x  + (- 8a b c + 2b )x  + (- 8a b c  + 2b c)x)
+--R            *
+--R               log(x)
+--R           + 
+--R                  2 2       2   2            2     3          3    2 2
+--R             (- 6a c  + 2a b c)x  + (- 7a b c  + 2b c)x - 4a c  + b c
+--R        *
+--R            +---------+
+--R            |        2
+--R           \|4a c - b
+--R    /
+--R                                                                   +---------+
+--R           2 4      2 3  3          4    3 3  2        5    2 4    |        2
+--R       ((4a c  - a b c )x  + (4a b c  - b c )x  + (4a c  - b c )x)\|4a c - b
+--R     ]
+--R                                     Type: Union(List Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.279~~~~~$\displaystyle
+\int{\frac{dx}{x^m(ax^2+bx+c)^n}}$}
+$$\begin{array}{lr}
+\displaystyle\int{\frac{1}{x^m(ax^2+bx+c)^n}}=
+&\displaystyle-\frac{1}{(m-1)cx^{m-1}(ax^2+bx+c)^{n-1}}\\
+&\\
+&\displaystyle-\frac{(m+2n-3)a}{(m-1)c}\int{\frac{1}{x^{m-2}(ax^2+bx+c)^n}}\\
+&\\
+&\displaystyle-\frac{(m+n-2)b}{(m-1)c}\int{\frac{1}{x^{m-1}(ax^2+bx+c)^n}}
+\end{array}
+$$
+<<*>>=
+)clear all
+
+--S 15 of 15
+aa:=integrate(1/(x^m*(a*x^2+b*x+c)^n),x)
+--R 
+--R
+--R           x
+--R         ++            1
+--R   (1)   |   --------------------- d%N
+--R        ++     m              2  n
+--R             %N (c + %N b + %N a)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+)spool
+)lisp (bye)
+@
+
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} Spiegel, Murray R.
+{\sl Mathematical Handbook of Formulas and Tables}\\
+Schaum's Outline Series McGraw-Hill 1968 p71
+\end{thebibliography}
+\end{document}



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More integrals

=========================================================================
diff --git a/changelog b/changelog
index a9a8d1b..6f6fcb0 100644
--- a/changelog
+++ b/changelog
@@ -1,3 +1,7 @@
+20080401 tpd src/input/Makefile add integration regression testing
+20080401 tpd src/input/schaum14.input integrals of x^3+a^3
+20080401 tpd src/input/schaum13.input integrals of sqrt(ax^2+bx+c)
+20080401 tpd src/input/schaum12.input fix typo
 20080331 tpd src/input/Makefile add integration regression testing
 20080331 tpd src/input/schaum12.input integrals of ax^2+bx+c
 20080330 tpd src/input/Makefile add integration regression testing
diff --git a/src/input/Makefile.pamphlet b/src/input/Makefile.pamphlet
index e42c5c0..2f109e9 100644
--- a/src/input/Makefile.pamphlet
+++ b/src/input/Makefile.pamphlet
@@ -358,6 +358,7 @@ REGRES= algaggr.regress algbrbf.regress  algfacob.regress alist.regress  \
     schaum1.regress   schaum2.regress  schaum3.regress  schaum4.regress \
     schaum5.regress   schaum6.regress  schaum7.regress  schaum8.regress \
     schaum9.regress   schaum10.regress schaum11.regress schaum12.regress \
+    schaum13.regress  schaum14.regress \
     scherk.regress    scope.regress    seccsc.regress \
     segbind.regress   seg.regress \
     series2.regress   series.regress   sersolve.regress set.regress \
@@ -633,7 +634,8 @@ FILES= ${OUT}/algaggr.input  ${OUT}/algbrbf.input    ${OUT}/algfacob.input \
        ${OUT}/schaum2.input  ${OUT}/schaum3.input    ${OUT}/schaum4.input \
        ${OUT}/schaum5.input  ${OUT}/schaum6.input    ${OUT}/schaum7.input \
        ${OUT}/schaum8.input  ${OUT}/schaum9.input    ${OUT}/schaum10.input \
-       ${OUT}/schaum11.input ${OUT}/schaum12.input \
+       ${OUT}/schaum11.input ${OUT}/schaum12.input   ${OUT}/schaum13.input \
+       ${OUT}/schaum14.input \
        ${OUT}/saddle.input \
        ${OUT}/scherk.input   ${OUT}/scope.input      ${OUT}/seccsc.input \
        ${OUT}/segbind.input  ${OUT}/seg.input        ${OUT}/series2.input \
@@ -938,6 +940,7 @@ DOCFILES= \
   ${DOC}/schaum7.input.dvi     ${DOC}/schaum8.input.dvi \
   ${DOC}/schaum9.input.dvi     ${DOC}/schaum10.input.dvi \
   ${DOC}/schaum11.input.dvi    ${DOC}/schaum12.input.dvi \
+  ${DOC}/schaum13.input.dvi    ${DOC}/schaum14.input.dvi \
   ${DOC}/s01eaf.input.dvi      ${DOC}/s13aaf.input.dvi     \
   ${DOC}/s13acf.input.dvi      ${DOC}/s13adf.input.dvi     \
   ${DOC}/s14aaf.input.dvi      ${DOC}/s14abf.input.dvi     \
diff --git a/src/input/schaum12.input.pamphlet b/src/input/schaum12.input.pamphlet
index 6027801..6669ade 100644
--- a/src/input/schaum12.input.pamphlet
+++ b/src/input/schaum12.input.pamphlet
@@ -321,13 +321,14 @@ $$
 )clear all
 
 --S 7 of 15
-aa:=integrate(1/(x^n*(ax^2+bx+c)),x)
+aa:=integrate(1/(x^n*(a*x^2+b*x+c)),x)
 --R 
 --R
---R                               x
---R   (1)  - ------------------------------------------
---R                       2                2   n log(x)
---R          ((c + bx + ax )n - c - bx - ax )%e
+--R           x
+--R         ++            1
+--R   (1)   |   -------------------- d%N
+--R        ++                 2    n
+--R             (c + %N b + %N a)%N
 --R                                          Type: Union(Expression Integer,...)
 --E 
 @
diff --git a/src/input/schaum13.input.pamphlet b/src/input/schaum13.input.pamphlet
new file mode 100644
index 0000000..04551e6
--- /dev/null
+++ b/src/input/schaum13.input.pamphlet
@@ -0,0 +1,1266 @@
+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/input schaum13.input}
+\author{Timothy Daly}
+\maketitle
+\eject
+\tableofcontents
+\eject
+\section{\cite{1}:14.280~~~~~$\displaystyle
+\int{\frac{dx}{\sqrt{ax^2+bx+c}}}$}
+$$\int{\frac{1}{\sqrt{ax^2+bx+c}}}=
+\left\{
+\begin{array}{l}
+\displaystyle
+\frac{1}{\sqrt{a}}\ln\left(2\sqrt{a}\sqrt{ax^2+bx+c}+2ax+b\right)\\
+\\
+\displaystyle
+-\frac{1}{\sqrt{-a}}\sin{-1}\left(\frac{2ax+b}{\sqrt{b^2-4ac}}\right)\\
+\\
+\displaystyle
+\frac{1}{\sqrt{a}}\sinh^{-1}\left(\frac{2ax+b}{\sqrt{4ac-b^2}}\right)
+\end{array}
+\right.
+$$
+<<*>>=
+)spool schaum13.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1 of 19
+aa:=integrate(1/sqrt(a*x^2+b*x+c),x)
+--R 
+--R
+--R   (1)
+--R   [
+--R       log
+--R                                 +--------------+
+--R                 +-+ +-+         |   2                   +-+
+--R              (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
+--R            + 
+--R                     2             +-+
+--R              (- 2a x  - b x - 2c)\|a
+--R         /
+--R                  +--------------+
+--R              +-+ |   2
+--R            2\|c \|a x  + b x + c  - b x - 2c
+--R    /
+--R        +-+
+--R       \|a
+--R     ,
+--R                 +--------------+
+--R           +---+ |   2               +---+ +-+
+--R          \|- a \|a x  + b x + c  - \|- a \|c
+--R    2atan(------------------------------------)
+--R                           a x
+--R    -------------------------------------------]
+--R                        +---+
+--R                       \|- a
+--R                                     Type: Union(List Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.281~~~~~$\displaystyle
+\int{\frac{x~dx}{\sqrt{ax^2+bx+c}}}$}
+$$\int{\frac{x}{\sqrt{ax^2+bx+c}}}=
+\frac{\sqrt{ax^2+bx+c}}{a}-\frac{b}{2a}\int{\frac{1}{\sqrt{ax^2+bx+c}}}
+$$
+<<*>>=
+)clear all
+
+--S 2 of 19
+aa:=integrate(x/sqrt(a*x^2+b*x+c),x)
+--R 
+--R
+--R   (1)
+--R   [
+--R                   +--------------+
+--R               +-+ |   2               2
+--R           (2b\|c \|a x  + b x + c  - b x - 2b c)
+--R        *
+--R           log
+--R                                     +--------------+
+--R                     +-+ +-+         |   2                   +-+
+--R                  (2\|a \|c  + 2a x)\|a x  + b x + c  - 2a x\|c
+--R                + 
+--R                         2             +-+
+--R                  (- 2a x  - b x - 2c)\|a
+--R             /
+--R                      +--------------+
+--R                  +-+ |   2
+--R                2\|c \|a x  + b x + c  - b x - 2c
+--R       + 
+--R                    +--------------+
+--R                +-+ |   2                   2         +-+ +-+
+--R         - 2b x\|a \|a x  + b x + c  + (4a x  + 2b x)\|a \|c
+--R    /
+--R                  +--------------+
+--R          +-+ +-+ |   2                                +-+
+--R       4a\|a \|c \|a x  + b x + c  + (- 2a b x - 4a c)\|a
+--R     ,
+--R
+--R                     +--------------+
+--R                 +-+ |   2               2
+--R           (- 2b\|c \|a x  + b x + c  + b x + 2b c)
+--R        *
+--R                       +--------------+
+--R                 +---+ |   2               +---+ +-+
+--R                \|- a \|a x  + b x + c  - \|- a \|c
+--R           atan(------------------------------------)
+--R                                 a x
+--R       + 
+--R                     +--------------+
+--R               +---+ |   2                   2        +---+ +-+
+--R         - b x\|- a \|a x  + b x + c  + (2a x  + b x)\|- a \|c
+--R    /
+--R                    +--------------+
+--R          +---+ +-+ |   2                               +---+
+--R       2a\|- a \|c \|a x  + b x + c  + (- a b x - 2a c)\|- a
+--R     ]
+--R                                     Type: Union(List Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.282~~~~~$\displaystyle
+\int{\frac{x^2dx}{\sqrt{ax^2+bx+c}}}$}
+$$\int{\frac{x^2}{\sqrt{ax^2+bx+c}}}=
+\frac{2ax-3b}{4a^2}\sqrt{ax^2+bx+c}+\frac{3b^2-4ac}{8a^2}
+\int{\frac{1}{\sqrt{ax^2+bx+c}}}
+$$
+<<*>>=
+)clear all
+
+--S 3 of 19
+aa:=integrate(x^2/(a*x^2+b*x+c),x)
+--R 
+--R
+--R   (1)
+--R   [
+--R                    2
+--R           (2a c - b )
+--R        *
+--R           log
+--R                                               +-----------+
+--R                     2 2                    2  |          2         2        2
+--R                  (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
+--R                + 
+--R                              3
+--R                  - 4a b c + b
+--R             /
+--R                   2
+--R                a x  + b x + c
+--R       + 
+--R                                          +-----------+
+--R                     2                    |          2
+--R         (- b log(a x  + b x + c) + 2a x)\|- 4a c + b
+--R    /
+--R           +-----------+
+--R         2 |          2
+--R       2a \|- 4a c + b
+--R     ,
+--R
+--R                                       +---------+
+--R                                       |        2
+--R                     2      (2a x + b)\|4a c - b
+--R         (- 4a c + 2b )atan(----------------------)
+--R                                           2
+--R                                   4a c - b
+--R       + 
+--R                                          +---------+
+--R                     2                    |        2
+--R         (- b log(a x  + b x + c) + 2a x)\|4a c - b
+--R    /
+--R           +---------+
+--R         2 |        2
+--R       2a \|4a c - b
+--R     ]
+--R                                     Type: Union(List Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.283~~~~~$\displaystyle
+\int{\frac{dx}{x\sqrt{ax^2+bx+c}}}$}
+$$\int{\frac{1}{x\sqrt{ax^2+bx+c}}}=
+\left\{
+\begin{array}{l}
+\displaystyle
+-\frac{1}{\sqrt{c}}
+\ln\left(\frac{2\sqrt{c}{\sqrt{ax^2+bx+c}}+bx+2c}{x}\right)\\
+\\
+\displaystyle
+\frac{1}{\sqrt{-c}}\sin^{-1}\left(\frac{bx+2c}{|x|\sqrt{b^2-4ac}}\right)\\
+\\
+\displaystyle
+-\frac{1}{\sqrt{c}}\sinh^{-1}\left(\frac{bx+2c}{|x|\sqrt{4ac-b^2}}\right)
+\end{array}
+\right.
+$$
+<<*>>=
+)clear all
+
+--S 4 of 19
+aa:=integrate(1/x*(a*x^2+b*x+c),x)
+--R 
+--R
+--R                       2
+--R        2c log(x) + a x  + 2b x
+--R   (1)  -----------------------
+--R                   2
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.284~~~~~$\displaystyle
+\int{\frac{dx}{x^2\sqrt{ax^2+bx+c}}}$}
+$$\int{\frac{1}{x^2\sqrt{ax^2+bx+c}}}=
+-\frac{\sqrt{ax^2+bx+c}}{cx}-\frac{b}{2c}\int{\frac{1}{x\sqrt{ax^2+bx+c}}}
+$$
+<<*>>=
+)clear all
+
+--S 5 of 19
+aa:=integrate(1/(x^2*(a*x^2+b*x+c)),x)
+--R 
+--R
+--R   (1)
+--R   [
+--R                    2
+--R           (2a c - b )x
+--R        *
+--R           log
+--R                                               +-----------+
+--R                     2 2                    2  |          2         2        2
+--R                  (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
+--R                + 
+--R                              3
+--R                  - 4a b c + b
+--R             /
+--R                   2
+--R                a x  + b x + c
+--R       + 
+--R                                                      +-----------+
+--R                     2                                |          2
+--R         (b x log(a x  + b x + c) - 2b x log(x) - 2c)\|- 4a c + b
+--R    /
+--R            +-----------+
+--R         2  |          2
+--R       2c x\|- 4a c + b
+--R     ,
+--R
+--R                                         +---------+
+--R                                         |        2
+--R                     2        (2a x + b)\|4a c - b
+--R         (- 4a c + 2b )x atan(----------------------)
+--R                                             2
+--R                                     4a c - b
+--R       + 
+--R                                                      +---------+
+--R                     2                                |        2
+--R         (b x log(a x  + b x + c) - 2b x log(x) - 2c)\|4a c - b
+--R    /
+--R            +---------+
+--R         2  |        2
+--R       2c x\|4a c - b
+--R     ]
+--R                                     Type: Union(List Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.285~~~~~$\displaystyle
+\int{\sqrt{ax^2+bx+c}}~dx$}
+$$\int{\sqrt{ax^2+bx+c}}=
+\frac{(2ax+b)\sqrt{ax^2+bx+c}}{4a}+
+\frac{4ac-b^2}{8a}\int{\frac{1}{\sqrt{ax^2+bx+c}}}
+$$
+<<*>>=
+)clear all
+
+--S 6 of 19
+aa:=integrate(sqrt(a*x^2+b*x+c),x)
+--R 
+--R
+--R   (1)
+--R   [
+--R                                                    +--------------+
+--R                           3          2     2   +-+ |   2
+--R             ((16a b c - 4b )x + 32a c  - 8b c)\|c \|a x  + b x + c
+--R           + 
+--R                   2 2    4  2             2     3           3     2 2
+--R             (- 16a c  + b )x  + (- 32a b c  + 8b c)x - 32a c  + 8b c
+--R        *
+--R           log
+--R                                     +--------------+
+--R                     +-+ +-+         |   2                   +-+
+--R                  (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
+--R                + 
+--R                         2             +-+
+--R                  (- 2a x  - b x - 2c)\|a
+--R             /
+--R                      +--------------+
+--R                  +-+ |   2
+--R                2\|c \|a x  + b x + c  - b x - 2c
+--R       + 
+--R                  2        2  3                  3  2           2     2     +-+
+--R           ((- 16a c - 4a b )x  + (- 40a b c - 2b )x  + (- 32a c  - 8b c)x)\|a
+--R        *
+--R            +--------------+
+--R            |   2
+--R           \|a x  + b x + c
+--R       + 
+--R                  2   4       2         2  3                3  2
+--R               16a b x  + (32a c + 24a b )x  + (56a b c + 6b )x
+--R             + 
+--R                     2     2
+--R               (32a c  + 8b c)x
+--R        *
+--R            +-+ +-+
+--R           \|a \|c
+--R    /
+--R                                   +--------------+
+--R                           +-+ +-+ |   2
+--R         (32a b x + 64a c)\|a \|c \|a x  + b x + c
+--R       + 
+--R                2        2  2                    2  +-+
+--R         ((- 32a c - 8a b )x  - 64a b c x - 64a c )\|a
+--R     ,
+--R
+--R                                                    +--------------+
+--R                           3          2     2   +-+ |   2
+--R             ((16a b c - 4b )x + 32a c  - 8b c)\|c \|a x  + b x + c
+--R           + 
+--R                   2 2    4  2             2     3           3     2 2
+--R             (- 16a c  + b )x  + (- 32a b c  + 8b c)x - 32a c  + 8b c
+--R        *
+--R                       +--------------+
+--R                 +---+ |   2               +---+ +-+
+--R                \|- a \|a x  + b x + c  - \|- a \|c
+--R           atan(------------------------------------)
+--R                                 a x
+--R       + 
+--R                 2        2  3                 3  2           2     2     +---+
+--R           ((- 8a c - 2a b )x  + (- 20a b c - b )x  + (- 16a c  - 4b c)x)\|- a
+--R        *
+--R            +--------------+
+--R            |   2
+--R           \|a x  + b x + c
+--R       + 
+--R              2   4       2         2  3                3  2         2     2
+--R           (8a b x  + (16a c + 12a b )x  + (28a b c + 3b )x  + (16a c  + 4b c)x)
+--R        *
+--R            +---+ +-+
+--R           \|- a \|c
+--R    /
+--R                                     +--------------+
+--R                           +---+ +-+ |   2
+--R         (16a b x + 32a c)\|- a \|c \|a x  + b x + c
+--R       + 
+--R                2        2  2                    2  +---+
+--R         ((- 16a c - 4a b )x  - 32a b c x - 32a c )\|- a
+--R     ]
+--R                                     Type: Union(List Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.286~~~~~$\displaystyle
+\int{x\sqrt{ax^2+bx+c}}~dx$}
+$$
+\begin{array}{rl}
+\displaystyle
+\int{x\sqrt{ax^2+bx+c}}=&\displaystyle\frac{(ax^2+bx+c)^{3/2}}{3a}\\
+&\\
+&\displaystyle-\frac{b(2ax+b)}{8a^2}\sqrt{ax^2+bx+c}\\
+&\\
+&\displaystyle-\frac{b(4ac-b^2)}{16a^2}\int{\frac{1}{\sqrt{ax^2+bx+c}}}
+\end{array}
+$$
+<<*>>=
+)clear all
+
+--S 7 of 19
+aa:=integrate(x*sqrt(a*x^2+b*x+c),x)
+--R 
+--R
+--R   (1)
+--R   [
+--R                     2   2        3       5  2          2 2      4
+--R                 (96a b c  + 48a b c - 18b )x  + (384a b c  - 96b c)x
+--R               + 
+--R                         3      3 2
+--R                 384a b c  - 96b c
+--R            *
+--R                    +--------------+
+--R                +-+ |   2
+--R               \|c \|a x  + b x + c
+--R           + 
+--R                    2 2 2        4      6  3
+--R             (- 144a b c  + 24a b c + 3b )x
+--R           + 
+--R                    2   3         3 2      5   2            2 3       4 2
+--R             (- 288a b c  - 144a b c  + 54b c)x  + (- 576a b c  + 144b c )x
+--R           + 
+--R                       4      3 3
+--R             - 384a b c  + 96b c
+--R        *
+--R           log
+--R                                     +--------------+
+--R                     +-+ +-+         |   2                   +-+
+--R                  (2\|a \|c  + 2a x)\|a x  + b x + c  - 2a x\|c
+--R                + 
+--R                         2             +-+
+--R                  (- 2a x  - b x - 2c)\|a
+--R             /
+--R                      +--------------+
+--R                  +-+ |   2
+--R                2\|c \|a x  + b x + c  - b x - 2c
+--R       + 
+--R                    3         2 3  5          3 2       2 2        4  4
+--R             (- 192a b c - 16a b )x  + (- 384a c  - 336a b c - 4a b )x
+--R           + 
+--R                     2   2        3      5  3
+--R             (- 1056a b c  - 16a b c + 6b )x
+--R           + 
+--R                    2 3         2 2      4   2              3      3 2
+--R             (- 768a c  - 288a b c  + 72b c)x  + (- 384a b c  + 96b c )x
+--R        *
+--R                +--------------+
+--R            +-+ |   2
+--R           \|a \|a x  + b x + c
+--R       + 
+--R                  4       3 2  6        3          2 3  5
+--R             (128a c + 96a b )x  + (672a b c + 120a b )x
+--R           + 
+--R                  3 2       2 2         4  4         2   2        3       5  3
+--R             (768a c  + 816a b c - 12a b )x  + (1632a b c  + 64a b c - 30b )x
+--R           + 
+--R                  2 3         2 2       4   2            3      3 2
+--R             (768a c  + 480a b c  - 120b c)x  + (384a b c  - 96b c )x
+--R        *
+--R            +-+ +-+
+--R           \|a \|c
+--R    /
+--R                 3        2 2  2        2             2 2  +-+ +-+
+--R           ((384a c + 288a b )x  + 1536a b c x + 1536a c )\|a \|c
+--R        *
+--R            +--------------+
+--R            |   2
+--R           \|a x  + b x + c
+--R       + 
+--R                    3         2 3  3           3 2       2 2   2        2   2
+--R             (- 576a b c - 48a b )x  + (- 1152a c  - 864a b c)x  - 2304a b c x
+--R           + 
+--R                    2 3
+--R             - 1536a c
+--R        *
+--R            +-+
+--R           \|a
+--R     ,
+--R
+--R                       2   2        3       5  2            2 2      4
+--R                 (- 96a b c  - 48a b c + 18b )x  + (- 384a b c  + 96b c)x
+--R               + 
+--R                           3      3 2
+--R                 - 384a b c  + 96b c
+--R            *
+--R                    +--------------+
+--R                +-+ |   2
+--R               \|c \|a x  + b x + c
+--R           + 
+--R                  2 2 2        4      6  3        2   3         3 2      5   2
+--R             (144a b c  - 24a b c - 3b )x  + (288a b c  + 144a b c  - 54b c)x
+--R           + 
+--R                    2 3       4 2             4      3 3
+--R             (576a b c  - 144b c )x + 384a b c  - 96b c
+--R        *
+--R                       +--------------+
+--R                 +---+ |   2               +---+ +-+
+--R                \|- a \|a x  + b x + c  - \|- a \|c
+--R           atan(------------------------------------)
+--R                                 a x
+--R       + 
+--R                   3        2 3  5          3 2       2 2        4  4
+--R             (- 96a b c - 8a b )x  + (- 192a c  - 168a b c - 2a b )x
+--R           + 
+--R                    2   2       3      5  3          2 3         2 2      4   2
+--R             (- 528a b c  - 8a b c + 3b )x  + (- 384a c  - 144a b c  + 36b c)x
+--R           + 
+--R                        3      3 2
+--R             (- 192a b c  + 48b c )x
+--R        *
+--R                  +--------------+
+--R            +---+ |   2
+--R           \|- a \|a x  + b x + c
+--R       + 
+--R                 4       3 2  6        3         2 3  5
+--R             (64a c + 48a b )x  + (336a b c + 60a b )x
+--R           + 
+--R                  3 2       2 2        4  4        2   2        3       5  3
+--R             (384a c  + 408a b c - 6a b )x  + (816a b c  + 32a b c - 15b )x
+--R           + 
+--R                  2 3         2 2      4   2            3      3 2
+--R             (384a c  + 240a b c  - 60b c)x  + (192a b c  - 48b c )x
+--R        *
+--R            +---+ +-+
+--R           \|- a \|c
+--R    /
+--R                 3        2 2  2       2            2 2  +---+ +-+
+--R           ((192a c + 144a b )x  + 768a b c x + 768a c )\|- a \|c
+--R        *
+--R            +--------------+
+--R            |   2
+--R           \|a x  + b x + c
+--R       + 
+--R                    3         2 3  3          3 2       2 2   2        2   2
+--R             (- 288a b c - 24a b )x  + (- 576a c  - 432a b c)x  - 1152a b c x
+--R           + 
+--R                   2 3
+--R             - 768a c
+--R        *
+--R            +---+
+--R           \|- a
+--R     ]
+--R                                     Type: Union(List Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.287~~~~~$\displaystyle
+\int{x^2\sqrt{ax^2+bx+c}}~dx$}
+$$\int{x^2\sqrt{ax^2+bx+c}}=
+\frac{6ax-5b}{24a^2}(ax^2+bx+c)^{3/2}+
+\frac{5b^2-4ac}{16a^2}\int{\sqrt{ax^2+bx+c}}
+$$
+<<*>>=
+)clear all
+
+--S 8 of 19
+aa:=integrate(x^2*sqrt(a*x^2+b*x+c),x)
+--R 
+--R
+--R   (1)
+--R   [
+--R                       3   3        2 3 2        5        7  3
+--R                 (1536a b c  - 1920a b c  - 96a b c + 120b )x
+--R               + 
+--R                       3 4       2 2 3          4 2        6   2
+--R                 (3072a c  - 768a b c  - 4800a b c  + 1200b c)x
+--R               + 
+--R                       2   4           3 3        5 2          2 5          2 4
+--R                 (9216a b c  - 13824a b c  + 2880b c )x + 6144a c  - 9216a b c
+--R               + 
+--R                      4 3
+--R                 1920b c
+--R            *
+--R                    +--------------+
+--R                +-+ |   2
+--R               \|c \|a x  + b x + c
+--R           + 
+--R                    4 4        2 4 2         6       8  4
+--R             (- 768a c  + 1440a b c  - 288a b c - 15b )x
+--R           + 
+--R                     3   4        2 3 3         5 2       7   3
+--R             (- 6144a b c  + 7680a b c  + 384a b c  - 480b c)x
+--R           + 
+--R                     3 5        2 2 4          4 3        6 2  2
+--R             (- 6144a c  + 1536a b c  + 9600a b c  - 2400b c )x
+--R           + 
+--R                      2   5           3 4        5 3          2 6          2 5
+--R             (- 12288a b c  + 18432a b c  - 3840b c )x - 6144a c  + 9216a b c
+--R           + 
+--R                    4 4
+--R             - 1920b c
+--R        *
+--R           log
+--R                                     +--------------+
+--R                     +-+ +-+         |   2                   +-+
+--R                  (2\|a \|c  + 2a x)\|a x  + b x + c  - 2a x\|c
+--R                + 
+--R                         2             +-+
+--R                  (- 2a x  - b x - 2c)\|a
+--R             /
+--R                      +--------------+
+--R                  +-+ |   2
+--R                2\|c \|a x  + b x + c  - b x - 2c
+--R       + 
+--R                     5 2        4 2       3 4  7
+--R             (- 1536a c  - 2304a b c - 96a b )x
+--R           + 
+--R                      4   2        3 3       2 5  6
+--R             (- 12544a b c  - 3456a b c - 16a b )x
+--R           + 
+--R                      4 3         3 2 2      2 4         6  5
+--R             (- 13056a c  - 18240a b c  - 80a b c + 20a b )x
+--R           + 
+--R                      3   3       2 3 2        5       7  4
+--R             (- 31104a b c  + 480a b c  + 24a b c - 30b )x
+--R           + 
+--R                      3 4       2 2 3          4 2       6   3
+--R             (- 18432a c  + 768a b c  + 2816a b c  - 720b c)x
+--R           + 
+--R                     2   4           3 3        5 2  2
+--R             (- 7680a b c  + 11520a b c  - 2400b c )x
+--R           + 
+--R                     2 5          2 4        4 3
+--R             (- 6144a c  + 9216a b c  - 1920b c )x
+--R        *
+--R                +--------------+
+--R            +-+ |   2
+--R           \|a \|a x  + b x + c
+--R       + 
+--R                   5          4 3  8         5 2         4 2        3 4  7
+--R             (3072a b c + 768a b )x  + (6144a c  + 11264a b c + 896a b )x
+--R           + 
+--R                    4   2        3 3       2 5  6
+--R             (30208a b c  + 9984a b c - 32a b )x
+--R           + 
+--R                    4 3         3 2 2       2 4         6  5
+--R             (21504a c  + 31488a b c  - 320a b c + 80a b )x
+--R           + 
+--R                    3   3        2 3 2         5        7  4
+--R             (42624a b c  - 4896a b c  + 152a b c + 210b )x
+--R           + 
+--R                    3 4        2 2 3          4 2        6   3
+--R             (21504a c  - 2304a b c  - 6464a b c  + 1680b c)x
+--R           + 
+--R                    2   4           3 3        5 2  2
+--R             (10752a b c  - 16128a b c  + 3360b c )x
+--R           + 
+--R                   2 5          2 4        4 3
+--R             (6144a c  - 9216a b c  + 1920b c )x
+--R        *
+--R            +-+ +-+
+--R           \|a \|c
+--R    /
+--R                    4           3 3  3          4 2         3 2   2
+--R             (12288a b c + 3072a b )x  + (24576a c  + 30720a b c)x
+--R           + 
+--R                   3   2          3 3
+--R             73728a b c x + 49152a c
+--R        *
+--R                    +--------------+
+--R            +-+ +-+ |   2
+--R           \|a \|c \|a x  + b x + c
+--R       + 
+--R                     5 2        4 2        3 4  4
+--R             (- 6144a c  - 9216a b c - 384a b )x
+--R           + 
+--R                      4   2         3 3   3            4 3         3 2 2  2
+--R             (- 49152a b c  - 12288a b c)x  + (- 49152a c  - 61440a b c )x
+--R           + 
+--R                     3   3          3 4
+--R             - 98304a b c x - 49152a c
+--R        *
+--R            +-+
+--R           \|a
+--R     ,
+--R
+--R                         3   3        2 3 2        5        7  3
+--R                 (- 1536a b c  + 1920a b c  + 96a b c - 120b )x
+--R               + 
+--R                         3 4       2 2 3          4 2        6   2
+--R                 (- 3072a c  + 768a b c  + 4800a b c  - 1200b c)x
+--R               + 
+--R                         2   4           3 3        5 2          2 5
+--R                 (- 9216a b c  + 13824a b c  - 2880b c )x - 6144a c
+--R               + 
+--R                        2 4        4 3
+--R                 9216a b c  - 1920b c
+--R            *
+--R                    +--------------+
+--R                +-+ |   2
+--R               \|c \|a x  + b x + c
+--R           + 
+--R                  4 4        2 4 2         6       8  4
+--R             (768a c  - 1440a b c  + 288a b c + 15b )x
+--R           + 
+--R                   3   4        2 3 3         5 2       7   3
+--R             (6144a b c  - 7680a b c  - 384a b c  + 480b c)x
+--R           + 
+--R                   3 5        2 2 4          4 3        6 2  2
+--R             (6144a c  - 1536a b c  - 9600a b c  + 2400b c )x
+--R           + 
+--R                    2   5           3 4        5 3          2 6          2 5
+--R             (12288a b c  - 18432a b c  + 3840b c )x + 6144a c  - 9216a b c
+--R           + 
+--R                  4 4
+--R             1920b c
+--R        *
+--R                       +--------------+
+--R                 +---+ |   2               +---+ +-+
+--R                \|- a \|a x  + b x + c  - \|- a \|c
+--R           atan(------------------------------------)
+--R                                 a x
+--R       + 
+--R                    5 2        4 2       3 4  7
+--R             (- 768a c  - 1152a b c - 48a b )x
+--R           + 
+--R                     4   2        3 3      2 5  6
+--R             (- 6272a b c  - 1728a b c - 8a b )x
+--R           + 
+--R                     4 3        3 2 2      2 4         6  5
+--R             (- 6528a c  - 9120a b c  - 40a b c + 10a b )x
+--R           + 
+--R                      3   3       2 3 2        5       7  4
+--R             (- 15552a b c  + 240a b c  + 12a b c - 15b )x
+--R           + 
+--R                     3 4       2 2 3          4 2       6   3
+--R             (- 9216a c  + 384a b c  + 1408a b c  - 360b c)x
+--R           + 
+--R                     2   4          3 3        5 2  2
+--R             (- 3840a b c  + 5760a b c  - 1200b c )x
+--R           + 
+--R                     2 5          2 4       4 3
+--R             (- 3072a c  + 4608a b c  - 960b c )x
+--R        *
+--R                  +--------------+
+--R            +---+ |   2
+--R           \|- a \|a x  + b x + c
+--R       + 
+--R                   5          4 3  8         5 2        4 2        3 4  7
+--R             (1536a b c + 384a b )x  + (3072a c  + 5632a b c + 448a b )x
+--R           + 
+--R                    4   2        3 3       2 5  6
+--R             (15104a b c  + 4992a b c - 16a b )x
+--R           + 
+--R                    4 3         3 2 2       2 4         6  5
+--R             (10752a c  + 15744a b c  - 160a b c + 40a b )x
+--R           + 
+--R                    3   3        2 3 2        5        7  4
+--R             (21312a b c  - 2448a b c  + 76a b c + 105b )x
+--R           + 
+--R                    3 4        2 2 3          4 2       6   3
+--R             (10752a c  - 1152a b c  - 3232a b c  + 840b c)x
+--R           + 
+--R                   2   4          3 3        5 2  2
+--R             (5376a b c  - 8064a b c  + 1680b c )x
+--R           + 
+--R                   2 5          2 4       4 3
+--R             (3072a c  - 4608a b c  + 960b c )x
+--R        *
+--R            +---+ +-+
+--R           \|- a \|c
+--R    /
+--R                   4           3 3  3          4 2         3 2   2
+--R             (6144a b c + 1536a b )x  + (12288a c  + 15360a b c)x
+--R           + 
+--R                   3   2          3 3
+--R             36864a b c x + 24576a c
+--R        *
+--R                      +--------------+
+--R            +---+ +-+ |   2
+--R           \|- a \|c \|a x  + b x + c
+--R       + 
+--R                     5 2        4 2        3 4  4
+--R             (- 3072a c  - 4608a b c - 192a b )x
+--R           + 
+--R                      4   2        3 3   3            4 3         3 2 2  2
+--R             (- 24576a b c  - 6144a b c)x  + (- 24576a c  - 30720a b c )x
+--R           + 
+--R                     3   3          3 4
+--R             - 49152a b c x - 24576a c
+--R        *
+--R            +---+
+--R           \|- a
+--R     ]
+--R                                     Type: Union(List Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.288~~~~~$\displaystyle
+\int{\frac{\sqrt{ax^2+bx+c}}{x}}~dx$}
+$$\int{\frac{\sqrt{ax^2+bx+c}}{x}}=
+\sqrt{ax^2+bx+c}+\frac{b}{2}\int{\frac{1}{\sqrt{ax^2+bx+c}}}
++c\int{\frac{1}{x\sqrt{ax^2+bx+c}}}
+$$
+<<*>>=
+)clear all
+
+--S 9 of 19
+aa:=integrate(sqrt(a*x^2+b*x+c)/x,x)
+--R 
+--R
+--R   (1)
+--R   [
+--R                   +--------------+
+--R               +-+ |   2                            +-+ +-+
+--R           (4c\|a \|a x  + b x + c  + (- 2b x - 4c)\|a \|c )
+--R        *
+--R                     +--------------+
+--R                 +-+ |   2
+--R               2\|c \|a x  + b x + c  - b x - 2c
+--R           log(---------------------------------)
+--R                                +-+
+--R                             2x\|c
+--R       + 
+--R                   +--------------+
+--R               +-+ |   2               2
+--R           (2b\|c \|a x  + b x + c  - b x - 2b c)
+--R        *
+--R           log
+--R                              2           +-+          2              2  +-+
+--R                    ((- 2a b x  - 8a c x)\|c  + (4a c x  + 4b c x + 8c )\|a )
+--R                 *
+--R                     +--------------+
+--R                     |   2
+--R                    \|a x  + b x + c
+--R                + 
+--R                           3              2  2              2  +-+ +-+     2   3
+--R                  (- 2a b x  + (- 8a c - b )x  - 8b c x - 8c )\|a \|c  + 4a c x
+--R                + 
+--R                          2       2
+--R                  6a b c x  + 8a c x
+--R             /
+--R                                 +--------------+
+--R                              2  |   2
+--R                  (4b c x + 8c )\|a x  + b x + c
+--R                + 
+--R                              2  2              2  +-+
+--R                  ((- 4a c - b )x  - 8b c x - 8c )\|c
+--R       + 
+--R                    +--------------+
+--R                +-+ |   2                   2         +-+ +-+
+--R         - 2b x\|a \|a x  + b x + c  + (4a x  + 2b x)\|a \|c
+--R    /
+--R                 +--------------+
+--R         +-+ +-+ |   2                            +-+
+--R       4\|a \|c \|a x  + b x + c  + (- 2b x - 4c)\|a
+--R     ,
+--R
+--R                     +--------------+
+--R               +---+ |   2                           +---+ +-+
+--R           (2c\|- a \|a x  + b x + c  + (- b x - 2c)\|- a \|c )
+--R        *
+--R                     +--------------+
+--R                 +-+ |   2
+--R               2\|c \|a x  + b x + c  - b x - 2c
+--R           log(---------------------------------)
+--R                                +-+
+--R                             2x\|c
+--R       + 
+--R                   +--------------+
+--R               +-+ |   2               2
+--R           (2b\|c \|a x  + b x + c  - b x - 2b c)
+--R        *
+--R                           +--------------+
+--R                 +---+ +-+ |   2                +---+
+--R                \|- a \|c \|a x  + b x + c  - c\|- a
+--R           atan(-------------------------------------)
+--R                                   +-+
+--R                               a x\|c
+--R       + 
+--R                     +--------------+
+--R               +---+ |   2                   2        +---+ +-+
+--R         - b x\|- a \|a x  + b x + c  + (2a x  + b x)\|- a \|c
+--R    /
+--R                   +--------------+
+--R         +---+ +-+ |   2                           +---+
+--R       2\|- a \|c \|a x  + b x + c  + (- b x - 2c)\|- a
+--R     ]
+--R                                     Type: Union(List Expression Integer,...)
+--E
+@
+
+\section{\cite{1}:14.289~~~~~$\displaystyle
+\int{\frac{\sqrt{ax^2+bx+c}}{x^2}}~dx$}
+$$\int{\frac{\sqrt{ax^2+bx+c}}{x^2}}=
+-\frac{\sqrt{ax^2+bx+c}}{x^2}
++a\int{\frac{1}{\sqrt{ax^2+bx+c}}}
++\frac{b}{2}\int{\frac{1}{x\sqrt{ax^2+bx+c}}}
+$$
+<<*>>=
+)clear all
+
+--S 10 of 19
+aa:=integrate(sqrt(a*x^2+b*x+c)/x^2,x)
+--R 
+--R
+--R   (1)
+--R   [
+--R                     +--------------+
+--R                 +-+ |   2                2 2
+--R           (4b x\|c \|a x  + b x + c  - 2b x  - 4b c x)
+--R        *
+--R                  +--------------+
+--R                  |   2                           +-+
+--R               2c\|a x  + b x + c  + (- b x - 2c)\|c
+--R           log(--------------------------------------)
+--R                                2c x
+--R       + 
+--R                     +--------------+
+--R                 +-+ |   2                     2         +-+ +-+
+--R           (8c x\|a \|a x  + b x + c  + (- 4b x  - 8c x)\|a \|c )
+--R        *
+--R                              +--------------+
+--R                +-+      +-+  |   2                 +-+ +-+       2
+--R             (2\|c  - 2x\|a )\|a x  + b x + c  + 2x\|a \|c  - 2a x  - b x - 2c
+--R         log(-----------------------------------------------------------------)
+--R                                   +--------------+
+--R                               +-+ |   2
+--R                             2\|c \|a x  + b x + c  - b x - 2c
+--R       + 
+--R                         +--------------+
+--R                     +-+ |   2                         2  2              2
+--R         (2b x + 8c)\|c \|a x  + b x + c  + (- 8a c + b )x  - 6b c x - 8c
+--R    /
+--R            +--------------+
+--R            |   2                     2         +-+
+--R       8c x\|a x  + b x + c  + (- 4b x  - 8c x)\|c
+--R     ,
+--R
+--R                     +--------------+
+--R                 +-+ |   2                2 2
+--R           (4b x\|c \|a x  + b x + c  - 2b x  - 4b c x)
+--R        *
+--R                  +--------------+
+--R                  |   2                           +-+
+--R               2c\|a x  + b x + c  + (- b x - 2c)\|c
+--R           log(--------------------------------------)
+--R                                2c x
+--R       + 
+--R                        +--------------+
+--R                  +---+ |   2                     2          +---+ +-+
+--R           (16c x\|- a \|a x  + b x + c  + (- 8b x  - 16c x)\|- a \|c )
+--R        *
+--R                 +--------------+
+--R                 |   2               +-+
+--R                \|a x  + b x + c  - \|c
+--R           atan(------------------------)
+--R                           +---+
+--R                         x\|- a
+--R       + 
+--R                         +--------------+
+--R                     +-+ |   2                         2  2              2
+--R         (2b x + 8c)\|c \|a x  + b x + c  + (- 8a c + b )x  - 6b c x - 8c
+--R    /
+--R            +--------------+
+--R            |   2                     2         +-+
+--R       8c x\|a x  + b x + c  + (- 4b x  - 8c x)\|c
+--R     ]
+--R                                     Type: Union(List Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.290~~~~~$\displaystyle
+\int{\frac{dx}{(ax^2+bx+c)^{3/2}}}$}
+$$
+\int{\frac{1}{(ax^2+bx+c)^{3/2}}}=
+\frac{2(2ax+b)}{(4ac-b^2)\sqrt{ax^2+bx+c}}
+$$
+<<*>>=
+)clear all
+
+--S 11 of 19
+aa:=integrate(1/(a*x^2+b*x+c)^(3/2),x)
+--R 
+--R
+--R                          +--------------+
+--R                          |   2                 +-+
+--R                     - 2x\|a x  + b x + c  + 2x\|c
+--R   (1)  --------------------------------------------------------
+--R                       +--------------+
+--R                   +-+ |   2                    2              2
+--R        (b x + 2c)\|c \|a x  + b x + c  - 2a c x  - 2b c x - 2c
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.291~~~~~$\displaystyle
+\int{\frac{x~dx}{(ax^2+bx+c)^{3/2}}}$}
+$$\int{\frac{x}{(ax^2+bx+c)^{3/2}}}=
+\frac{2(bx+2c)}{(b^2-4ac)\sqrt{ax^2+bx+c}}
+$$
+<<*>>=
+)clear all
+
+--S 12 of 19
+aa:=integrate(x/(a*x^2+b*x+c)^(3/2),x)
+--R 
+--R
+--R                                   2 +-+
+--R                                 2x \|c
+--R   (1)  --------------------------------------------------------
+--R                       +--------------+
+--R                   +-+ |   2                    2              2
+--R        (b x + 2c)\|c \|a x  + b x + c  - 2a c x  - 2b c x - 2c
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.292~~~~~$\displaystyle
+\int{\frac{x^2~dx}{(ax^2+bx+c)^{3/2}}}$}
+$$\int{\frac{x^2}{(ax^2+bx+c)^{3/2}}}=
+\frac{(2b^2-4ac)x+2bc}{a(4ac-b^2)\sqrt{ax^2+bx+c}}
++\frac{1}{a}\int{\frac{1}{\sqrt{ax^2+bx+c}}}
+$$
+<<*>>=
+)clear all
+
+--S 13 of 19
+aa:=integrate(x^2/(a*x^2+b*x+c)^(3/2),x)
+--R 
+--R
+--R   (1)
+--R   [
+--R                           +--------------+
+--R                       +-+ |   2                    2              2
+--R           ((b x + 2c)\|c \|a x  + b x + c  - 2a c x  - 2b c x - 2c )
+--R        *
+--R           log
+--R                                     +--------------+
+--R                     +-+ +-+         |   2                   +-+
+--R                  (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
+--R                + 
+--R                         2             +-+
+--R                  (- 2a x  - b x - 2c)\|a
+--R             /
+--R                      +--------------+
+--R                  +-+ |   2
+--R                2\|c \|a x  + b x + c  - b x - 2c
+--R       + 
+--R                  +--------------+
+--R              +-+ |   2                     2         +-+ +-+
+--R         2c x\|a \|a x  + b x + c  + (- 2b x  - 2c x)\|a \|c
+--R    /
+--R                                +--------------+
+--R                        +-+ +-+ |   2
+--R         (a b x + 2a c)\|a \|c \|a x  + b x + c
+--R       + 
+--R              2   2                  2  +-+
+--R         (- 2a c x  - 2a b c x - 2a c )\|a
+--R     ,
+--R
+--R                            +--------------+
+--R                        +-+ |   2                    2              2
+--R           ((2b x + 4c)\|c \|a x  + b x + c  - 4a c x  - 4b c x - 4c )
+--R        *
+--R                       +--------------+
+--R                 +---+ |   2               +---+ +-+
+--R                \|- a \|a x  + b x + c  - \|- a \|c
+--R           atan(------------------------------------)
+--R                                 a x
+--R       + 
+--R                    +--------------+
+--R              +---+ |   2                     2         +---+ +-+
+--R         2c x\|- a \|a x  + b x + c  + (- 2b x  - 2c x)\|- a \|c
+--R    /
+--R                                  +--------------+
+--R                        +---+ +-+ |   2
+--R         (a b x + 2a c)\|- a \|c \|a x  + b x + c
+--R       + 
+--R              2   2                  2  +---+
+--R         (- 2a c x  - 2a b c x - 2a c )\|- a
+--R     ]
+--R                                     Type: Union(List Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.293~~~~~$\displaystyle
+\int{\frac{dx}{x(ax^2+bx+c)^{3/2}}}$}
+$$\int{\frac{1}{x(ax^2+bx+c)^{3/2}}}=
+\frac{1}{c\sqrt{ax^2+bx+c}}
++\frac{1}{c}\int{\frac{1}{x\sqrt{ax^2+bx+c}}}
+-\frac{b}{2c}\int{\frac{1}{(ax^2+bx+c)^{3/2}}}
+$$
+<<*>>=
+)clear all
+
+--S 14 of 19
+aa:=integrate(1/(x*(a*x^2+b*x+c)^(3/2)),x)
+--R 
+--R
+--R   (1)
+--R                     +--------------+
+--R                     |   2                     2              +-+
+--R         ((b x + 2c)\|a x  + b x + c  + (- 2a x  - 2b x - 2c)\|c )
+--R      *
+--R                   +--------------+
+--R               +-+ |   2
+--R             2\|c \|a x  + b x + c  - b x - 2c
+--R         log(---------------------------------)
+--R                              +-+
+--R                           2x\|c
+--R     + 
+--R            +--------------+
+--R            |   2                     2         +-+
+--R       2b x\|a x  + b x + c  + (- 2a x  - 2b x)\|c
+--R  /
+--R                       +--------------+
+--R                2  +-+ |   2                  2 2       2      3
+--R     (b c x + 2c )\|c \|a x  + b x + c  - 2a c x  - 2b c x - 2c
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.294~~~~~$\displaystyle
+\int{\frac{dx}{x^2(ax^2+bx+c)^{3/2}}}$}
+$$\begin{array}{rl}
+\displaystyle\int{\frac{1}{x^2(ax^2+bx+c)^{3/2}}}=
+&\displaystyle-\frac{ax^2+bx+c}{c^2x\sqrt{ax^2+bx+c}}\\
+&\\
+&\displaystyle+\frac{b^2-2ac}{2c^2}\int{\frac{1}{(ax^2+bx+c)^{3/2}}}\\
+&\\
+&\displaystyle-\frac{3b}{2c^2}\int{\frac{1}{x\sqrt{ax^2+bx+c}}}
+\end{array}
+$$
+<<*>>=
+)clear all
+
+--S 15 of 19
+aa:=integrate(1/(x^2*(a*x^2+b*x+c)^(3/2)),x)
+--R 
+--R
+--R   (1)
+--R                                                          +--------------+
+--R                           3  3      2   2        2   +-+ |   2
+--R           ((- 24a b c - 6b )x  - 48b c x  - 48b c x)\|c \|a x  + b x + c
+--R         + 
+--R                2   4           2      3   3      2 2 2        3
+--R           24a b c x  + (48a b c  + 24b c)x  + 72b c x  + 48b c x
+--R      *
+--R                   +--------------+
+--R               +-+ |   2
+--R             2\|c \|a x  + b x + c  - b x - 2c
+--R         log(---------------------------------)
+--R                              +-+
+--R                           2x\|c
+--R     + 
+--R                      3  3         2      2   2        2       3  +-+
+--R         ((4a b c - 9b )x  + (64a c  - 24b c)x  + 40b c x + 32c )\|c
+--R      *
+--R          +--------------+
+--R          |   2
+--R         \|a x  + b x + c
+--R     + 
+--R             2 2        2   4             2      3   3           3     2 2  2
+--R       (- 32a c  + 24a b c)x  + (- 48a b c  + 24b c)x  + (- 80a c  + 8b c )x
+--R     + 
+--R              3       4
+--R       - 56b c x - 32c
+--R  /
+--R                                               +--------------+
+--R              4     2 3  3        4 2      5   |   2
+--R       ((16a c  + 4b c )x  + 32b c x  + 32c x)\|a x  + b x + c
+--R     + 
+--R                 3 4           4      2 3  3        4 2      5   +-+
+--R       (- 16a b c x  + (- 32a c  - 16b c )x  - 48b c x  - 32c x)\|c
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.295~~~~~$\displaystyle
+\int{(ax^2+bx+c)^{n+1/2}}~dx$}
+$$\begin{array}{rl}
+\displaystyle\int{(ax^2+bx+c)^{n+1/2}}=
+&\displaystyle\frac{(2ax+b)(ax^2+bx+c)^{n+1/2}}{4a(n+1)}\\
+&\\
+&\displaystyle+\frac{(2n+1)(4ac-b^2)}{8a(n+1)}
+\int{(ax^2+bx+c)^{n-1/2}}
+\end{array}
+$$
+<<*>>=
+)clear all
+
+--S 16 of 19
+aa:=integrate((a*x^2+b*x+c)^(n+1/2),x)
+--R 
+--R
+--R                              2n + 1
+--R           x                  ------
+--R         ++                2     2
+--R   (1)   |   (c + %N b + %N a)      d%N
+--R        ++
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.296~~~~~$\displaystyle
+\int{x(ax^2+bx+c)^{n+1/2}}~dx$}
+$$\int{x(ax^2+bx+c)^{n+1/2}}=
+\frac{(ax^2+bx+c)^{n+3/2}}{a(2n+3)}-
+\frac{b}{2a}\int{(ax^2+bx+c)^{n+1/2}}
+$$
+<<*>>=
+)clear all
+
+--S 17 of 19
+aa:=integrate(x*(a*x^2+b*x+c)^(n+1/2),x)
+--R 
+--R
+--R                                 2n + 1
+--R           x                     ------
+--R         ++                   2     2
+--R   (1)   |   %N (c + %N b + %N a)      d%N
+--R        ++
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.297~~~~~$\displaystyle
+\int{\frac{dx}{(ax^2+bx+c)^{n+1/2}}}$}
+$$\begin{array}{rl}
+\displaystyle\int{\frac{1}{(ax^2+bx+c)^{n+1/2}}}=
+&\displaystyle\frac{2(2ax+b)}{(2n-1)(4ac-b^2)(ax^2+bx+c)^{n-1/2}}\\
+&\\
+&\displaystyle
++\frac{8a(n-1)}{(2n-1)(4ac-b^2)}\int{\frac{1}{(ax^2+bx+c)^{n-1/2}}}
+\end{array}
+$$
+<<*>>=
+)clear all
+
+--S 18 of 19
+aa:=integrate(1/(a*x^2+b*x+c)^(n+1/2),x)
+--R 
+--R
+--R           x
+--R         ++             1
+--R   (1)   |   ----------------------- d%N
+--R        ++                    2n + 1
+--R                              ------
+--R                           2     2
+--R             (c + %N b + %N a)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.298~~~~~$\displaystyle
+\int{\frac{dx}{x(ax^2+bx+c)^{n+1/2}}}$}
+$$\begin{array}{rl}
+\displaystyle\int{\frac{1}{x(ax^2+bx+c)^{n+1/2}}}=
+&\displaystyle\frac{1}{(2n-1)c(ax^2+bx+c)^{n-1/2}}\\
+&\\
+&\displaystyle
++\frac{1}{c}\int{\frac{1}{x(ax^2+bx+c)^{n-1/2}}}\\
+&\\
+&\displaystyle
+-\frac{b}{2c}\int{\frac{1}{(ax^2+bx+c)^{n+1/2}}}
+\end{array}
+$$
+<<*>>=
+)clear all
+
+--S 19 of 19
+aa:=integrate(1/(x*(a*x^2+b*x+c)^(n+1/2)),x)
+--R 
+--R
+--R           x
+--R         ++               1
+--R   (1)   |   -------------------------- d%N
+--R        ++                       2n + 1
+--R                                 ------
+--R                              2     2
+--R             %N (c + %N b + %N a)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+)spool
+)lisp (bye)
+@
+
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} Spiegel, Murray R.
+{\sl Mathematical Handbook of Formulas and Tables}\\
+Schaum's Outline Series McGraw-Hill 1968 pp72-73
+\end{thebibliography}
+\end{document}
diff --git a/src/input/schaum14.input.pamphlet b/src/input/schaum14.input.pamphlet
new file mode 100644
index 0000000..560ab37
--- /dev/null
+++ b/src/input/schaum14.input.pamphlet
@@ -0,0 +1,305 @@
+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/input schaum14.input}
+\author{Timothy Daly}
+\maketitle
+\eject
+\tableofcontents
+\eject
+\section{\cite{1}:14.299~~~~~$\displaystyle
+\int{\frac{dx}{x^3+a^3}}$}
+$$\int{\frac{1}{x^3+a^3}}=
+\frac{1}{6a^2}\ln\frac{(x+a)^2}{x^2-ax+a^2}
++\frac{1}{a^2\sqrt{3}}\tan^{-1}\frac{2x-a}{a\sqrt{3}}
+$$
+<<*>>=
+)spool schaum14.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1 of 12
+aa:=integrate(1/(x^3+a^3),x)
+--R 
+--R
+--R                                                                    +-+
+--R           +-+     2          2      +-+                   (2x - a)\|3
+--R        - \|3 log(x  - a x + a ) + 2\|3 log(x + a) + 6atan(------------)
+--R                                                                3a
+--R   (1)  ----------------------------------------------------------------
+--R                                       2 +-+
+--R                                     6a \|3
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.300~~~~~$\displaystyle
+\int{\frac{x~dx}{x^3+a^3}}$}
+$$\int{\frac{x}{x^3+a^3}}=
+\frac{1}{6a}\ln\frac{x^2-ax+a^2}{(x+a)^2}
++\frac{1}{a\sqrt{3}}\tan^{-1}\frac{2x-a}{a\sqrt{3}}
+$$
+<<*>>=
+)clear all
+
+--S 2 of 12
+aa:=integrate(x/(x^3+a^3),x)
+--R 
+--R
+--R                                                                  +-+
+--R         +-+     2          2      +-+                   (2x - a)\|3
+--R        \|3 log(x  - a x + a ) - 2\|3 log(x + a) + 6atan(------------)
+--R                                                              3a
+--R   (1)  --------------------------------------------------------------
+--R                                       +-+
+--R                                    6a\|3
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.301~~~~~$\displaystyle
+\int{\frac{x^2~dx}{x^3+a^3}}$}
+$$\int{\frac{x^2}{x^3+a^3}}=
+\frac{1}{3}\ln(x^3+a^3)
+$$
+<<*>>=
+)clear all
+
+--S 3 of 12
+aa:=integrate(x^2/(x^3+a^3),x)
+--R 
+--R
+--R             3    3
+--R        log(x  + a )
+--R   (1)  ------------
+--R              3
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.302~~~~~$\displaystyle
+\int{\frac{dx}{x(x^3+a^3)}}$}
+$$\int{\frac{1}{x(x^3+a^3)}}=
+\frac{1}{3a^3}\ln\left(\frac{x^3}{x^3+a^3}\right)
+$$
+<<*>>=
+)clear all
+
+--S 4 of 12
+aa:=integrate(1/(x*(x^3+a^3)),x)
+--R 
+--R
+--R               3    3
+--R        - log(x  + a ) + 3log(x)
+--R   (1)  ------------------------
+--R                     3
+--R                   3a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.303~~~~~$\displaystyle
+\int{\frac{dx}{x^2(x^3+a^3)}}~dx$}
+$$\int{\frac{1}{x^2(x^3+a^3)}}=
+-\frac{1}{a^3x}-\frac{1}{6a^4}\ln\frac{x^2-ax+a^2}{(x+a)^2}
+-\frac{1}{a^4\sqrt{3}}\tan^{-1}\frac{2x-a}{a\sqrt{3}}
+$$
+<<*>>=
+)clear all
+
+--S 5 of 12
+aa:=integrate(1/(x^2*(x^3+a^3)),x)
+--R 
+--R
+--R   (1)
+--R                                                                   +-+
+--R       +-+     2          2       +-+                     (2x - a)\|3        +-+
+--R   - x\|3 log(x  - a x + a ) + 2x\|3 log(x + a) - 6x atan(------------) - 6a\|3
+--R                                                               3a
+--R   -----------------------------------------------------------------------------
+--R                                        4  +-+
+--R                                      6a x\|3
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.304~~~~~$\displaystyle
+\int{\frac{dx}{(x^3+a^3)^2}}$}
+$$\int{\frac{1}{(x^3+a^3)^2}}=
+\frac{x}{3a^3(x^3+a^3)}
++\frac{1}{9a^5}\ln\frac{(x+a)^2}{x^2-ax+a^2}
++\frac{2}{3a^5\sqrt{3}}\tan^{-1}\frac{2x-a}{a\sqrt{3}}
+$$
+<<*>>=
+)clear all
+
+--S 6 of 12
+aa:=integrate(1/(x^3+a^3)^2,x)
+--R 
+--R
+--R   (1)
+--R           3    3  +-+     2          2       3     3  +-+
+--R       (- x  - a )\|3 log(x  - a x + a ) + (2x  + 2a )\|3 log(x + a)
+--R     + 
+--R                                +-+
+--R          3     3      (2x - a)\|3       2  +-+
+--R       (6x  + 6a )atan(------------) + 3a x\|3
+--R                            3a
+--R  /
+--R        5 3     8  +-+
+--R     (9a x  + 9a )\|3
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.305~~~~~$\displaystyle
+\int{\frac{x~dx}{(x^3+a^3)^2}}$}
+$$\int{\frac{x}{(x^3+a^3)^2}}=
+\frac{x^2}{3a^3(x^3+a^3)}
++\frac{1}{18a^4}\ln\frac{x^2-ax+a^2}{(x+a)^2}
++\frac{1}{3a^4\sqrt{3}}\tan^{-1}\frac{2x-a}{a\sqrt{3}}
+$$
+<<*>>=
+)clear all
+
+--S 7 of 12
+aa:=integrate(x/(x^3+a^3)^2,x)
+--R 
+--R
+--R   (1)
+--R         3    3  +-+     2          2         3     3  +-+
+--R       (x  + a )\|3 log(x  - a x + a ) + (- 2x  - 2a )\|3 log(x + a)
+--R     + 
+--R                                +-+
+--R          3     3      (2x - a)\|3         2 +-+
+--R       (6x  + 6a )atan(------------) + 6a x \|3
+--R                            3a
+--R  /
+--R         4 3      7  +-+
+--R     (18a x  + 18a )\|3
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.306~~~~~$\displaystyle
+\int{\frac{x^2~dx}{(x^3+a^3)^2}}$}
+$$\int{\frac{x^2}{(x^3+a^3)^2}}=
+-\frac{1}{3(x^3+a^3)}
+$$
+<<*>>=
+)clear all
+
+--S 8 of 12
+aa:=integrate(x^2/(x^3+a^3)^2,x)
+--R 
+--R
+--R              1
+--R   (1)  - ---------
+--R            3     3
+--R          3x  + 3a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.307~~~~~$\displaystyle
+\int{\frac{dx}{x(x^3+a^3)^2}}$}
+$$\int{\frac{1}{x(x^3+a^3)^2}}=
+\frac{1}{3a^3(x^3+a^3)}+\frac{1}{3a^6}\ln\left(\frac{x^3}{x^3+a^3}\right)
+$$
+<<*>>=
+)clear all
+
+--S 9 of 12
+aa:=integrate(1/(x*(x^3+a^3)^2),x)
+--R 
+--R
+--R            3    3      3    3       3     3           3
+--R        (- x  - a )log(x  + a ) + (3x  + 3a )log(x) + a
+--R   (1)  ------------------------------------------------
+--R                             6 3     9
+--R                           3a x  + 3a
+--R                                          Type: Union(Expression Integer,...)
+--E
+@
+
+\section{\cite{1}:14.308~~~~~$\displaystyle
+\int{\frac{dx}{x^2(x^3+a^3)^2}}~dx$}
+$$\int{\frac{1}{x^2(x^3+a^3)^2}}=
+-\frac{1}{a^6x}-\frac{x^2}{3a^6(x^3+a^3)}
+-\frac{4}{3a^6}\int{\frac{x}{x^3+a^3}}
+$$
+<<*>>=
+)clear all
+
+--S 10 of 12
+aa:=integrate(1/(x^2*(x^3+a^3)^2),x)
+--R 
+--R
+--R   (1)
+--R            4     3   +-+     2          2       4     3   +-+
+--R       (- 2x  - 2a x)\|3 log(x  - a x + a ) + (4x  + 4a x)\|3 log(x + a)
+--R     + 
+--R                                     +-+
+--R             4      3       (2x - a)\|3             3     4  +-+
+--R       (- 12x  - 12a x)atan(------------) + (- 12a x  - 9a )\|3
+--R                                 3a
+--R  /
+--R        7 4     10   +-+
+--R     (9a x  + 9a  x)\|3
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.309~~~~~$\displaystyle
+\int{\frac{x^m~dx}{x^3+a^3}}$}
+$$\int{\frac{x^m}{x^3+a^3}}=
+\frac{x^{m-2}}{m-2}-a^3\int{\frac{x^{m-3}}{x^3+a^3}}
+$$
+<<*>>=
+)clear all
+
+--S 11 of 12
+aa:=integrate(x^m/(x^3+a^3),x)
+--R 
+--R
+--R           x      m
+--R         ++     %L
+--R   (1)   |   -------- d%L
+--R        ++    3     3
+--R             a  + %L
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.310~~~~~$\displaystyle
+\int{\frac{dx}{x^n(x^3+a^3)}}$}
+$$\int{\frac{1}{x^n(x^3+a^3)}}=
+\frac{-1}{a^3(n-1)x^{n-1}}-\frac{1}{a^3}\int{\frac{1}{x^{n-3}(x^3+a^3)}}
+$$
+<<*>>=
+)clear all
+
+--S 12 of 12
+aa:=integrate(1/(x^n*(x^3+a^3)),x)
+--R 
+--R
+--R           x
+--R         ++        1
+--R   (1)   |   ------------- d%L
+--R        ++     3     3   n
+--R             (a  + %L )%L
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+)spool
+)lisp (bye)
+@
+
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} Spiegel, Murray R.
+{\sl Mathematical Handbook of Formulas and Tables}\\
+Schaum's Outline Series McGraw-Hill 1968 p73
+\end{thebibliography}
+\end{document}



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Subject: [Axiom-developer] Re: Axiom Mar 2008 fedora8-64 src Problem (R. 1)!
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X-List-Received-Date: Sun, 30 Mar 2008 08:23:49 -0000

Joseph,

Yes, the fedora8-64 build required some hacking of GCL.
I need to upload the actual sources rather than the generic sources
for that particular platform. If I get a chance later today (its
4:20am here) I'll upload the actual source tree and send you a note.

Tim

=================================================================
Dear Mr. Tim Daly:


   I got Axiom Mar 2008 to work using bin: thank you!
   However, when I tried to make it from src, I got,

"
gcc -o raw_gcl /home/jos1/axiom330/axiom/obj/linux/lib/cfuns-c.o
/home/jos1/axiom330/axiom/obj/linux/lib/sockio-c.o \
                -L.  -Wl,-Map raw_gcl_map   -lgcl -lm  -lgmp
-lreadline -lncurses -lc -lgclp
/home/jos1/axiom330/axiom/obj/linux/lib/libspad.a
./libgcl.a(sys_gcl.o): In function `gcl_init_system':
sys_gcl.c:(.text+0x35bd): undefined reference to `init_gcl_cmpwt'
sys_gcl.c:(.text+0x363a): undefined reference to `init_gcl_predlib'
sys_gcl.c:(.text+0x36b7): undefined reference to `init_gcl_setf'
sys_gcl.c:(.text+0x3734): undefined reference to `init_gcl_assert'
sys_gcl.c:(.text+0x37b1): undefined reference to `init_gcl_arraylib'
sys_gcl.c:(.text+0x382e): undefined reference to `init_gcl_defstruct'
sys_gcl.c:(.text+0x38ab): undefined reference to `init_gcl_describe'
sys_gcl.c:(.text+0x3928): undefined reference to `init_gcl_numlib'
sys_gcl.c:(.text+0x39a5): undefined reference to `init_gcl_listlib'
sys_gcl.c:(.text+0x3a22): undefined reference to `init_gcl_seq'
sys_gcl.c:(.text+0x3a9f): undefined reference to `init_gcl_iolib'
sys_gcl.c:(.text+0x3b1c): undefined reference to `init_gcl_packlib'
sys_gcl.c:(.text+0x3b99): undefined reference to `init_gcl_mislib'
sys_gcl.c:(.text+0x3c16): undefined reference to `init_gcl_seqlib'
sys_gcl.c:(.text+0x3c93): undefined reference to `init_gcl_trace'
sys_gcl.c:(.text+0x3d10): undefined reference to `init_gcl_cmpenv'
sys_gcl.c:(.text+0x3d8d): undefined reference to `init_gcl_cmputil'
sys_gcl.c:(.text+0x3e0a): undefined reference to `init_gcl_cmploc'
sys_gcl.c:(.text+0x3e87): undefined reference to `init_gcl_loop'
sys_gcl.c:(.text+0x3f04): undefined reference to `init_gcl_cmpif'
sys_gcl.c:(.text+0x3f81): undefined reference to `init_gcl_cmpbind'
sys_gcl.c:(.text+0x3ffe): undefined reference to `init_gcl_cmptag'
sys_gcl.c:(.text+0x407b): undefined reference to `init_gcl_serror'
sys_gcl.c:(.text+0x40f8): undefined reference to `init_gcl_cmpflet'
sys_gcl.c:(.text+0x4175): undefined reference to `init_gcl_info'
sys_gcl.c:(.text+0x41f2): undefined reference to `init_gcl_cmpmulti'
sys_gcl.c:(.text+0x426f): undefined reference to `init_gcl_make_defpackage'
sys_gcl.c:(.text+0x42ec): undefined reference to `init_gcl_cmplam'
sys_gcl.c:(.text+0x4369): undefined reference to `init_gcl_cmpcall'
sys_gcl.c:(.text+0x43e6): undefined reference to `init_gcl_cmpvar'
sys_gcl.c:(.text+0x4463): undefined reference to `init_gcl_sloop'
sys_gcl.c:(.text+0x44e0): undefined reference to `init_gcl_cmpeval'
sys_gcl.c:(.text+0x455d): undefined reference to `init_gcl_debug'
sys_gcl.c:(.text+0x45da): undefined reference to `init_gcl_cmpmap'
sys_gcl.c:(.text+0x4657): undefined reference to `init_gcl_defpackage'
sys_gcl.c:(.text+0x46d4): undefined reference to `init_gcl_cmplabel'
sys_gcl.c:(.text+0x4751): undefined reference to `init_gcl_cmpblock'
sys_gcl.c:(.text+0x47ce): undefined reference to `init_gcl_cmptop'
sys_gcl.c:(.text+0x484b): undefined reference to `init_gcl_destructuring_bind'
sys_gcl.c:(.text+0x48c8): undefined reference to `init_gcl_cmpfun'
sys_gcl.c:(.text+0x4945): undefined reference to `init_gcl_cmptype'
sys_gcl.c:(.text+0x49c2): undefined reference to `init_gcl_cmpspecial'
sys_gcl.c:(.text+0x4a3f): undefined reference to `init_gcl_cmpinline'
sys_gcl.c:(.text+0x4abc): undefined reference to `init_gcl_cmplet'
sys_gcl.c:(.text+0x4b39): undefined reference to `init_gcl_cmpcatch'
sys_gcl.c:(.text+0x4bb2): undefined reference to `init_gcl_cmpvs'
./libgcl.a(sys_gcl.o): In function `gcl_init_init':
sys_gcl.c:(.text+0x525d): undefined reference to `init_gcl_defmacro'
sys_gcl.c:(.text+0x52c7): undefined reference to `init_gcl_evalmacros'
sys_gcl.c:(.text+0x5331): undefined reference to `init_gcl_top'
sys_gcl.c:(.text+0x539c): undefined reference to `init_gcl_module'
collect2: ld returned 1 exit status
make[4]: *** [raw_gcl_map] Error 1
make[4]: Leaving directory `/home/jos1/axiom330/axiom/lsp/gcl-2.6.8pre/unixport'
make[3]: *** [unixport/saved_gcl] Error 2
make[3]: Leaving directory `/home/jos1/axiom330/axiom/lsp/gcl-2.6.8pre'
/bin/sh: line 5: unixport/saved_gcl: No such file or directory
make[2]: *** [gcldir] Error 127
make[2]: Leaving directory `/home/jos1/axiom330/axiom/lsp'
make[1]: *** [lspdir] Error 2
make[1]: Leaving directory `/home/jos1/axiom330/axiom'
make: *** [all] Error 2
You have new mail in /var/spool/mail/root
[root@sco axiom]# axiom
-bash: axiom: command not found
[root@sco axiom]#
"
   Mayday, Veuillez M'Aider, s'il vous plait!
   Tempus fugit et ad augusta per angusta.


                                                             Nil
desparare (Gauss),

                                                             Joseph Roy D. North
                                                             Le
 Roi Du Nord
                                                             3220
Duval Road, Apt. 1110
                                                             Austin,
TX 78759-3524, USA

Scientia est Potentia!




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Date: Sun, 30 Mar 2008 10:08:54 -0500
From: "Joseph North" <joseph.north@gmail.com>
To: daly@axiom-developer.org
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Subject: [Axiom-developer] Re: Axiom Mar 2008 fedora8-64 src Problem (R. 1)!
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On Sun, Mar 30, 2008 at 4:37 AM, root <daly@axiom-developer.org> wrote:
> Joseph,
>
>  Yes, the fedora8-64 build required some hacking of GCL.
>  I need to upload the actual sources rather than the generic sources
>  for that particular platform. If I get a chance later today (its
>  4:20am here) I'll upload the actual source tree and send you a note.
>
>  Tim
>
>  =================================================================
>
>
> Dear Mr. Tim Daly:
>
>
>    I got Axiom Mar 2008 to work using bin: thank you!
>    However, when I tried to make it from src, I got,
>
>  "
>  gcc -o raw_gcl /home/jos1/axiom330/axiom/obj/linux/lib/cfuns-c.o
>  /home/jos1/axiom330/axiom/obj/linux/lib/sockio-c.o \
>                 -L.  -Wl,-Map raw_gcl_map   -lgcl -lm  -lgmp
>  -lreadline -lncurses -lc -lgclp
>  /home/jos1/axiom330/axiom/obj/linux/lib/libspad.a
>  ./libgcl.a(sys_gcl.o): In function `gcl_init_system':
>  sys_gcl.c:(.text+0x35bd): undefined reference to `init_gcl_cmpwt'
>  sys_gcl.c:(.text+0x363a): undefined reference to `init_gcl_predlib'
>  sys_gcl.c:(.text+0x36b7): undefined reference to `init_gcl_setf'
>  sys_gcl.c:(.text+0x3734): undefined reference to `init_gcl_assert'
>  sys_gcl.c:(.text+0x37b1): undefined reference to `init_gcl_arraylib'
>  sys_gcl.c:(.text+0x382e): undefined reference to `init_gcl_defstruct'
>  sys_gcl.c:(.text+0x38ab): undefined reference to `init_gcl_describe'
>  sys_gcl.c:(.text+0x3928): undefined reference to `init_gcl_numlib'
>  sys_gcl.c:(.text+0x39a5): undefined reference to `init_gcl_listlib'
>  sys_gcl.c:(.text+0x3a22): undefined reference to `init_gcl_seq'
>  sys_gcl.c:(.text+0x3a9f): undefined reference to `init_gcl_iolib'
>  sys_gcl.c:(.text+0x3b1c): undefined reference to `init_gcl_packlib'
>  sys_gcl.c:(.text+0x3b99): undefined reference to `init_gcl_mislib'
>  sys_gcl.c:(.text+0x3c16): undefined reference to `init_gcl_seqlib'
>  sys_gcl.c:(.text+0x3c93): undefined reference to `init_gcl_trace'
>  sys_gcl.c:(.text+0x3d10): undefined reference to `init_gcl_cmpenv'
>  sys_gcl.c:(.text+0x3d8d): undefined reference to `init_gcl_cmputil'
>  sys_gcl.c:(.text+0x3e0a): undefined reference to `init_gcl_cmploc'
>  sys_gcl.c:(.text+0x3e87): undefined reference to `init_gcl_loop'
>  sys_gcl.c:(.text+0x3f04): undefined reference to `init_gcl_cmpif'
>  sys_gcl.c:(.text+0x3f81): undefined reference to `init_gcl_cmpbind'
>  sys_gcl.c:(.text+0x3ffe): undefined reference to `init_gcl_cmptag'
>  sys_gcl.c:(.text+0x407b): undefined reference to `init_gcl_serror'
>  sys_gcl.c:(.text+0x40f8): undefined reference to `init_gcl_cmpflet'
>  sys_gcl.c:(.text+0x4175): undefined reference to `init_gcl_info'
>  sys_gcl.c:(.text+0x41f2): undefined reference to `init_gcl_cmpmulti'
>  sys_gcl.c:(.text+0x426f): undefined reference to `init_gcl_make_defpackage'
>  sys_gcl.c:(.text+0x42ec): undefined reference to `init_gcl_cmplam'
>  sys_gcl.c:(.text+0x4369): undefined reference to `init_gcl_cmpcall'
>  sys_gcl.c:(.text+0x43e6): undefined reference to `init_gcl_cmpvar'
>  sys_gcl.c:(.text+0x4463): undefined reference to `init_gcl_sloop'
>  sys_gcl.c:(.text+0x44e0): undefined reference to `init_gcl_cmpeval'
>  sys_gcl.c:(.text+0x455d): undefined reference to `init_gcl_debug'
>  sys_gcl.c:(.text+0x45da): undefined reference to `init_gcl_cmpmap'
>  sys_gcl.c:(.text+0x4657): undefined reference to `init_gcl_defpackage'
>  sys_gcl.c:(.text+0x46d4): undefined reference to `init_gcl_cmplabel'
>  sys_gcl.c:(.text+0x4751): undefined reference to `init_gcl_cmpblock'
>  sys_gcl.c:(.text+0x47ce): undefined reference to `init_gcl_cmptop'
>  sys_gcl.c:(.text+0x484b): undefined reference to `init_gcl_destructuring_bind'
>  sys_gcl.c:(.text+0x48c8): undefined reference to `init_gcl_cmpfun'
>  sys_gcl.c:(.text+0x4945): undefined reference to `init_gcl_cmptype'
>  sys_gcl.c:(.text+0x49c2): undefined reference to `init_gcl_cmpspecial'
>  sys_gcl.c:(.text+0x4a3f): undefined reference to `init_gcl_cmpinline'
>  sys_gcl.c:(.text+0x4abc): undefined reference to `init_gcl_cmplet'
>  sys_gcl.c:(.text+0x4b39): undefined reference to `init_gcl_cmpcatch'
>  sys_gcl.c:(.text+0x4bb2): undefined reference to `init_gcl_cmpvs'
>  ./libgcl.a(sys_gcl.o): In function `gcl_init_init':
>  sys_gcl.c:(.text+0x525d): undefined reference to `init_gcl_defmacro'
>  sys_gcl.c:(.text+0x52c7): undefined reference to `init_gcl_evalmacros'
>  sys_gcl.c:(.text+0x5331): undefined reference to `init_gcl_top'
>  sys_gcl.c:(.text+0x539c): undefined reference to `init_gcl_module'
>  collect2: ld returned 1 exit status
>  make[4]: *** [raw_gcl_map] Error 1
>  make[4]: Leaving directory `/home/jos1/axiom330/axiom/lsp/gcl-2.6.8pre/unixport'
>  make[3]: *** [unixport/saved_gcl] Error 2
>  make[3]: Leaving directory `/home/jos1/axiom330/axiom/lsp/gcl-2.6.8pre'
>  /bin/sh: line 5: unixport/saved_gcl: No such file or directory
>  make[2]: *** [gcldir] Error 127
>  make[2]: Leaving directory `/home/jos1/axiom330/axiom/lsp'
>  make[1]: *** [lspdir] Error 2
>  make[1]: Leaving directory `/home/jos1/axiom330/axiom'
>  make: *** [all] Error 2
>  You have new mail in /var/spool/mail/root
>  [root@sco axiom]# axiom
>  -bash: axiom: command not found
>  [root@sco axiom]#
>  "
>    Mayday, Veuillez M'Aider, s'il vous plait!
>    Tempus fugit et ad augusta per angusta.
>
>
>                                                              Nil
>  desparare (Gauss),
>
>                                                              Joseph Roy D. North
>                                                              Le
>   Roi Du Nord
>                                                              3220
>  Duval Road, Apt. 1110
>                                                              Austin,
>  TX 78759-3524, USA
>
>  Scientia est Potentia!
>
>




Hi Tim,


   OK, thanks for your assistance!
   Axiom (Mar 2008) be, ab initio, easier - i.e., more intuitive - to use than
SAGE 2.10.3, I feel, so I hope to do some of my Math. research
using your Axiom as a check.
   I haven't tried to evaluate its relative performance (i.e., speed),
though, wrt to bc, PARI/GP, SAGE, et caetera.  So,, have you
benchmarked Axiom, please?
   Your download server seems to be very slow, and unreliable,
unfortunately.
   Are you at CUNY?
   Tempus fugit et ad augusta per angusta.


 Nil desparare (Gauss),

 Joseph Roy D. North
 Le Roi Du Nord
 3220 Duval Road, Apt. 1110
 Austin, TX 78759-3524, USA

Scientia est Potentia!

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Date: Thu, 03 Apr 2008 00:17:50 -0400
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I ran a computation (computing the radical of an ideal) that
aborted after 9 days with this message:

-- f0 is y0^2-x0^3, and f1, f2, f3 are the first, second and
third derivative of f0
-- when x1, x2, x3 (and y1, y2, y3) are interpreted as
first, second and third
-- derivatives of x0 (and y0) respectively. However, this is
just an algebraic
-- computation

(14) -> id3:=ideal([f0,f1,f2,f3])

   (14)
        2     3
2                        2         2        2
   [y0  - x0 , 2y1 y0 - 3x1 x0 , 2y2 y0 - 3x2 x0  + 2y1  -
6x1 x0,

2                                          3
    2y3 y0 - 3x3 x0  + 6y2 y1 - 18x2 x1 x0 - 6x1 ]
Type: PolynomialIdeals(Fraction
Integer,DirectProduct(8,NonNegativeInteger),Orde
redVariableList
[y3,x3,y2,x2,y1,x1,y0,x0],DistributedMultivariatePolynomial([y3,

x3,y2,x2,y1,x1,y0,x0],Fraction Integer))

Time: 0 sec
(15) -> rid3:=radical(id3)


   >> System error:
   The storage for VECTOR is exhausted.
Currently, 10765 pages are allocated.
Use ALLOCATE to expand the space.

protected-symbol-warn called with (NIL)

Question: How exactly do I issue an ALLOCATE command? Also,
it is possible (if so, how) to continue the computation
after an ALLOCATE command or do I have to start over?
Thanks.

William





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Can you post an input file for this?



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Subject: [Axiom-developer] 20080402.01.tpd.patch (CATS integration
	regression testing)
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More integrals
=========================================================================
diff --git a/changelog b/changelog
index 6f6fcb0..102ba8b 100644
--- a/changelog
+++ b/changelog
@@ -1,3 +1,7 @@
+20080402 tpd src/input/Makefile add integration regression testing
+20080402 tpd src/input/schaum17.input integrals of sin(ax)
+20080402 tpd src/input/schaum16.input integrals of x^n \pm a^n
+20080402 tpd src/input/schaum15.input integrals of x^4 \pm a^4
 20080401 tpd src/input/Makefile add integration regression testing
 20080401 tpd src/input/schaum14.input integrals of x^3+a^3
 20080401 tpd src/input/schaum13.input integrals of sqrt(ax^2+bx+c)
diff --git a/src/input/Makefile.pamphlet b/src/input/Makefile.pamphlet
index 2f109e9..6de47f3 100644
--- a/src/input/Makefile.pamphlet
+++ b/src/input/Makefile.pamphlet
@@ -358,7 +358,8 @@ REGRES= algaggr.regress algbrbf.regress  algfacob.regress alist.regress  \
     schaum1.regress   schaum2.regress  schaum3.regress  schaum4.regress \
     schaum5.regress   schaum6.regress  schaum7.regress  schaum8.regress \
     schaum9.regress   schaum10.regress schaum11.regress schaum12.regress \
-    schaum13.regress  schaum14.regress \
+    schaum13.regress  schaum14.regress schaum15.regress schaum16.regress \
+    schaum17.regress \
     scherk.regress    scope.regress    seccsc.regress \
     segbind.regress   seg.regress \
     series2.regress   series.regress   sersolve.regress set.regress \
@@ -635,7 +636,8 @@ FILES= ${OUT}/algaggr.input  ${OUT}/algbrbf.input    ${OUT}/algfacob.input \
        ${OUT}/schaum5.input  ${OUT}/schaum6.input    ${OUT}/schaum7.input \
        ${OUT}/schaum8.input  ${OUT}/schaum9.input    ${OUT}/schaum10.input \
        ${OUT}/schaum11.input ${OUT}/schaum12.input   ${OUT}/schaum13.input \
-       ${OUT}/schaum14.input \
+       ${OUT}/schaum14.input ${OUT}/schaum15.input   ${OUT}/schaum16.input \
+       ${OUT}/schaum17.input \
        ${OUT}/saddle.input \
        ${OUT}/scherk.input   ${OUT}/scope.input      ${OUT}/seccsc.input \
        ${OUT}/segbind.input  ${OUT}/seg.input        ${OUT}/series2.input \
@@ -941,6 +943,8 @@ DOCFILES= \
   ${DOC}/schaum9.input.dvi     ${DOC}/schaum10.input.dvi \
   ${DOC}/schaum11.input.dvi    ${DOC}/schaum12.input.dvi \
   ${DOC}/schaum13.input.dvi    ${DOC}/schaum14.input.dvi \
+  ${DOC}/schaum15.input.dvi    ${DOC}/schaum16.input.dvi \
+  ${DOC}/schaum17.input.dvi \
   ${DOC}/s01eaf.input.dvi      ${DOC}/s13aaf.input.dvi     \
   ${DOC}/s13acf.input.dvi      ${DOC}/s13adf.input.dvi     \
   ${DOC}/s14aaf.input.dvi      ${DOC}/s14abf.input.dvi     \
diff --git a/src/input/schaum15.input.pamphlet b/src/input/schaum15.input.pamphlet
new file mode 100644
index 0000000..51a6094
--- /dev/null
+++ b/src/input/schaum15.input.pamphlet
@@ -0,0 +1,409 @@
+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/input schaum15.input}
+\author{Timothy Daly}
+\maketitle
+\eject
+\tableofcontents
+\eject
+\section{\cite{1}:14.311~~~~~$\displaystyle
+\int{\frac{dx}{x^4+a^4}}$}
+$$\int{\frac{1}{x^4+a^4}}=
+\frac{1}{4a^3\sqrt{2}}
+\ln\left(\frac{x^2+ax\sqrt{2}+a^2}{x^2-ax\sqrt{2}+a^2}\right)
+-\frac{1}{2a^3\sqrt{2}}\tan^{-1}\frac{ax\sqrt{2}}{x^2-a^2}
+$$
+<<*>>=
+)spool schaum15.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1 of 14
+aa:=integrate(1/(x^4+a^4),x)
+--R 
+--R
+--R   (1)
+--R        +------+          +------+2            +------+
+--R        |   1          8  |   1        4  +-+  |   1      2
+--R        |------ log(16a   |------  + 4a x\|2   |------ + x )
+--R       4|    12          4|    12             4|    12
+--R       \|256a            \|256a               \|256a
+--R     + 
+--R          +------+          +------+2            +------+
+--R          |   1          8  |   1        4  +-+  |   1      2
+--R       -  |------ log(16a   |------  - 4a x\|2   |------ + x )
+--R         4|    12          4|    12             4|    12
+--R         \|256a            \|256a               \|256a
+--R     + 
+--R                              +------+                               +------+
+--R                           4  |   1                               4  |   1
+--R                         4a   |------                           4a   |------
+--R        +------+             4|    12          +------+             4|    12
+--R        |   1                \|256a            |   1                \|256a
+--R     2  |------ atan(-------------------- - 2  |------ atan(--------------------)
+--R       4|    12           +------+            4|    12           +------+
+--R       \|256a          4  |   1       +-+     \|256a          4  |   1       +-+
+--R                     4a   |------ - x\|2                    4a   |------ + x\|2
+--R                         4|    12                               4|    12
+--R                         \|256a                                 \|256a
+--R  /
+--R      +-+
+--R     \|2
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.312~~~~~$\displaystyle
+\int{\frac{x~dx}{x^4+a^4}}$}
+$$\int{\frac{x}{x^4+a^4}}=
+\frac{1}{2a^2}\tan^{-1}\frac{x^2}{a^2}
+$$
+<<*>>=
+)clear all
+
+--S 2 of 14
+aa:=integrate(x/(x^4+a^4),x)
+--R 
+--R
+--R              2
+--R             x
+--R        atan(--)
+--R              2
+--R             a
+--R   (1)  --------
+--R             2
+--R           2a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.313~~~~~$\displaystyle
+\int{\frac{x^2~dx}{x^4+a^4}}$}
+$$\int{\frac{x^2}{x^4+a^4}}=
+\frac{1}{4a\sqrt{2}}
+\ln\left(\frac{x^2-ax\sqrt{2}+a^2}{x^2+ax\sqrt{2}+a^2}\right)
+-\frac{1}{2a\sqrt{2}}\tan^{-1}\frac{ax\sqrt{2}}{x^2-a^2}
+$$
+<<*>>=
+)clear all
+
+--S 3 of 14
+aa:=integrate(x^2/(x^4+a^4),x)
+--R 
+--R
+--R   (1)
+--R          +-----+               +-----+3        +-----+2
+--R          |  1          4  +-+  |  1         4  |  1       2
+--R       -  |----- log(64a x\|2   |-----  + 16a   |-----  + x )
+--R         4|    4               4|    4         4|    4
+--R         \|256a                \|256a          \|256a
+--R     + 
+--R        +-----+                 +-----+3        +-----+2
+--R        |  1            4  +-+  |  1         4  |  1       2
+--R        |----- log(- 64a x\|2   |-----  + 16a   |-----  + x )
+--R       4|    4                 4|    4         4|    4
+--R       \|256a                  \|256a          \|256a
+--R     + 
+--R                              +-----+3                               +-----+3
+--R                           4  |  1                                4  |  1
+--R                        64a   |-----                           64a   |-----
+--R        +-----+              4|    4           +-----+              4|    4
+--R        |  1                 \|256a            |  1                 \|256a
+--R     2  |----- atan(--------------------- - 2  |----- atan(---------------------)
+--R       4|    4            +-----+3            4|    4            +-----+3
+--R       \|256a          4  |  1        +-+     \|256a          4  |  1        +-+
+--R                    64a   |-----  - x\|2                   64a   |-----  + x\|2
+--R                         4|    4                                4|    4
+--R                         \|256a                                 \|256a
+--R  /
+--R      +-+
+--R     \|2
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.314~~~~~$\displaystyle
+\int{\frac{x^3~dx}{x^4+a^4}}$}
+$$\int{\frac{x^3}{x^4+a^4}}=
+\frac{1}{4}\ln(x^4+a^4)
+$$
+<<*>>=
+)clear all
+
+--S 4 of 14
+aa:=integrate(x^3/(x^4+a^4),x)
+--R 
+--R
+--R             4    4
+--R        log(x  + a )
+--R   (1)  ------------
+--R              4
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.315~~~~~$\displaystyle
+\int{\frac{dx}{x(x^4+a^4)}}~dx$}
+$$\int{\frac{1}{x(x^4+a^4)}}=
+\frac{1}{4a^4}\ln\left(\frac{x^4}{x^4+a^4}\right)
+$$
+<<*>>=
+)clear all
+
+--S 5 of 14
+aa:=integrate(1/(x*(x^4+a^4)),x)
+--R 
+--R
+--R               4    4
+--R        - log(x  + a ) + 4log(x)
+--R   (1)  ------------------------
+--R                     4
+--R                   4a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.316~~~~~$\displaystyle
+\int{\frac{dx}{x^2(x^4+a^4)}}$}
+$$\int{\frac{1}{x^2(x^4+a^4)}}=
+-\frac{1}{a^4x}-\frac{1}{4a^5\sqrt{2}}
+\ln\left(\frac{x^2-ax\sqrt{2}+a^2}{x^2+ax\sqrt{2}+a^2}\right)
++\frac{1}{2a^5\sqrt{2}}\tan^{-1}\frac{ax\sqrt{2}}{x^2-a^2}
+$$
+<<*>>=
+)clear all
+
+--S 6 of 14
+aa:=integrate(1/(x^2*(x^4+a^4)),x)
+--R 
+--R
+--R   (1)
+--R            +------+                +------+3         +------+2
+--R        4   |   1          16  +-+  |   1         12  |   1       2
+--R       a x  |------ log(64a  x\|2   |------  + 16a    |------  + x )
+--R           4|    20                4|    20          4|    20
+--R           \|256a                  \|256a            \|256a
+--R     + 
+--R              +------+                  +------+3         +------+2
+--R          4   |   1            16  +-+  |   1         12  |   1       2
+--R       - a x  |------ log(- 64a  x\|2   |------  + 16a    |------  + x )
+--R             4|    20                  4|    20          4|    20
+--R             \|256a                    \|256a            \|256a
+--R     + 
+--R                                       +------+3
+--R                                   16  |   1
+--R                                64a    |------
+--R               +------+               4|    20
+--R           4   |   1                  \|256a
+--R       - 2a x  |------ atan(-----------------------)
+--R              4|    20             +------+3
+--R              \|256a           16  |   1        +-+
+--R                            64a    |------  - x\|2
+--R                                  4|    20
+--R                                  \|256a
+--R     + 
+--R                                     +------+3
+--R                                 16  |   1
+--R                              64a    |------
+--R             +------+               4|    20
+--R         4   |   1                  \|256a           +-+
+--R       2a x  |------ atan(----------------------- - \|2
+--R            4|    20             +------+3
+--R            \|256a           16  |   1        +-+
+--R                          64a    |------  + x\|2
+--R                                4|    20
+--R                                \|256a
+--R  /
+--R      4  +-+
+--R     a x\|2
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.317~~~~~$\displaystyle
+\int{\frac{dx}{x^3(x^4+a^4)}}$}
+$$\int{\frac{1}{x^3(x^4+a^4)}}=
+-\frac{1}{2a^4x^2}-\frac{1}{2a^6}\tan^{-1}\frac{x^2}{a^2}
+$$
+<<*>>=
+)clear all
+
+--S 7 of 14
+aa:=integrate(1/(x^3*(x^4+a^4)),x)
+--R 
+--R
+--R                  2
+--R           2     x      2
+--R        - x atan(--) - a
+--R                  2
+--R                 a
+--R   (1)  -----------------
+--R                6 2
+--R              2a x
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.318~~~~~$\displaystyle
+\int{\frac{dx}{(x^4-a^4)}}$}
+$$\int{\frac{1}{(x^4-a^4)}}=
+\frac{1}{4a^3}\ln\left(\frac{x-a}{x+a}\right)
+-\frac{1}{2a^3}\tan^{-1}\frac{x}{a}
+$$
+<<*>>=
+)clear all
+
+--S 8 of 14
+aa:=integrate(1/(x^4-a^4),x)
+--R 
+--R
+--R                                          x
+--R        - log(x + a) + log(x - a) - 2atan(-)
+--R                                          a
+--R   (1)  ------------------------------------
+--R                           3
+--R                         4a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.319~~~~~$\displaystyle
+\int{\frac{x~dx}{(x^4-a^4)}}$}
+$$\int{\frac{x}{(x^4-a^4)}}=
+\frac{1}{4a^2}\ln\left(\frac{x^2-a^2}{x^2+a^2}\right)
+$$
+<<*>>=
+)clear all
+
+--S 9 of 14
+aa:=integrate(x/(x^4-a^4),x)
+--R 
+--R
+--R               2    2         2    2
+--R        - log(x  + a ) + log(x  - a )
+--R   (1)  -----------------------------
+--R                       2
+--R                     4a
+--R                                          Type: Union(Expression Integer,...)
+--E
+@
+
+\section{\cite{1}:14.320~~~~~$\displaystyle
+\int{\frac{x^2~dx}{x^4-a^4}}$}
+$$\int{\frac{x^2}{x^4-a^4}}=
+\frac{1}{4a}\ln\left(\frac{x-a}{x+a}\right)
++\frac{1}{2a}\tan^{-1}\frac{x}{a}
+$$
+<<*>>=
+)clear all
+
+--S 10 of 14
+aa:=integrate(x^2/(x^4-a^4),x)
+--R 
+--R
+--R                                          x
+--R        - log(x + a) + log(x - a) + 2atan(-)
+--R                                          a
+--R   (1)  ------------------------------------
+--R                         4a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.321~~~~~$\displaystyle
+\int{\frac{x^3~dx}{x^4-a^4}}$}
+$$\int{\frac{x^3}{x^4-a^4}}=
+\frac{1}{4}\ln(x^4-a^4)
+$$
+<<*>>=
+)clear all
+
+--S 11 of 14
+aa:=integrate(x^3/(x^4-a^4),x)
+--R 
+--R
+--R             4    4
+--R        log(x  - a )
+--R   (1)  ------------
+--R              4
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.322~~~~~$\displaystyle
+\int{\frac{dx}{x(x^4-a^4)}}$}
+$$\int{\frac{1}{x(x^4-a^4)}}=
+\frac{1}{4a^4}\ln\left(\frac{x^4-a^4}{x^4}\right)
+$$
+<<*>>=
+)clear all
+
+--S 12 of 14
+aa:=integrate(1/(x*(x^4-a^4)),x)
+--R 
+--R
+--R             4    4
+--R        log(x  - a ) - 4log(x)
+--R   (1)  ----------------------
+--R                    4
+--R                  4a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.323~~~~~$\displaystyle
+\int{\frac{dx}{x^2(x^4-a^4)}}$}
+$$\int{\frac{1}{x^2(x^4-a^4)}}=
+\frac{1}{a^4x}+\frac{1}{4a^5}\ln\left(\frac{x-a}{x+a}\right)
++\frac{1}{2a^5}\tan^{-1}\frac{x}{a}
+$$
+<<*>>=
+)clear all
+
+--S 13 of 14
+aa:=integrate(1/(x^2*(x^4-a^4)),x)
+--R 
+--R
+--R                                                x
+--R        - x log(x + a) + x log(x - a) + 2x atan(-) + 4a
+--R                                                a
+--R   (1)  -----------------------------------------------
+--R                                5
+--R                              4a x
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.324~~~~~$\displaystyle
+\int{\frac{dx}{x^3(x^4-a^4)}}$}
+$$\int{\frac{1}{x^3(x^4-a^4)}}=
+\frac{1}{2a^4x^2}+\frac{1}{4a^6}\ln\left(\frac{x^2-a^2}{x^2+a^2}\right)
+$$
+<<*>>=
+)clear all
+
+--S 14 of 14
+aa:=integrate(1/(x^3*(x^4-a^4)),x)
+--R 
+--R
+--R           2     2    2     2     2    2      2
+--R        - x log(x  + a ) + x log(x  - a ) + 2a
+--R   (1)  ---------------------------------------
+--R                           6 2
+--R                         4a x
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+)spool
+)lisp (bye)
+@
+
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} Spiegel, Murray R.
+{\sl Mathematical Handbook of Formulas and Tables}\\
+Schaum's Outline Series McGraw-Hill 1968 pp73-74
+\end{thebibliography}
+\end{document}
diff --git a/src/input/schaum16.input.pamphlet b/src/input/schaum16.input.pamphlet
new file mode 100644
index 0000000..2246f9a
--- /dev/null
+++ b/src/input/schaum16.input.pamphlet
@@ -0,0 +1,394 @@
+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/input schaum16.input}
+\author{Timothy Daly}
+\maketitle
+\eject
+\tableofcontents
+\eject
+\section{\cite{1}:14.325~~~~~$\displaystyle
+\int{\frac{dx}{x(x^n+a^n)}}$}
+$$\int{\frac{1}{x(x^n+a^n)}}=
+\frac{1}{na^n}\ln\frac{x^n}{x^n+a^n}
+$$
+<<*>>=
+)spool schaum16.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1 of 14
+aa:=integrate(1/x*(x^n+a^n),x)
+--R 
+--R
+--R          n log(x)            n
+--R        %e         + n log(x)a
+--R   (1)  -----------------------
+--R                   n
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.326~~~~~$\displaystyle
+\int{\frac{x^{n-1}~dx}{x^n+a^n}}$}
+$$\int{\frac{x^{n-1}}{x^n+a^n}}=
+\frac{1}{n}\ln(x^n+a^n)
+$$
+<<*>>=
+)clear all
+
+--S 2 of 14
+aa:=integrate(x^(n-1)/(x^n+a^n),x)
+--R 
+--R
+--R              n log(x)    n
+--R        log(%e         + a )
+--R   (1)  --------------------
+--R                  n
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.327~~~~~$\displaystyle
+\int{\frac{x^m~dx}{(x^n+a^n)^r}}$}
+$$\int{\frac{x^m}{(x^n+a^n)^r}}=
+\int{\frac{x^{m-n}}{(x^n+a^n)^{r-1}}}
+-a^n\int{\frac{x^{m-n}}{(x^n+a^n)^r}}
+$$
+<<*>>=
+)clear all
+
+--S 3 of 14
+aa:=integrate(x^m/(x^n+a^n)^r,x)
+--R 
+--R
+--R           x       m
+--R         ++      %J
+--R   (1)   |   ----------- d%J
+--R        ++     n     n r
+--R             (a  + %J )
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.328~~~~~$\displaystyle
+\int{\frac{dx}{x^m(x^n+a^n)^r}}$}
+$$\int{\frac{1}{x^m(x^n+a^n)^r}}=
+\frac{1}{a^n}\int{\frac{1}{x^m(x^n+a^n)^{r-1}}}
+-\frac{1}{a^n}\int{\frac{1}{x^{m-n}(x^n+a^n)^r}}
+$$
+<<*>>=
+)clear all
+
+--S 4 of 14
+aa:=integrate(1/(x^m*(x^n+a^n)^r),x)
+--R 
+--R
+--R           x
+--R         ++         1
+--R   (1)   |   -------------- d%J
+--R        ++     m  n     n r
+--R             %J (a  + %J )
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.329~~~~~$\displaystyle
+\int{\frac{dx}{x\sqrt{x^n+a^n}}}$}
+$$\int{\frac{1}{x\sqrt{x^n+a^n}}}=
+\frac{1}{n\sqrt{a^n}}\ln\left(\frac{\sqrt{x^n+a^n}-\sqrt{a^n}}
+{\sqrt{x^n+a^n}+\sqrt{a^n}}\right)
+$$
+<<*>>=
+)clear all
+
+--S 5 of 14
+aa:=integrate(1/(x*sqrt(x^n+a^n)),x)
+--R 
+--R
+--R   (1)
+--R              +---------------+                      +--+
+--R            n |  n log(x)    n       n log(x)     n  | n
+--R        - 2a \|%e         + a   + (%e         + 2a )\|a
+--R    log(-------------------------------------------------)
+--R                              n log(x)
+--R                            %e
+--R   [------------------------------------------------------,
+--R                              +--+
+--R                              | n
+--R                            n\|a
+--R             +----+ +---------------+
+--R             |   n  |  n log(x)    n
+--R            \|- a  \|%e         + a
+--R      2atan(-------------------------)
+--R                         n
+--R                        a
+--R    - --------------------------------]
+--R                    +----+
+--R                    |   n
+--R                  n\|- a
+--R                                     Type: Union(List Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.330~~~~~$\displaystyle
+\int{\frac{dx}{x(x^n-a^n)}}$}
+$$\int{\frac{1}{x(x^n-a^n)}}=
+\frac{1}{na^n}\ln\left(\frac{x^n-a^n}{x^n}\right)
+$$
+<<*>>=
+)clear all
+
+--S 6 of 14
+aa:=integrate(1/(x*(x^n-a^n)),x)
+--R 
+--R
+--R              n log(x)    n
+--R        log(%e         - a ) - n log(x)
+--R   (1)  -------------------------------
+--R                         n
+--R                      n a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.331~~~~~$\displaystyle
+\int{\frac{x^{n-1}dx}{x^n-a^n}}$}
+$$\int{\frac{x^{n-1}}{x^n-a^n}}=
+\frac{1}{n}\ln(x^n-a^n)
+$$
+<<*>>=
+)clear all
+
+--S 7 of 14
+aa:=integrate(x^(n-1)/(x^n-a^n),x)
+--R 
+--R
+--R              n log(x)    n
+--R        log(%e         - a )
+--R   (1)  --------------------
+--R                  n
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.332~~~~~$\displaystyle
+\int{\frac{x^m~dx}{(x^n-a^n)^r}}$}
+$$\int{\frac{x^m}{(x^n-a^n)^r}}=
+a^n\int{\frac{x^{m-n}}{(x^n-a^n)^r}}
++\int{\frac{x^{m-n}}{(x^n-a^n)^{r-1}}}
+$$
+<<*>>=
+)clear all
+
+--S 8 of 14
+aa:=integrate(x^m/(x^n-a^n)^r,x)
+--R 
+--R
+--R           x        m
+--R         ++       %J
+--R   (1)   |   ------------- d%J
+--R        ++       n     n r
+--R             (- a  + %J )
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.333~~~~~$\displaystyle
+\int{\frac{dx}{x^m(x^n-a^n)^r}}$}
+$$\int{\frac{1}{x^m(x^n-a^n)^r}}=
+\frac{1}{a^n}\int{\frac{1}{x^{m-n}(x^n-a^n)^r}}
+-\frac{1}{a^n}\int{\frac{1}{x^m(x^n-a^n)^{r-1}}}
+$$
+<<*>>=
+)clear all
+
+--S 9 of 14
+aa:=integrate(1/(x^m*(x^n-a^n)^r),x)
+--R 
+--R
+--R           x
+--R         ++          1
+--R   (1)   |   ---------------- d%J
+--R        ++     m    n     n r
+--R             %J (- a  + %J )
+--R                                          Type: Union(Expression Integer,...)
+--E
+@
+
+\section{\cite{1}:14.334~~~~~$\displaystyle
+\int{\frac{dx}{x\sqrt{x^n-a^n}}}$}
+$$\int{\frac{1}{x\sqrt{x^n-a^n}}}=
+\frac{2}{n\sqrt{a^n}}\cos^{-1}\sqrt{\frac{a^n}{x^n}}
+$$
+<<*>>=
+)clear all
+
+--S 10 of 14
+aa:=integrate(1/(x*sqrt(x^n-a^n)),x)
+--R 
+--R
+--R   (1)
+--R            +---------------+                      +----+
+--R          n |  n log(x)    n       n log(x)     n  |   n
+--R        2a \|%e         - a   + (%e         - 2a )\|- a
+--R    log(-------------------------------------------------)
+--R                              n log(x)
+--R                            %e
+--R   [------------------------------------------------------,
+--R                             +----+
+--R                             |   n
+--R                           n\|- a
+--R           +--+ +---------------+
+--R           | n  |  n log(x)    n
+--R          \|a  \|%e         - a
+--R    2atan(-----------------------)
+--R                      n
+--R                     a
+--R    ------------------------------]
+--R                  +--+
+--R                  | n
+--R                n\|a
+--R                                     Type: Union(List Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.335~~~~~$\displaystyle
+\int{\frac{x^{p-1}~dx}{x^{2m}+a^{2m}}}$ provided $0<p\le 2m$}
+$$\begin{array}{rl}
+\displaystyle\int{\frac{x^{p-1}}{x^{2m}+a^{2m}}}=
+&\displaystyle\frac{1}{ma^{2m-p}}\sum_{k=1}^m{\sin\frac{(2k-1)p\pi}{2m}
+\tan^{-1}\left(\frac{x+a\cos\left((2k-1)\pi/2m\right)}
+{a\sin\left((2k-1)\pi/2m\right)}\right)}\\
+&\\
+&\displaystyle-\frac{1}{2ma^{2m-p}}\sum_{k=1}^m{\cos\frac{(2k-1)p\pi}{2m}
+\ln\left(x^2+2ax\cos\frac{(2k-1)\pi}{2m}+a^2\right)}
+\end{array}
+$$
+<<*>>=
+)clear all
+
+--S 11 of 14
+aa:=integrate(x^(p-1)/(x^(2*m)+a^(2*m)),x)
+--R 
+--R
+--R           x     p - 1
+--R         ++    %J
+--R   (1)   |   ---------- d%J
+--R        ++    2m     2m
+--R             a   + %J
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.336~~~~~$\displaystyle
+\int{\frac{x^{p-1}dx}{x^{2m}-a^{2m}}}$ provided $0<p\le 2m$}
+$$\begin{array}{rl}
+\displaystyle
+\int{\frac{x^{p-1}}{x^{2m}-a^{2m}}}=
+&\displaystyle\frac{1}{2ma^{2m-p}}\sum_{k=1}^{m-1}\cos\frac{kp\pi}{m}
+\ln\left(x^2-2ax\cos\frac{k\pi}{m}+a^2\right)\\
+&\\
+&\displaystyle-\frac{1}{ma^{2m-p}}\sum_{k=1}^{m-1}\sin\frac{kp\pi}{m}
+\tan^{-1}\left(\frac{x-a\cos(k\pi/m)}{a\sin(k\pi/m)}\right)\\
+&\\
+&\displaystyle+\frac{1}{2ma^{2m-p}}\left(\ln(x-a)+(-1)^p\ln(x+a)\right)
+\end{array}
+$$
+<<*>>=
+)clear all
+
+--S 12 of 14
+aa:=integrate(x^(p-1)/(x^(2*m)-a^(2*m)),x)
+--R 
+--R
+--R           x       p - 1
+--R         ++      %J
+--R   (1)   |   - ---------- d%J
+--R        ++      2m     2m
+--R               a   - %J
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.337~~~~~$\displaystyle
+\int{\frac{x^{p-1}~dx}{x^{2m+1}+a^{2m+1}}}$ provided $0<p\le 2m+1$}
+$$\begin{array}{rl}
+\displaystyle\int{\frac{x^{p-1}}{x^{2m+1}+a^{2m+1}}}=&\hbox{\hskip 6.5cm}
+\end{array}
+$$
+$$\begin{array}{rl}
+\hbox{\hskip 1cm}&\displaystyle
+\frac{2(-1)^{p-1}}{(2m+1)a^{2m-p+1}}\sum_{k=1}^m{\sin\frac{2kp\pi}{2m+1}
+\tan^{-1}\left(\frac{x+a\cos\left(2k\pi/(2m+1)\right)}
+{a\sin\left(2k\pi/(2m+1)\right)}\right)}\\
+&\displaystyle
+-\frac{(-1)^{p-1}}{(2m+1)a^{2m-p+1}}\sum_{k=1}^m{\cos\frac{2kp\pi}{2m+1}
+\ln\left(x^2+2ax\cos\frac{2k\pi}{2m+1}+a^2\right)}\\
+&\\
+&\displaystyle+\frac{(-1)^{p-1}\ln(x+a)}{(2m+1)a^{2m-p+1}}
+\end{array}
+$$
+<<*>>=
+)clear all
+
+--S 13 of 14
+aa:=integrate(x^(p-1)/(x^(2*m+1)+a^(2*m+1)),x)
+--R 
+--R
+--R           x         p - 1
+--R         ++        %J
+--R   (1)   |   ------------------ d%J
+--R        ++    2m + 1     2m + 1
+--R             a       + %J
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.338~~~~~$\displaystyle
+\int{\frac{x^{p-1}~dx}{x^{2m+1}-a^{2m+1}}}$ provided $0<p\le 2m+1$}
+$$\begin{array}{rl}
+\displaystyle\int{\frac{x^{p-1}}{x^{2m+1}-a^{2m+1}}}=&\hbox{\hskip 6cm}
+\end{array}
+$$
+$$\begin{array}{rl}
+\hbox{\hskip 1cm}&\displaystyle
+\frac{2}{(2m+1)a^{2m-p+1}}\sum_{k=1}^m{\sin\frac{2kp\pi}{2m+1}
+\tan^{-1}\left(\frac{x-a\cos\left(2kp\pi/(2m+1)\right)}
+{a\sin\left(2k\pi/(2m+1)\right)}\right)}\\
+&\\
+&\hbox{\hskip 1cm}\displaystyle
++\frac{1}{(2m+1)a^{2m-p+1}}\sum_{k=1}^m{\cos\frac{2kp\pi}{2m+1}
+\ln\left(x^2-2ax\cos\frac{2k\pi}{2m+1}+a^2\right)}\\
+&\\
+&\hbox{\hskip 1cm}\displaystyle
++\frac{\ln(x-a)}{(2m+1)a^{2m-p+1}}
+\end{array}
+$$
+<<*>>=
+)clear all
+
+--S 14 of 14
+aa:=integrate(x^(p-1)/(x^(2*m+1)-a^(2*m+1)),x)
+--R 
+--R
+--R           x           p - 1
+--R         ++          %J
+--R   (1)   |   - ------------------ d%J
+--R        ++      2m + 1     2m + 1
+--R               a       - %J
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+)spool
+)lisp (bye)
+@
+
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} Spiegel, Murray R.
+{\sl Mathematical Handbook of Formulas and Tables}\\
+Schaum's Outline Series McGraw-Hill 1968 pp74-75
+\end{thebibliography}
+\end{document}
diff --git a/src/input/schaum17.input.pamphlet b/src/input/schaum17.input.pamphlet
new file mode 100644
index 0000000..7ab11d7
--- /dev/null
+++ b/src/input/schaum17.input.pamphlet
@@ -0,0 +1,779 @@
+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/input schaum17.input}
+\author{Timothy Daly}
+\maketitle
+\eject
+\tableofcontents
+\eject
+\section{\cite{1}:14.339~~~~~$\displaystyle
+\int{\sin ax ~dx}$}
+$$\int{\sin ax}=
+-\frac{\cos{ax}}{a}
+$$
+<<*>>=
+)spool schaum17.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1 of 30
+aa:=integrate(sin(a*x),x)
+--R 
+--R
+--R          cos(a x)
+--R   (1)  - --------
+--R              a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.340~~~~~$\displaystyle
+\int{x\sin{ax}~dx}$}
+$$\int{x\sin{ax}}=
+\frac{sin{ax}}{a^2}-\frac{x\cos{ax}}{a}
+$$
+<<*>>=
+)clear all
+
+--S 2 of 30
+aa:=integrate(x*sin(a*x),x)
+--R 
+--R
+--R        sin(a x) - a x cos(a x)
+--R   (1)  -----------------------
+--R                    2
+--R                   a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.341~~~~~$\displaystyle
+\int{x^2\sin{ax}~dx}$}
+$$\int{x^2\sin{ax}}=
+\frac{2x}{a^2}\sin{ax}+\left(\frac{2}{a^3}-\frac{x^2}{a}\right)\cos{ax}
+$$
+<<*>>=
+)clear all
+
+--S 3 of 30
+aa:=integrate(x^2*sin(a*x),x)
+--R 
+--R
+--R                            2 2
+--R        2a x sin(a x) + (- a x  + 2)cos(a x)
+--R   (1)  ------------------------------------
+--R                          3
+--R                         a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.342~~~~~$\displaystyle
+\int{x^3\sin{ax}~dx}$}
+$$\int{x^3\sin{ax}}=
+\left(\frac{3x^2}{a^2}-\frac{6}{a^4}\right)\sin{ax}
++\left(\frac{6x}{a^3}-\frac{x^3}{a}\right)\cos{ax}
+$$
+<<*>>=
+)clear all
+
+--S 4 of 30
+aa:=integrate(x^3*sin(a*x),x)
+--R 
+--R
+--R           2 2                    3 3
+--R        (3a x  - 6)sin(a x) + (- a x  + 6a x)cos(a x)
+--R   (1)  ---------------------------------------------
+--R                               4
+--R                              a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.343~~~~~$\displaystyle
+\int{\frac{\sin{ax}}{x}}~dx$}
+$$\int{\frac{\sin{ax}}{x}}=
+ax-\frac{(ax)^3}{3\cdot 3!}+\frac{(ax)^5}{5\cdot 5!}-\cdots
+$$
+<<*>>=
+)clear all
+
+--S 5 of 30
+aa:=integrate(sin(x)/x,x)
+--R 
+--R
+--R   (1)  Si(x)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.344~~~~~$\displaystyle
+\int{\frac{\sin{ax}}{x^2}}~dx$}
+$$\int{\frac{\sin{ax}}{x^2}}=
+-\frac{\sin{ax}}{x}+a\int{\frac{\cos{ax}}{x}}
+$$
+<<*>>=
+)clear all
+
+--S 6 of 30
+aa:=integrate(sin(a*x)/x^2,x)
+--R 
+--R
+--R           x
+--R         ++  sin(%I a)
+--R   (1)   |   --------- d%I
+--R        ++        2
+--R                %I
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.345~~~~~$\displaystyle
+\int{\frac{dx}{\sin{ax}}}$}
+$$\int{\frac{1}{\sin{ax}}}=
+\frac{1}{a}\ln(\csc{ax}-\cot{ax})=
+\frac{1}{a}\ln\tan\frac{ax}{2}
+$$
+<<*>>=
+)clear all
+
+--S 7 of 30
+aa:=integrate(1/sin(a*x),x)
+--R 
+--R
+--R              sin(a x)
+--R        log(------------)
+--R            cos(a x) + 1
+--R   (1)  -----------------
+--R                a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.346~~~~~$\displaystyle
+\int{\frac{x~dx}{\sin{ax}}}$}
+$$\int{\frac{x}{\sin{ax}}}=
+\frac{1}{a^2}\left\{
+ax+\frac{(ax)^3}{18}+\frac{7(ax)^5}{1800}+\cdots+
+\frac{2(2^{2n-1}-1)B_n(ax)^{2n+1}}{(2n+1)!}+\cdots\right\}
+$$
+<<*>>=
+)clear all
+
+--S 8 of 30
+aa:=integrate(x/sin(a*x),x)
+--R 
+--R
+--R           x
+--R         ++      %I
+--R   (1)   |   --------- d%I
+--R        ++   sin(%I a)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.347~~~~~$\displaystyle
+\int{\sin^2{ax}}~dx$}
+$$\int{\sin^2{ax}}=
+\frac{x}{2}-\frac{\sin{2ax}}{4a}
+$$
+<<*>>=
+)clear all
+
+--S 9 of 30
+aa:=integrate(sin(a*x)^2,x)
+--R 
+--R
+--R        - cos(a x)sin(a x) + a x
+--R   (1)  ------------------------
+--R                   2a
+--R                                          Type: Union(Expression Integer,...)
+--E
+@
+
+\section{\cite{1}:14.348~~~~~$\displaystyle
+\int{x\sin^2{ax}}~dx$}
+$$\int{x\sin^2{ax}}=
+\frac{x^2}{4}-\frac{x\sin{2ax}}{4a}-\frac{\cos{2ax}}{8a^2}
+$$
+<<*>>=
+)clear all
+
+--S 10 of 30
+aa:=integrate(x*sin(a*x)^2,x)
+--R 
+--R
+--R                                          2    2 2
+--R        - 2a x cos(a x)sin(a x) - cos(a x)  + a x
+--R   (1)  ------------------------------------------
+--R                              2
+--R                            4a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.349~~~~~$\displaystyle
+\int{\sin^3{ax}}~dx$}
+$$\int{\sin^3{ax}}=
+-\frac{\cos{ax}}{a}+\frac{\cos^3{ax}}{3a}
+$$
+<<*>>=
+)clear all
+
+--S 11 of 30
+aa:=integrate(sin(a*x)^3,x)
+--R 
+--R
+--R                3
+--R        cos(a x)  - 3cos(a x)
+--R   (1)  ---------------------
+--R                  3a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.350~~~~~$\displaystyle
+\int{\sin^4{ax}}~dx$}
+$$\int{\sin^4{ax}}=
+\frac{3x}{8}-\frac{\sin{2ax}}{4a}+\frac{\sin{4ax}}{32a}
+$$
+<<*>>=
+)clear all
+
+--S 12 of 30
+aa:=integrate(sin(a*x)^4,x)
+--R 
+--R
+--R                  3
+--R        (2cos(a x)  - 5cos(a x))sin(a x) + 3a x
+--R   (1)  ---------------------------------------
+--R                           8a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.351~~~~~$\displaystyle
+\int{\frac{dx}{\sin^2{ax}}}$}
+$$\int{\frac{1}{\sin^2{ax}}}=
+-\frac{1}{a}\cot{ax}
+$$
+<<*>>=
+)clear all
+
+--S 13 of 30
+aa:=integrate(1/sin(a*x)^2,x)
+--R 
+--R
+--R           cos(a x)
+--R   (1)  - ----------
+--R          a sin(a x)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.352~~~~~$\displaystyle
+\int{\frac{dx}{\sin^3{ax}}}$}
+$$\int{\frac{1}{\sin^3{ax}}}=
+-\frac{\cos{ax}}{2a\sin^2{ax}}+\frac{1}{2a}\ln\tan\frac{ax}{2}
+$$
+<<*>>=
+)clear all
+
+--S 14 of 30
+aa:=integrate(1/sin(a*x)^3,x)
+--R 
+--R
+--R                 2           sin(a x)
+--R        (cos(a x)  - 1)log(------------) + cos(a x)
+--R                           cos(a x) + 1
+--R   (1)  -------------------------------------------
+--R                                2
+--R                     2a cos(a x)  - 2a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.353~~~~~$\displaystyle
+\int{\sin{px}\sin{qx}}~dx$}
+$$\int{\sin{px}\sin{qx}}=
+\frac{\sin{(p-q)x}}{2(p-q)}-\frac{\sin{(p+q)x}}{2(p+q)}
+$$
+<<*>>=
+)clear all
+
+--S 15 of 30
+aa:=integrate(sin(p*x)*sin(q*x),x)
+--R 
+--R
+--R        p cos(p x)sin(q x) - q cos(q x)sin(p x)
+--R   (1)  ---------------------------------------
+--R                         2    2
+--R                        q  - p
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.354~~~~~$\displaystyle
+\int{\frac{dx}{1-\sin{ax}}}$}
+$$\int{\frac{1}{1-\sin{ax}}}=
+\frac{1}{a}\tan\left(\frac{\pi}{4}+\frac{ax}{2}\right)
+$$
+<<*>>=
+)clear all
+
+--S 16 of 30
+aa:=integrate(1/(1-sin(a*x)),x)
+--R 
+--R
+--R              - 2cos(a x) - 2
+--R   (1)  ---------------------------
+--R        a sin(a x) - a cos(a x) - a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.355~~~~~$\displaystyle
+\int{\frac{x~dx}{1-\sin{ax}}}$}
+$$\int{\frac{x}{1-\sin{ax}}}=
+\frac{x}{a}\tan\left(\frac{\pi}{4}+\frac{ax}{2}\right)
++\frac{2}{a^2}\ln~\sin\left(\frac{\pi}{4}-\frac{ax}{2}\right)
+$$
+<<*>>=
+)clear all
+
+--S 17 of 30
+aa:=integrate(x/(1-sin(ax)),x)
+--R 
+--R
+--R                2
+--R               x
+--R   (1)  - ------------
+--R          2sin(ax) - 2
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.356~~~~~$\displaystyle
+\int{\frac{dx}{1+\sin{ax}}}$}
+$$\int{\frac{1}{1+\sin{ax}}}=
+-\frac{1}{a}\tan\left(\frac{\pi}{4}-\frac{ax}{2}\right)
+$$
+<<*>>=
+)clear all
+
+--S 18 of 30
+aa:=integrate(1/(1+sin(ax)),x)
+--R 
+--R
+--R             x
+--R   (1)  -----------
+--R        sin(ax) + 1
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.357~~~~~$\displaystyle
+\int{\frac{x~dx}{1+\sin{ax}}}$}
+$$\int{\frac{x}{1+\sin{ax}}}=
+-\frac{x}{a}\tan\left(\frac{\pi}{4}-\frac{ax}{2}\right)
++\frac{2}{a^2}\ln~\sin\left(\frac{\pi}{4}+\frac{ax}{2}\right)
+$$
+<<*>>=
+)clear all
+
+--S 19 of 30
+aa:=integrate(x/(1+sin(a*x)),x)
+--R 
+--R
+--R   (1)
+--R                                      sin(a x) + cos(a x) + 1
+--R       (2sin(a x) + 2cos(a x) + 2)log(-----------------------)
+--R                                            cos(a x) + 1
+--R     + 
+--R                                            2
+--R       (- sin(a x) - cos(a x) - 1)log(------------) + a x sin(a x)
+--R                                      cos(a x) + 1
+--R     + 
+--R       - a x cos(a x) - a x
+--R  /
+--R      2            2            2
+--R     a sin(a x) + a cos(a x) + a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.358~~~~~$\displaystyle
+\int{\frac{dx}{(1-\sin{ax})^2}}$}
+$$\int{\frac{1}{(1-\sin{ax})^2}}=
+\frac{1}{2a}\tan\left(\frac{\pi}{4}+\frac{ax}{2}\right)
++\frac{1}{6a}\tan^3\left(\frac{\pi}{4}+\frac{ax}{2}\right)
+$$
+<<*>>=
+)clear all
+
+--S 20 of 30
+aa:=integrate(1/(1-sin(a*x))^2,x)
+--R 
+--R
+--R                                               2
+--R             (3cos(a x) + 3)sin(a x) + cos(a x)  - 4cos(a x) - 5
+--R   (1)  ------------------------------------------------------------
+--R                                                2
+--R        (3a cos(a x) + 6a)sin(a x) + 3a cos(a x)  - 3a cos(a x) - 6a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.359~~~~~$\displaystyle
+\int{\frac{dx}{(1+\sin{ax})^2}}$}
+$$\int{\frac{1}{(1+\sin{ax})^2}}=
+-\frac{1}{2a}\tan\left(\frac{\pi}{4}-\frac{ax}{2}\right)
+-\frac{1}{6a}\tan^3\left(\frac{\pi}{4}-\frac{ax}{2}\right)
+$$
+<<*>>=
+)clear all
+
+--S 21 of 30
+aa:=integrate(1/(1+sin(a*x))^2,x)
+--R 
+--R
+--R                                                2
+--R            (- 3cos(a x) - 3)sin(a x) + cos(a x)  - 4cos(a x) - 5
+--R   (1)  ------------------------------------------------------------
+--R                                                2
+--R        (3a cos(a x) + 6a)sin(a x) - 3a cos(a x)  + 3a cos(a x) + 6a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.360~~~~~$\displaystyle
+\int{\frac{dx}{p+q\sin{ax}}}$}
+$$\int{\frac{1}{p+q\sin{ax}}}=
+\left\{
+\begin{array}{l}
+\displaystyle
+\frac{2}{a\sqrt{p^2-q^q}}
+\tan^{-1}\frac{p\tan{\frac{1}{2}ax}+q}{\sqrt{p^2-q^2}}\\
+\\
+\displaystyle
+\frac{1}{a\sqrt{q^2-p^2}}\ln\left(\frac{p\tan{\frac{1}{2}ax}+q-\sqrt{q^2-p^2}}
+{p\tan{\frac{1}{2}ax}+q+\sqrt{q^2-p^2}}\right)
+\end{array}
+\right.
+$$
+<<*>>=
+)clear all
+
+--S 22 of 30
+aa:=integrate(1/(p+q*sin(a*x)),x)
+--R 
+--R
+--R   (1)
+--R   [
+--R       log
+--R                                                      +-------+
+--R                                2    2             2  | 2    2
+--R              (p q sin(a x) + (q  - p )cos(a x) + q )\|q  - p
+--R            + 
+--R                    2    3                3    2              3    2
+--R              (- p q  + p )sin(a x) + (- q  + p q)cos(a x) - q  + p q
+--R         /
+--R            q sin(a x) + p
+--R    /
+--R         +-------+
+--R         | 2    2
+--R       a\|q  - p
+--R     ,
+--R                                          +---------+
+--R                                          |   2    2
+--R            (p sin(a x) + q cos(a x) + q)\|- q  + p
+--R      2atan(-----------------------------------------)
+--R                     2    2             2    2
+--R                   (q  - p )cos(a x) + q  - p
+--R    - ------------------------------------------------]
+--R                          +---------+
+--R                          |   2    2
+--R                        a\|- q  + p
+--R                                     Type: Union(List Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.361~~~~~$\displaystyle
+\int{\frac{dx}{(p+q\sin{ax})^2}}$}
+$$\int{\frac{1}{(p+q\sin{ax})^2}}=
+\frac{q\cos{ax}}{a(p^2-q^2)(p+q\sin{ax})}
++\frac{p}{p^2-q^2}\int{\frac{1}{p+q\sin{ax}}}
+$$
+<<*>>=
+)clear all
+
+--S 23 of 30
+aa:=integrate(1/(p+q*sin(a*x))^2,x)
+--R 
+--R
+--R   (1)
+--R   [
+--R             2              3
+--R           (p q sin(a x) + p )
+--R        *
+--R           log
+--R                                                          +-------+
+--R                                    2    2             2  | 2    2
+--R                  (p q sin(a x) + (q  - p )cos(a x) + q )\|q  - p
+--R                + 
+--R                      2    3              3    2              3    2
+--R                  (p q  - p )sin(a x) + (q  - p q)cos(a x) + q  - p q
+--R             /
+--R                q sin(a x) + p
+--R       + 
+--R                                             +-------+
+--R             2                               | 2    2
+--R         (- q sin(a x) - p q cos(a x) - p q)\|q  - p
+--R    /
+--R                                                  +-------+
+--R              3      3                2 2      4  | 2    2
+--R       ((a p q  - a p q)sin(a x) + a p q  - a p )\|q  - p
+--R     ,
+--R
+--R                                                                 +---------+
+--R                                                                 |   2    2
+--R            2               3      (p sin(a x) + q cos(a x) + q)\|- q  + p
+--R         (2p q sin(a x) + 2p )atan(-----------------------------------------)
+--R                                            2    2             2    2
+--R                                          (q  - p )cos(a x) + q  - p
+--R       + 
+--R                                             +---------+
+--R             2                               |   2    2
+--R         (- q sin(a x) - p q cos(a x) - p q)\|- q  + p
+--R    /
+--R                                                  +---------+
+--R              3      3                2 2      4  |   2    2
+--R       ((a p q  - a p q)sin(a x) + a p q  - a p )\|- q  + p
+--R     ]
+--R                                     Type: Union(List Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.362~~~~~$\displaystyle
+\int{\frac{dx}{p^2+q^2\sin^2{ax}}}$}
+$$\int{\frac{1}{p^2+q^2\sin^2{ax}}}=
+\frac{1}{ap\sqrt{p^2+q^2}}\tan^{-1}\frac{\sqrt{p^2+q^2}\tan{ax}}{p}
+$$
+<<*>>=
+)clear all
+
+--S 24 of 30
+aa:=integrate(1/(p^2+a^2*sin(a*x)),x)
+--R 
+--R
+--R   (1)
+--R   [
+--R       log
+--R                                                        +---------+
+--R                2 2               4    4             4  |   4    4
+--R              (a p sin(a x) + (- p  + a )cos(a x) + a )\|- p  + a
+--R            + 
+--R                6    4 2              2 4    6             2 4    6
+--R              (p  - a p )sin(a x) + (a p  - a )cos(a x) + a p  - a
+--R         /
+--R             2            2
+--R            a sin(a x) + p
+--R    /
+--R         +---------+
+--R         |   4    4
+--R       a\|- p  + a
+--R     ,
+--R                                         +-------+
+--R            2            2            2  | 4    4
+--R          (p sin(a x) + a cos(a x) + a )\|p  - a
+--R    2atan(----------------------------------------)
+--R                   4    4             4    4
+--R                 (p  - a )cos(a x) + p  - a
+--R    -----------------------------------------------]
+--R                        +-------+
+--R                        | 4    4
+--R                      a\|p  - a
+--R                                     Type: Union(List Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.363~~~~~$\displaystyle
+\int{\frac{dx}{p^2-q^2\sin^2{ax}}}$}
+$$\int{\frac{1}{p^2-q^2\sin^2{ax}}}=
+\left\{
+\begin{array}{l}
+\displaystyle
+\frac{1}{ap\sqrt{p^2-q^2}}\tan^{-1}\frac{\sqrt{p^2-q^2}\tan{ax}}{p}\\
+\\
+\displaystyle
+\frac{1}{2ap\sqrt{q^2-p^2}}\ln\left(\frac{\sqrt{q^2-p^2}\tan{ax}+p}
+{\sqrt{q^2-p^2}\tan{ax}-p}\right)
+\end{array}
+\right.
+$$
+<<*>>=
+)clear all
+
+--S 25 of 30
+aa:=integrate(1/(p^2-q^2*sin(a*x)^2),x)
+--R 
+--R
+--R   (1)
+--R   [
+--R       log
+--R                                                +-------+
+--R                   2     2         2    2    2  | 2    2
+--R              ((- q  + 2p )cos(a x)  + q  - p )\|q  - p
+--R            + 
+--R                   2     3
+--R              (2p q  - 2p )cos(a x)sin(a x)
+--R         /
+--R             2        2    2    2
+--R            q cos(a x)  - q  + p
+--R    /
+--R            +-------+
+--R            | 2    2
+--R       2a p\|q  - p
+--R     ,
+--R
+--R                                +---------+
+--R                                |   2    2
+--R                     p sin(a x)\|- q  + p
+--R         - atan(-------------------------------)
+--R                   2     2              2     2
+--R                (2q  - 2p )cos(a x) + 2q  - 2p
+--R       + 
+--R                      2    2              2     2
+--R                  ((2q  - p )cos(a x) + 2q  - 2p )sin(a x)
+--R         - atan(-------------------------------------------)
+--R                                                +---------+
+--R                           2                    |   2    2
+--R                (p cos(a x)  + 2p cos(a x) + p)\|- q  + p
+--R    /
+--R           +---------+
+--R           |   2    2
+--R       a p\|- q  + p
+--R     ]
+--R                                     Type: Union(List Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.364~~~~~$\displaystyle
+\int{x^m\sin{ax}}~dx$}
+$$\int{x^m\sin{ax}}=
+-\frac{x^m\cos{ax}}{a}+\frac{mx^{m-1}\sin{ax}}{a^2}
+-\frac{m(m-1)}{a^2}\int{x^{m-2}\sin{ax}}
+$$
+<<*>>=
+)clear all
+
+--S 26 of 30
+aa:=integrate(x^m*sin(a*x),x)
+--R 
+--R
+--R           x
+--R         ++             m
+--R   (1)   |   sin(%I a)%I d%I
+--R        ++
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.365~~~~~$\displaystyle
+\int{\frac{\sin{ax}}{x^n}}~dx$}
+$$\int{\frac{\sin{ax}}{x^n}}=
+-\frac{\sin{ax}}{(n-1)x^{n-1}}+\frac{a}{n-1}\int{\frac{\cos{ax}}{x^{n-1}}}
+$$
+<<*>>=
+)clear all
+
+--S 26 of 30
+aa:=integrate(sin(a*x)/x^n,x)
+--R 
+--R
+--R           x
+--R         ++  sin(%I a)
+--R   (1)   |   --------- d%I
+--R        ++        n
+--R                %I
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.366~~~~~$\displaystyle
+\int{\sin^n{ax}}~dx$}
+$$\int{\sin^n{ax}}=
+-\frac{\sin^{n-1}{ax}\cos{ax}}{an}+\frac{n-1}{n}\int{\sin^{n-2}{ax}}
+$$
+<<*>>=
+)clear all
+
+--S 28 of 30
+aa:=integrate(sin(a*x)^n,x)
+--R 
+--R
+--R           x
+--R         ++           n
+--R   (1)   |   sin(%I a) d%I
+--R        ++
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.367~~~~~$\displaystyle
+\int{\frac{1}{\sin^n{ax}}}~dx$}
+$$\int{\frac{1}{\sin^n{ax}}}=
+\frac{-\cos{ax}}{a(n-1)\sin^{n-1}{ax}}
++\frac{n-2}{n-1}\int{\frac{1}{\sin^{n-2}{ax}}}
+$$
+<<*>>=
+)clear all
+
+--S 29 of 30
+aa:=integrate(1/(sin(a*x))^n,x)
+--R 
+--R
+--R           x
+--R         ++       1
+--R   (1)   |   ---------- d%I
+--R        ++            n
+--R             sin(%I a)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.368~~~~~$\displaystyle
+\int{\frac{x~dx}{sin^n{ax}}}$}
+$$\int{\frac{x}{sin^n{ax}}}=
+\frac{-x\cos{ax}}{a(n-1)\sin^{n-1}{ax}}
+-\frac{1}{a^2(n-1)(n-2)\sin^{n-2}{ax}}
++\frac{n-2}{n-1}\int{\frac{x}{\sin^{n-2}{ax}}}
+$$
+<<*>>=
+)clear all
+
+--S 30 of 30
+aa:=integrate(x/sin(a*x)^n,x)
+--R 
+--R
+--R           x
+--R         ++      %I
+--R   (1)   |   ---------- d%I
+--R        ++            n
+--R             sin(%I a)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+)spool
+)lisp (bye)
+@
+
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} Spiegel, Murray R.
+{\sl Mathematical Handbook of Formulas and Tables}\\
+Schaum's Outline Series McGraw-Hill 1968 pp75-76
+\end{thebibliography}
+\end{document}



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From: "Fabio S." <f.stumbo@unife.it>
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>   >> System error:
>   The storage for VECTOR is exhausted.
> Currently, 10765 pages are allocated.
> Use ALLOCATE to expand the space.
>
> protected-symbol-warn called with (NIL)
>
> Question: How exactly do I issue an ALLOCATE command? Also,
> it is possible (if so, how) to continue the computation
> after an ALLOCATE command or do I have to start over?
> Thanks.

I never wrote to the mailing list about this, but in the last two months I 
ran many time exactly in the same problem (computing groebner basis).
I also would like to know more about how to control such situation.
Is there some reference on the documentation?

Thanks

Fabio



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> Question: How exactly do I issue an ALLOCATE command?
For me a command like
)lisp (si::allocate-contiguous-pages 30000 t)
seemed to work, although only at the beginning of a session.
You can get memory information with
)lisp (room)

I found this somewhere on the axiom-wiki and do not know any background.

regards,
Franz



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Date: Thu, 03 Apr 2008 16:28:30 +0200
From: Ralf Hemmecke <ralf@hemmecke.de>
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Subject: [Axiom-developer] Use ! as factorial
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On 04/03/2008 02:56 PM, Francois Maltey wrote:
> factorial is very common for *my* use of CAS :
> 50% of numerical analysis, 50% of algebraic transformations.
> 
> And all? other Computer Algebra System uses ! for factorial.
> 
> I feel that ! is the standard function for factorial.
> 
> I remember a first play with axiom for an other teacher.
> He wants to see a big number, so he tests 123!. 
> This day he doesn't find axiom as usual as other CAS.

Hmm, does anybody see a reason that ! could not be a special keyword of 
SPAD/Aldor that behaves as postfix operator similar to the douple dot 
operator ".." in Aldor?

Ralf



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Date: Fri, 04 Apr 2008 00:07:19 -0400
From: William Sit <wyscc@sci.ccny.cuny.edu>
Subject: Re: [Axiom-developer] out of space
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Franz Lehner wrote:

> > Question: How exactly do I issue an ALLOCATE command?
> For me a command like
> )lisp (si::allocate-contiguous-pages 30000 t)
> seemed to work, although only at the beginning of a session.
> You can get memory information with
> )lisp (room)
>
> I found this somewhere on the axiom-wiki and do not know any background.
>
> regards,
> Franz

Thanks. I'll give that a try. Thanks also to Mike Hansen for providing the
generators of the radical ideal. Per Tim's request, here is the input file:

dmp3:=DMP([y3,x3,y2,x2,y1,x1,y0,x0],INT)
f0:dmp3:=y0^2-x0^3
f1:dmp3:=2*y0*y1-3*x0^2*x1
f2:dmp3:=2*y1^2+2*y2*y0 - 3*x2*x0^2 - 6*x1^2*x0
f3:dmp3:= 2*y3*y0 + 2*y2*y1 - 3*x3*x0^2 - 18*x2*x1*x0 + 4*y1*y2 - 6*x1^3
id3:=ideal([f0,f1,f2,f3])
rid3:=radical(id3)

The output at abort:

>> System error:
   The storage for VECTOR is exhausted.
Currently, 10765 pages are allocated.
Use ALLOCATE to expand the space.

protected-symbol-warn called with (NIL)

The following is the info after issueing
)lisp (room)
after the abort:


(15) -> )list (room)
   Unknown system command: list
(15) -> )lisp (room)

 53886/90154  37.6%   10244 CONS RATIO COMPLEX STRUCTURE
   721/721        66.3%     364  FIXNUM SHORT-FLOAT CHARACTER RANDOM-STATE
READTABLE NIL
   219/500        99.5%             SYMBOL STREAM
     1/8             23.1%             PACKAGE
 10765/14244  76.6%     585  ARRAY HASH-TABLE VECTOR BIT-VECTOR PATHNAME
CCLOSURE FAT-STRING
   108/500        69.9%            STRING
 10613/13376  55.3%     180  CFUN BIGNUM LONG-FLOAT
    33/89          99.5%             SFUN GFUN CFDATA SPICE NIL
  4294/5347                       1  contiguous (246 blocks)
       2000                               hole
       22029       81.7%    3545 relocatable

     76346 pages for cells
    104669 total pages
         0 pages available
     26403 pages in heap but not gc'd + pages needed for gc marking
    131072 maximum pages
Value = NIL


However, I do not know what the info mean. It seems that the problem is with
array hash-table vector.




William












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More integrals
========================================================================
diff --git a/changelog b/changelog
index 102ba8b..13f5f2e 100644
--- a/changelog
+++ b/changelog
@@ -1,3 +1,10 @@
+20080403 tpd src/input/Makefile add integration regression testing
+20080403 tpd src/input/schaum18.input integrals of cos(ax)
+20080403 tpd src/input/schaum17.input ignore gensyms
+20080403 tpd src/input/schaum16.input ignore gensyms
+20080403 tpd src/input/schaum14.input ignore gensyms
+20080403 tpd src/input/schaum13.input ignore gensyms
+20080403 tpd src/input/schaum12.input ignore gensyms
 20080402 tpd src/input/Makefile add integration regression testing
 20080402 tpd src/input/schaum17.input integrals of sin(ax)
 20080402 tpd src/input/schaum16.input integrals of x^n \pm a^n
diff --git a/src/input/Makefile.pamphlet b/src/input/Makefile.pamphlet
index 6de47f3..dbeb3d7 100644
--- a/src/input/Makefile.pamphlet
+++ b/src/input/Makefile.pamphlet
@@ -359,7 +359,7 @@ REGRES= algaggr.regress algbrbf.regress  algfacob.regress alist.regress  \
     schaum5.regress   schaum6.regress  schaum7.regress  schaum8.regress \
     schaum9.regress   schaum10.regress schaum11.regress schaum12.regress \
     schaum13.regress  schaum14.regress schaum15.regress schaum16.regress \
-    schaum17.regress \
+    schaum17.regress  schaum18.regress \
     scherk.regress    scope.regress    seccsc.regress \
     segbind.regress   seg.regress \
     series2.regress   series.regress   sersolve.regress set.regress \
@@ -637,7 +637,7 @@ FILES= ${OUT}/algaggr.input  ${OUT}/algbrbf.input    ${OUT}/algfacob.input \
        ${OUT}/schaum8.input  ${OUT}/schaum9.input    ${OUT}/schaum10.input \
        ${OUT}/schaum11.input ${OUT}/schaum12.input   ${OUT}/schaum13.input \
        ${OUT}/schaum14.input ${OUT}/schaum15.input   ${OUT}/schaum16.input \
-       ${OUT}/schaum17.input \
+       ${OUT}/schaum17.input ${OUT}/schaum18.input \
        ${OUT}/saddle.input \
        ${OUT}/scherk.input   ${OUT}/scope.input      ${OUT}/seccsc.input \
        ${OUT}/segbind.input  ${OUT}/seg.input        ${OUT}/series2.input \
@@ -944,7 +944,7 @@ DOCFILES= \
   ${DOC}/schaum11.input.dvi    ${DOC}/schaum12.input.dvi \
   ${DOC}/schaum13.input.dvi    ${DOC}/schaum14.input.dvi \
   ${DOC}/schaum15.input.dvi    ${DOC}/schaum16.input.dvi \
-  ${DOC}/schaum17.input.dvi \
+  ${DOC}/schaum17.input.dvi    ${DOC}/schaum18.input.dvi \
   ${DOC}/s01eaf.input.dvi      ${DOC}/s13aaf.input.dvi     \
   ${DOC}/s13acf.input.dvi      ${DOC}/s13adf.input.dvi     \
   ${DOC}/s14aaf.input.dvi      ${DOC}/s14abf.input.dvi     \
diff --git a/src/input/schaum12.input.pamphlet b/src/input/schaum12.input.pamphlet
index 6669ade..644ebed 100644
--- a/src/input/schaum12.input.pamphlet
+++ b/src/input/schaum12.input.pamphlet
@@ -189,10 +189,10 @@ aa:=integrate(x^m/(a*x^2+b*x+c),x)
 --R 
 --R
 --R           x         m
---R         ++        %N
---R   (1)   |   --------------- d%N
+--I         ++        %N
+--I   (1)   |   --------------- d%N
 --R        ++                2
---R             c + %N b + %N a
+--I             c + %N b + %N a
 --R                                          Type: Union(Expression Integer,...)
 --E 
 @
@@ -326,9 +326,9 @@ aa:=integrate(1/(x^n*(a*x^2+b*x+c)),x)
 --R
 --R           x
 --R         ++            1
---R   (1)   |   -------------------- d%N
+--I   (1)   |   -------------------- d%N
 --R        ++                 2    n
---R             (c + %N b + %N a)%N
+--I             (c + %N b + %N a)%N
 --R                                          Type: Union(Expression Integer,...)
 --E 
 @
@@ -519,10 +519,10 @@ aa:=integrate(x^m/(a*x^2+b*x+c)^n,x)
 --R 
 --R
 --R           x           m
---R         ++          %N
---R   (1)   |   ------------------ d%N
+--I         ++          %N
+--I   (1)   |   ------------------ d%N
 --R        ++                 2  n
---R             (c + %N b + %N a)
+--I             (c + %N b + %N a)
 --R                                          Type: Union(Expression Integer,...)
 --E 
 @
@@ -546,10 +546,10 @@ aa:=integrate(x^(2*n-1)/(a*x^2+b*x+c)^n,x)
 --R 
 --R
 --R           x        2n - 1
---R         ++       %N
---R   (1)   |   ------------------ d%N
+--I         ++       %N
+--I   (1)   |   ------------------ d%N
 --R        ++                 2  n
---R             (c + %N b + %N a)
+--I             (c + %N b + %N a)
 --R                                          Type: Union(Expression Integer,...)
 --E 
 @
@@ -762,9 +762,9 @@ aa:=integrate(1/(x^m*(a*x^2+b*x+c)^n),x)
 --R
 --R           x
 --R         ++            1
---R   (1)   |   --------------------- d%N
+--I   (1)   |   --------------------- d%N
 --R        ++     m              2  n
---R             %N (c + %N b + %N a)
+--I             %N (c + %N b + %N a)
 --R                                          Type: Union(Expression Integer,...)
 --E 
 
diff --git a/src/input/schaum13.input.pamphlet b/src/input/schaum13.input.pamphlet
index 04551e6..eb1a6eb 100644
--- a/src/input/schaum13.input.pamphlet
+++ b/src/input/schaum13.input.pamphlet
@@ -1167,7 +1167,7 @@ aa:=integrate((a*x^2+b*x+c)^(n+1/2),x)
 --R                              2n + 1
 --R           x                  ------
 --R         ++                2     2
---R   (1)   |   (c + %N b + %N a)      d%N
+--I   (1)   |   (c + %N b + %N a)      d%N
 --R        ++
 --R                                          Type: Union(Expression Integer,...)
 --E 
@@ -1189,7 +1189,7 @@ aa:=integrate(x*(a*x^2+b*x+c)^(n+1/2),x)
 --R                                 2n + 1
 --R           x                     ------
 --R         ++                   2     2
---R   (1)   |   %N (c + %N b + %N a)      d%N
+--I   (1)   |   %N (c + %N b + %N a)      d%N
 --R        ++
 --R                                          Type: Union(Expression Integer,...)
 --E 
@@ -1214,11 +1214,11 @@ aa:=integrate(1/(a*x^2+b*x+c)^(n+1/2),x)
 --R
 --R           x
 --R         ++             1
---R   (1)   |   ----------------------- d%N
+--I   (1)   |   ----------------------- d%N
 --R        ++                    2n + 1
 --R                              ------
 --R                           2     2
---R             (c + %N b + %N a)
+--I             (c + %N b + %N a)
 --R                                          Type: Union(Expression Integer,...)
 --E 
 @
@@ -1245,11 +1245,11 @@ aa:=integrate(1/(x*(a*x^2+b*x+c)^(n+1/2)),x)
 --R
 --R           x
 --R         ++               1
---R   (1)   |   -------------------------- d%N
+--I   (1)   |   -------------------------- d%N
 --R        ++                       2n + 1
 --R                                 ------
 --R                              2     2
---R             %N (c + %N b + %N a)
+--I             %N (c + %N b + %N a)
 --R                                          Type: Union(Expression Integer,...)
 --E 
 
diff --git a/src/input/schaum14.input.pamphlet b/src/input/schaum14.input.pamphlet
index 560ab37..532a38a 100644
--- a/src/input/schaum14.input.pamphlet
+++ b/src/input/schaum14.input.pamphlet
@@ -264,10 +264,10 @@ aa:=integrate(x^m/(x^3+a^3),x)
 --R 
 --R
 --R           x      m
---R         ++     %L
---R   (1)   |   -------- d%L
+--I         ++     %L
+--I   (1)   |   -------- d%L
 --R        ++    3     3
---R             a  + %L
+--I             a  + %L
 --R                                          Type: Union(Expression Integer,...)
 --E 
 @
@@ -286,9 +286,9 @@ aa:=integrate(1/(x^n*(x^3+a^3)),x)
 --R
 --R           x
 --R         ++        1
---R   (1)   |   ------------- d%L
+--I   (1)   |   ------------- d%L
 --R        ++     3     3   n
---R             (a  + %L )%L
+--I             (a  + %L )%L
 --R                                          Type: Union(Expression Integer,...)
 --E 
 
diff --git a/src/input/schaum16.input.pamphlet b/src/input/schaum16.input.pamphlet
index 2246f9a..f6b849c 100644
--- a/src/input/schaum16.input.pamphlet
+++ b/src/input/schaum16.input.pamphlet
@@ -64,10 +64,10 @@ aa:=integrate(x^m/(x^n+a^n)^r,x)
 --R 
 --R
 --R           x       m
---R         ++      %J
---R   (1)   |   ----------- d%J
+--I         ++      %J
+--I   (1)   |   ----------- d%J
 --R        ++     n     n r
---R             (a  + %J )
+--I             (a  + %J )
 --R                                          Type: Union(Expression Integer,...)
 --E 
 @
@@ -87,9 +87,9 @@ aa:=integrate(1/(x^m*(x^n+a^n)^r),x)
 --R
 --R           x
 --R         ++         1
---R   (1)   |   -------------- d%J
+--I   (1)   |   -------------- d%J
 --R        ++     m  n     n r
---R             %J (a  + %J )
+--I             %J (a  + %J )
 --R                                          Type: Union(Expression Integer,...)
 --E 
 @
@@ -187,10 +187,10 @@ aa:=integrate(x^m/(x^n-a^n)^r,x)
 --R 
 --R
 --R           x        m
---R         ++       %J
---R   (1)   |   ------------- d%J
+--I         ++       %J
+--I   (1)   |   ------------- d%J
 --R        ++       n     n r
---R             (- a  + %J )
+--I             (- a  + %J )
 --R                                          Type: Union(Expression Integer,...)
 --E 
 @
@@ -210,9 +210,9 @@ aa:=integrate(1/(x^m*(x^n-a^n)^r),x)
 --R
 --R           x
 --R         ++          1
---R   (1)   |   ---------------- d%J
+--I   (1)   |   ---------------- d%J
 --R        ++     m    n     n r
---R             %J (- a  + %J )
+--I             %J (- a  + %J )
 --R                                          Type: Union(Expression Integer,...)
 --E
 @
@@ -274,10 +274,10 @@ aa:=integrate(x^(p-1)/(x^(2*m)+a^(2*m)),x)
 --R 
 --R
 --R           x     p - 1
---R         ++    %J
---R   (1)   |   ---------- d%J
+--I         ++    %J
+--I   (1)   |   ---------- d%J
 --R        ++    2m     2m
---R             a   + %J
+--I             a   + %J
 --R                                          Type: Union(Expression Integer,...)
 --E 
 @
@@ -304,10 +304,10 @@ aa:=integrate(x^(p-1)/(x^(2*m)-a^(2*m)),x)
 --R 
 --R
 --R           x       p - 1
---R         ++      %J
---R   (1)   |   - ---------- d%J
+--I         ++      %J
+--I   (1)   |   - ---------- d%J
 --R        ++      2m     2m
---R               a   - %J
+--I               a   - %J
 --R                                          Type: Union(Expression Integer,...)
 --E 
 @
@@ -338,10 +338,10 @@ aa:=integrate(x^(p-1)/(x^(2*m+1)+a^(2*m+1)),x)
 --R 
 --R
 --R           x         p - 1
---R         ++        %J
---R   (1)   |   ------------------ d%J
+--I         ++        %J
+--I   (1)   |   ------------------ d%J
 --R        ++    2m + 1     2m + 1
---R             a       + %J
+--I             a       + %J
 --R                                          Type: Union(Expression Integer,...)
 --E 
 @
@@ -374,10 +374,10 @@ aa:=integrate(x^(p-1)/(x^(2*m+1)-a^(2*m+1)),x)
 --R 
 --R
 --R           x           p - 1
---R         ++          %J
---R   (1)   |   - ------------------ d%J
+--I         ++          %J
+--I   (1)   |   - ------------------ d%J
 --R        ++      2m + 1     2m + 1
---R               a       - %J
+--I               a       - %J
 --R                                          Type: Union(Expression Integer,...)
 --E 
 
diff --git a/src/input/schaum17.input.pamphlet b/src/input/schaum17.input.pamphlet
index 7ab11d7..fd40132 100644
--- a/src/input/schaum17.input.pamphlet
+++ b/src/input/schaum17.input.pamphlet
@@ -32,7 +32,7 @@ aa:=integrate(sin(a*x),x)
 \section{\cite{1}:14.340~~~~~$\displaystyle
 \int{x\sin{ax}~dx}$}
 $$\int{x\sin{ax}}=
-\frac{sin{ax}}{a^2}-\frac{x\cos{ax}}{a}
+\frac{\sin{ax}}{a^2}-\frac{x\cos{ax}}{a}
 $$
 <<*>>=
 )clear all
@@ -122,10 +122,10 @@ aa:=integrate(sin(a*x)/x^2,x)
 --R 
 --R
 --R           x
---R         ++  sin(%I a)
---R   (1)   |   --------- d%I
+--I         ++  sin(%I a)
+--I   (1)   |   --------- d%I
 --R        ++        2
---R                %I
+--I                %I
 --R                                          Type: Union(Expression Integer,...)
 --E 
 @
@@ -167,9 +167,9 @@ aa:=integrate(x/sin(a*x),x)
 --R 
 --R
 --R           x
---R         ++      %I
---R   (1)   |   --------- d%I
---R        ++   sin(%I a)
+--I         ++      %I
+--I   (1)   |   --------- d%I
+--I        ++   sin(%I a)
 --R                                          Type: Union(Expression Integer,...)
 --E 
 @
@@ -675,7 +675,7 @@ aa:=integrate(x^m*sin(a*x),x)
 --R
 --R           x
 --R         ++             m
---R   (1)   |   sin(%I a)%I d%I
+--I   (1)   |   sin(%I a)%I d%I
 --R        ++
 --R                                          Type: Union(Expression Integer,...)
 --E 
@@ -694,10 +694,10 @@ aa:=integrate(sin(a*x)/x^n,x)
 --R 
 --R
 --R           x
---R         ++  sin(%I a)
---R   (1)   |   --------- d%I
+--I         ++  sin(%I a)
+--I   (1)   |   --------- d%I
 --R        ++        n
---R                %I
+--I                %I
 --R                                          Type: Union(Expression Integer,...)
 --E 
 @
@@ -716,7 +716,7 @@ aa:=integrate(sin(a*x)^n,x)
 --R
 --R           x
 --R         ++           n
---R   (1)   |   sin(%I a) d%I
+--I   (1)   |   sin(%I a) d%I
 --R        ++
 --R                                          Type: Union(Expression Integer,...)
 --E 
@@ -737,9 +737,9 @@ aa:=integrate(1/(sin(a*x))^n,x)
 --R
 --R           x
 --R         ++       1
---R   (1)   |   ---------- d%I
+--I   (1)   |   ---------- d%I
 --R        ++            n
---R             sin(%I a)
+--i             sin(%I a)
 --R                                          Type: Union(Expression Integer,...)
 --E 
 @
@@ -759,10 +759,10 @@ aa:=integrate(x/sin(a*x)^n,x)
 --R 
 --R
 --R           x
---R         ++      %I
---R   (1)   |   ---------- d%I
+--I         ++      %I
+--I   (1)   |   ---------- d%I
 --R        ++            n
---R             sin(%I a)
+--I             sin(%I a)
 --R                                          Type: Union(Expression Integer,...)
 --E 
 
diff --git a/src/input/schaum18.input.pamphlet b/src/input/schaum18.input.pamphlet
new file mode 100644
index 0000000..3cb4766
--- /dev/null
+++ b/src/input/schaum18.input.pamphlet
@@ -0,0 +1,754 @@
+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/input schaum18.input}
+\author{Timothy Daly}
+\maketitle
+\eject
+\tableofcontents
+\eject
+\section{\cite{1}:14.369~~~~~$\displaystyle
+\int{\cos ax ~dx}$}
+$$\int{\cos ax}=
+\frac{\sin{ax}}{a}
+$$
+<<*>>=
+)spool schaum18.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1 of 30
+aa:=integrate(cos(a*x),x)
+--R 
+--R
+--R        sin(a x)
+--R   (1)  --------
+--R            a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.370~~~~~$\displaystyle
+\int{x\cos{ax}~dx}$}
+$$\int{x\cos{ax}}=
+\frac{\cos{ax}}{a^2}+\frac{x\sin{ax}}{a}
+$$
+<<*>>=
+)clear all
+
+--S 2 of 30
+aa:=integrate(x*cos(a*x),x)
+--R 
+--R
+--R        a x sin(a x) + cos(a x)
+--R   (1)  -----------------------
+--R                    2
+--R                   a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.371~~~~~$\displaystyle
+\int{x^2\cos{ax}~dx}$}
+$$\int{x^2\cos{ax}}=
+\frac{2x}{a^2}\cos{ax}+\left(\frac{x^2}{a}-\frac{2}{a^3}\right)\sin{ax}
+$$
+<<*>>=
+)clear all
+
+--S 3 of 30
+aa:=integrate(x^2*cos(a*x),x)
+--R 
+--R
+--R          2 2
+--R        (a x  - 2)sin(a x) + 2a x cos(a x)
+--R   (1)  ----------------------------------
+--R                         3
+--R                        a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.372~~~~~$\displaystyle
+\int{x^3\cos{ax}~dx}$}
+$$\int{x^3\cos{ax}}=
+\left(\frac{3x^2}{a^2}-\frac{6}{a^4}\right)\cos{ax}
++\left(\frac{x^3}{a}-\frac{6x}{a^3}\right)\sin{ax}
+$$
+<<*>>=
+)clear all
+
+--S 4 of 30
+aa:=integrate(x^3*cos(a*x),x)
+--R 
+--R
+--R          3 3                      2 2
+--R        (a x  - 6a x)sin(a x) + (3a x  - 6)cos(a x)
+--R   (1)  -------------------------------------------
+--R                              4
+--R                             a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.373~~~~~$\displaystyle
+\int{\frac{\cos{ax}}{x}}~dx$}
+$$\int{\frac{\cos{ax}}{x}}=
+\ln{x}-\frac{(ax)^2}{2\cdot 2!}+\frac{(ax)^4}{4\cdot 4!}
+-\frac{(ax)^6}{6\cdot 6!}+\cdots
+$$
+<<*>>=
+)clear all
+
+--S 5 of 30
+aa:=integrate(cos(x)/x,x)
+--R 
+--R
+--R   (1)  Ci(x)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.374~~~~~$\displaystyle
+\int{\frac{\cos{ax}}{x^2}}~dx$}
+$$\int{\frac{\cos{ax}}{x^2}}=
+-\frac{\cos{ax}}{x}-a\int{\frac{\sin{ax}}{x}}
+$$
+<<*>>=
+)clear all
+
+--S 6 of 30
+aa:=integrate(cos(a*x)/x^2,x)
+--R 
+--R
+--R           x
+--I         ++  cos(%I a)
+--I   (1)   |   --------- d%I
+--R        ++        2
+--I                %I
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.375~~~~~$\displaystyle
+\int{\frac{dx}{\cos{ax}}}$}
+$$\int{\frac{1}{\cos{ax}}}=
+\frac{1}{a}\ln(\sec{ax}-\tan{ax})=
+\frac{1}{a}\ln\tan\left(\frac{\pi}{4}+\frac{ax}{2}\right)
+$$
+<<*>>=
+)clear all
+
+--S 7 of 30
+aa:=integrate(1/cos(a*x),x)
+--R 
+--R
+--R            sin(a x) + cos(a x) + 1        sin(a x) - cos(a x) - 1
+--R        log(-----------------------) - log(-----------------------)
+--R                  cos(a x) + 1                   cos(a x) + 1
+--R   (1)  -----------------------------------------------------------
+--R                                     a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.376~~~~~$\displaystyle
+\int{\frac{x~dx}{\cos{ax}}}$}
+$$\int{\frac{x}{\cos{ax}}}=
+\frac{1}{a^2}\left\{
+\frac{(ax)^2}{2}+\frac{(ax)^4}{8}+\frac{5(ax)^6}{144}+\cdots+
+\frac{E_n(ax)^{2n+2}}{(2n+2)(2n)!}+\cdots
+\right\}
+$$
+<<*>>=
+)clear all
+
+--S 8 of 30
+aa:=integrate(x/cos(a*x),x)
+--R 
+--R
+--R           x
+--I         ++      %I
+--I   (1)   |   --------- d%I
+--I        ++   cos(%I a)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.377~~~~~$\displaystyle
+\int{\cos^2{ax}}~dx$}
+$$\int{\cos^2{ax}}=
+\frac{x}{2}+\frac{\sin{2ax}}{4a}
+$$
+<<*>>=
+)clear all
+
+--S 9 of 30
+aa:=integrate(cos(a*x)^2,x)
+--R 
+--R
+--R        cos(a x)sin(a x) + a x
+--R   (1)  ----------------------
+--R                  2a
+--R                                          Type: Union(Expression Integer,...)
+--E
+@
+
+\section{\cite{1}:14.378~~~~~$\displaystyle
+\int{x\cos^2{ax}}~dx$}
+$$\int{x\cos^2{ax}}=
+\frac{x^2}{4}+\frac{x\sin{2ax}}{4a}+\frac{\cos{2ax}}{8a^2}
+$$
+<<*>>=
+)clear all
+
+--S 10 of 30
+aa:=integrate(x*cos(a*x)^2,x)
+--R 
+--R
+--R                                        2    2 2
+--R        2a x cos(a x)sin(a x) + cos(a x)  + a x
+--R   (1)  ----------------------------------------
+--R                             2
+--R                           4a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.379~~~~~$\displaystyle
+\int{\cos^3{ax}}~dx$}
+$$\int{\cos^3{ax}}=
+\frac{\sin{ax}}{a}-\frac{\sin^3{ax}}{3a}
+$$
+<<*>>=
+)clear all
+
+--S 11 of 30
+aa:=integrate(cos(a*x)^3,x)
+--R 
+--R
+--R                 2
+--R        (cos(a x)  + 2)sin(a x)
+--R   (1)  -----------------------
+--R                   3a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.380~~~~~$\displaystyle
+\int{\cos^4{ax}}~dx$}
+$$\int{\cos^4{ax}}=
+\frac{3x}{8}+\frac{\sin{2ax}}{4a}+\frac{\sin{4ax}}{32a}
+$$
+<<*>>=
+)clear all
+
+--S 12 of 30
+aa:=integrate(cos(a*x)^4,x)
+--R 
+--R
+--R                  3
+--R        (2cos(a x)  + 3cos(a x))sin(a x) + 3a x
+--R   (1)  ---------------------------------------
+--R                           8a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.381~~~~~$\displaystyle
+\int{\frac{dx}{\cos^2{ax}}}$}
+$$\int{\frac{1}{\cos^2{ax}}}=
+\frac{\tan{ax}}{a}
+$$
+<<*>>=
+)clear all
+
+--S 13 of 30
+aa:=integrate(1/cos(a*x)^2,x)
+--R 
+--R
+--R         sin(a x)
+--R   (1)  ----------
+--R        a cos(a x)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.382~~~~~$\displaystyle
+\int{\frac{dx}{\cos^3{ax}}}$}
+$$\int{\frac{1}{\cos^3{ax}}}=
+\frac{\sin{ax}}{2a\cos^2{ax}}
++\frac{1}{2a}\ln\tan\left(\frac{\pi}{4}+\frac{ax}{2}\right)
+$$
+<<*>>=
+)clear all
+
+--S 14 of 30
+aa:=integrate(1/cos(a*x)^3,x)
+--R 
+--R
+--R   (1)
+--R               2    sin(a x) + cos(a x) + 1
+--R       cos(a x) log(-----------------------)
+--R                          cos(a x) + 1
+--R     + 
+--R                 2    sin(a x) - cos(a x) - 1
+--R       - cos(a x) log(-----------------------) + sin(a x)
+--R                            cos(a x) + 1
+--R  /
+--R                2
+--R     2a cos(a x)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.383~~~~~$\displaystyle
+\int{\cos{px}\cos{qx}}~dx$}
+$$\int{\cos{ax}\cos{px}}=
+\frac{\sin{(a-p)x}}{2(a-p)}+\frac{\sin{(a+p)x}}{2(a+p)}
+$$
+<<*>>=
+)clear all
+
+--S 15 of 30
+aa:=integrate(cos(p*x)*cos(q*x),x)
+--R 
+--R
+--R        q cos(p x)sin(q x) - p cos(q x)sin(p x)
+--R   (1)  ---------------------------------------
+--R                         2    2
+--R                        q  - p
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.384~~~~~$\displaystyle
+\int{\frac{dx}{1-\cos{ax}}}$}
+$$\int{\frac{1}{1-\cos{ax}}}=
+-\frac{1}{a}\cot\frac{ax}{2}
+$$
+<<*>>=
+)clear all
+
+--S 16 of 30
+aa:=integrate(1/(1-cos(a*x)),x)
+--R 
+--R
+--R        - cos(a x) - 1
+--R   (1)  --------------
+--R          a sin(a x)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.385~~~~~$\displaystyle
+\int{\frac{x~dx}{1-\cos{ax}}}$}
+$$\int{\frac{x}{1-\cos{ax}}}=
+-\frac{x}{a}\cot\frac{ax}{2}
++\frac{2}{a^2}\ln~\sin\frac{ax}{2}
+$$
+<<*>>=
+)clear all
+
+--S 17 of 30
+aa:=integrate(x/(1-cos(ax)),x)
+--R 
+--R
+--R                2
+--R               x
+--R   (1)  - ------------
+--R          2cos(ax) - 2
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.386~~~~~$\displaystyle
+\int{\frac{dx}{1+\cos{ax}}}$}
+$$\int{\frac{1}{1+\cos{ax}}}=
+\frac{1}{a}\tan\frac{ax}{2}
+$$
+<<*>>=
+)clear all
+
+--S 18 of 30
+aa:=integrate(1/(1+cos(ax)),x)
+--R 
+--R
+--R             x
+--R   (1)  -----------
+--R        cos(ax) + 1
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.387~~~~~$\displaystyle
+\int{\frac{x~dx}{1+\cos{ax}}}$}
+$$\int{\frac{x}{1+\cos{ax}}}=
+\frac{x}{a}\tan\frac{ax}{2}
++\frac{2}{a^2}\ln~\cos\frac{ax}{2}
+$$
+<<*>>=
+)clear all
+
+--S 19 of 30
+aa:=integrate(x/(1+cos(a*x)),x)
+--R 
+--R
+--R                                  2
+--R        (- cos(a x) - 1)log(------------) + a x sin(a x)
+--R                            cos(a x) + 1
+--R   (1)  ------------------------------------------------
+--R                          2            2
+--R                         a cos(a x) + a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.388~~~~~$\displaystyle
+\int{\frac{dx}{(1-\cos{ax})^2}}$}
+$$\int{\frac{1}{(1-\cos{ax})^2}}=
+-\frac{1}{2a}\cot\frac{ax}{2}
+-\frac{1}{6a}\cot^3\frac{ax}{2}
+$$
+<<*>>=
+)clear all
+
+--S 20 of 30
+aa:=integrate(1/(1-cos(a*x))^2,x)
+--R 
+--R
+--R                  2
+--R        - cos(a x)  + cos(a x) + 2
+--R   (1)  --------------------------
+--R        (3a cos(a x) - 3a)sin(a x)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.389~~~~~$\displaystyle
+\int{\frac{dx}{(1+\cos{ax})^2}}$}
+$$\int{\frac{1}{(1+\cos{ax})^2}}=
+\frac{1}{2a}\tan\frac{ax}{2}
++\frac{1}{6a}\tan^3\frac{ax}{2}
+$$
+<<*>>=
+)clear all
+
+--S 21 of 30
+aa:=integrate(1/(1+cos(a*x))^2,x)
+--R 
+--R
+--R             (cos(a x) + 2)sin(a x)
+--R   (1)  -------------------------------
+--R                   2
+--R        3a cos(a x)  + 6a cos(a x) + 3a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.390~~~~~$\displaystyle
+\int{\frac{dx}{p+q\cos{ax}}}$}
+$$\int{\frac{1}{p+q\cos{ax}}}=
+\left\{
+\begin{array}{l}
+\displaystyle
+\frac{2}{a\sqrt{p^2-q^q}}
+\tan^{-1}\sqrt{(p-q)/(p+q)}\tan\frac{1}{2}ax
+\\
+\displaystyle
+\frac{1}{a\sqrt{q^2-p^2}}\ln\left(
+\frac{\tan\frac{1}{2}ax+\sqrt{(q+p)/(q-p)}}
+{\tan\frac{1}{2}ax-\sqrt{(q+p)(q-p)}}\right)
+\end{array}
+\right.
+$$
+<<*>>=
+)clear all
+
+--S 22 of 30
+aa:=integrate(1/(p+q*cos(a*x)),x)
+--R 
+--R
+--R   (1)
+--R                           +-------+
+--R                           | 2    2        2    2
+--R        (- p cos(a x) - q)\|q  - p   + (- q  + p )sin(a x)
+--R    log(--------------------------------------------------)
+--R                          q cos(a x) + p
+--R   [-------------------------------------------------------,
+--R                            +-------+
+--R                            | 2    2
+--R                          a\|q  - p
+--R                     +---------+
+--R                     |   2    2
+--R            sin(a x)\|- q  + p
+--R    2atan(-----------------------)
+--R          (q + p)cos(a x) + q + p
+--R    ------------------------------]
+--R               +---------+
+--R               |   2    2
+--R             a\|- q  + p
+--R                                     Type: Union(List Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.391~~~~~$\displaystyle
+\int{\frac{dx}{(p+q\cos{ax})^2}}$}
+$$\int{\frac{1}{(p+q\cos{ax})^2}}=
+\frac{q\sin{ax}}{a(q^2-p^2)(p+q\cos{ax})}
+-\frac{p}{q^2-p^2}\int{\frac{1}{p+q\cos{ax}}}
+$$
+<<*>>=
+)clear all
+
+--S 23 of 30
+aa:=integrate(1/(p+q*cos(a*x))^2,x)
+--R 
+--R
+--R   (1)
+--R   [
+--R                            2
+--R           (p q cos(a x) + p )
+--R        *
+--R                                  +-------+
+--R                                  | 2    2      2    2
+--R               (- p cos(a x) - q)\|q  - p   + (q  - p )sin(a x)
+--R           log(------------------------------------------------)
+--R                                q cos(a x) + p
+--R       + 
+--R                    +-------+
+--R                    | 2    2
+--R         q sin(a x)\|q  - p
+--R    /
+--R                                                +-------+
+--R            3      2                  2      3  | 2    2
+--R       ((a q  - a p q)cos(a x) + a p q  - a p )\|q  - p
+--R     ,
+--R
+--R                                                +---------+
+--R                                                |   2    2
+--R                              2        sin(a x)\|- q  + p
+--R         (- 2p q cos(a x) - 2p )atan(-----------------------)
+--R                                     (q + p)cos(a x) + q + p
+--R       + 
+--R                    +---------+
+--R                    |   2    2
+--R         q sin(a x)\|- q  + p
+--R    /
+--R                                                +---------+
+--R            3      2                  2      3  |   2    2
+--R       ((a q  - a p q)cos(a x) + a p q  - a p )\|- q  + p
+--R     ]
+--R                                     Type: Union(List Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.392~~~~~$\displaystyle
+\int{\frac{dx}{p^2+q^2\cos^2{ax}}}$}
+$$\int{\frac{1}{p^2+q^2\cos^2{ax}}}=
+\frac{1}{ap\sqrt{p^2+q^2}}\tan^{-1}\frac{p\tan{ax}}{\sqrt{p^2+q^2}}
+$$
+<<*>>=
+)clear all
+
+--S 24 of 30
+aa:=integrate(1/(p^2+a^2*cos(a*x)),x)
+--R 
+--R
+--R   (1)
+--R                            +---------+
+--R            2            2  |   4    4      4    4
+--R        (- p cos(a x) - a )\|- p  + a   + (p  - a )sin(a x)
+--R    log(---------------------------------------------------)
+--R                           2            2
+--R                          a cos(a x) + p
+--R   [--------------------------------------------------------,
+--R                            +---------+
+--R                            |   4    4
+--R                          a\|- p  + a
+--R                        +-------+
+--R                        | 4    4
+--R               sin(a x)\|p  - a
+--R    2atan(---------------------------)
+--R            2    2             2    2
+--R          (p  + a )cos(a x) + p  + a
+--R    ----------------------------------]
+--R                  +-------+
+--R                  | 4    4
+--R                a\|p  - a
+--R                                     Type: Union(List Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.393~~~~~$\displaystyle
+\int{\frac{dx}{p^2-q^2\cos^2{ax}}}$}
+$$\int{\frac{1}{p^2-q^2\cos^2{ax}}}=
+\left\{
+\begin{array}{l}
+\displaystyle
+\frac{1}{ap\sqrt{p^2-q^2}}\tan^{-1}\frac{p\tan{ax}}{\sqrt{p^2-q^2}}\\
+\\
+\displaystyle
+\frac{1}{2ap\sqrt{q^2-p^2}}\ln\left(\frac{p\tan{ax}-\sqrt{q^2-p^2}}
+{p\tan{ax}+\sqrt{q^2-p^2}}\right)
+\end{array}
+\right.
+$$
+<<*>>=
+)clear all
+
+--S 25 of 30
+aa:=integrate(1/(p^2-q^2*cos(a*x)^2),x)
+--R 
+--R
+--R   (1)
+--R                                   +-------+
+--R           2     2         2    2  | 2    2           2     3
+--R        ((q  - 2p )cos(a x)  + p )\|q  - p   + (- 2p q  + 2p )cos(a x)sin(a x)
+--R    log(----------------------------------------------------------------------)
+--R                                    2        2    2
+--R                                   q cos(a x)  - p
+--R   [---------------------------------------------------------------------------,
+--R                                        +-------+
+--R                                        | 2    2
+--R                                   2a p\|q  - p
+--R
+--R                       +---------+
+--R                       |   2    2
+--R              sin(a x)\|- q  + p
+--R         atan(--------------------)
+--R                2p cos(a x) + 2p
+--R       + 
+--R                      2    2              2
+--R                   ((q  + p )cos(a x) + 2p )sin(a x)
+--R         atan(-------------------------------------------)
+--R                                              +---------+
+--R                         2                    |   2    2
+--R              (p cos(a x)  + 2p cos(a x) + p)\|- q  + p
+--R    /
+--R           +---------+
+--R           |   2    2
+--R       a p\|- q  + p
+--R     ]
+--R                                     Type: Union(List Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.394~~~~~$\displaystyle
+\int{x^m\cos{ax}}~dx$}
+$$\int{x^m\cos{ax}}=
+\frac{x^m\sin{ax}}{a}+\frac{mx^{m-1}}{a^2}\cos{ax}
+-\frac{m(m-1)}{a^2}\int{x^{m-2}\cos{ax}}
+$$
+<<*>>=
+)clear all
+
+--S 26 of 30
+aa:=integrate(x^m*cos(a*x),x)
+--R 
+--R
+--R           x
+--R         ++             m
+--I   (1)   |   cos(%I a)%I d%I
+--R        ++
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.395~~~~~$\displaystyle
+\int{\frac{\cos{ax}}{x^n}}~dx$}
+$$\int{\frac{\cos{ax}}{x^n}}=
+-\frac{\cos{ax}}{(n-1)x^{n-1}}-\frac{a}{n-1}\int{\frac{\sin{ax}}{x^{n-1}}}
+$$
+<<*>>=
+)clear all
+
+--S 26 of 30
+aa:=integrate(cos(a*x)/x^n,x)
+--R 
+--R
+--R           x
+--I         ++  cos(%I a)
+--I   (1)   |   --------- d%I
+--R        ++        n
+--I                %I
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.396~~~~~$\displaystyle
+\int{\cos^n{ax}}~dx$}
+$$\int{\cos^n{ax}}=
+\frac{\sin{ax}\cos^{n-1}{ax}}{an}+\frac{n-1}{n}\int{\cos^{n-2}{ax}}
+$$
+<<*>>=
+)clear all
+
+--S 28 of 30
+aa:=integrate(cos(a*x)^n,x)
+--R 
+--R
+--R           x
+--R         ++           n
+--I   (1)   |   cos(%I a) d%I
+--R        ++
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.397~~~~~$\displaystyle
+\int{\frac{1}{\cos^n{ax}}}~dx$}
+$$\int{\frac{1}{\cos^n{ax}}}=
+\frac{\sin{ax}}{a(n-1)\cos^{n-1}{ax}}
++\frac{n-2}{n-1}\int{\frac{1}{\cos^{n-2}{ax}}}
+$$
+<<*>>=
+)clear all
+
+--S 29 of 30
+aa:=integrate(1/(cos(a*x))^n,x)
+--R 
+--R
+--R           x
+--R         ++       1
+--I   (1)   |   ---------- d%I
+--R        ++            n
+--I             cos(%I a)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.398~~~~~$\displaystyle
+\int{\frac{x~dx}{cos^n{ax}}}$}
+$$\int{\frac{x}{cos^n{ax}}}=
+\frac{x\sin{ax}}{a(n-1)\cos^{n-1}{ax}}
+-\frac{1}{a^2(n-1)(n-2)\cos^{n-2}{ax}}
++\frac{n-2}{n-1}\int{\frac{x}{\cos^{n-2}{ax}}}
+$$
+<<*>>=
+)clear all
+
+--S 30 of 30
+aa:=integrate(x/cos(a*x)^n,x)
+--R 
+--R
+--R           x
+--I         ++      %I
+--I   (1)   |   ---------- d%I
+--R        ++            n
+--I             cos(%I a)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+)spool
+)lisp (bye)
+@
+
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} Spiegel, Murray R.
+{\sl Mathematical Handbook of Formulas and Tables}\\
+Schaum's Outline Series McGraw-Hill 1968 pp77-78
+\end{thebibliography}
+\end{document}



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FAQ items added after legal consultations.

========================================================================
diff --git a/changelog b/changelog
index 13f5f2e..98ee5e5 100644
--- a/changelog
+++ b/changelog
@@ -1,3 +1,5 @@
+20080404 tpd faq FAQ 46: Axiom Trademark information
+20080404 tpd faq FAQ 45: Axiom Copyright information
 20080403 tpd src/input/Makefile add integration regression testing
 20080403 tpd src/input/schaum18.input integrals of cos(ax)
 20080403 tpd src/input/schaum17.input ignore gensyms
diff --git a/faq b/faq
index 0465fd7..ac41077 100644
--- a/faq
+++ b/faq
@@ -43,6 +43,8 @@ FAQ 41: How can I work in lisp from Axiom?
 FAQ 42: How can I output equations as lisp s-expressions?
 FAQ 43: Is Axiom's License compatible with the GPL?
 FAQ 44: I don't have the math fonts
+FAQ 45: Axiom copyright information
+FAQ 46: Axiom trademark information
 
 ===================================================================
 FAQ 0: How do I use Axiom?
@@ -1605,3 +1607,51 @@ missing fonts can be found at:
 http://www.stixfonts.org
 http://www.alanwood.net/unicode
 http://support.wolfram.com/mathematica/systems/windows/general/latestfonts.html
+
+===================================================================
+FAQ 45: Axiom Copyright information
+===================================================================
+Axiom is intended for not-for-profit, personal, educational use.
+Any other use is permitted but not endorsed.
+
+A fundamental project goal is to document the system for future
+educational, research, and scientific use.
+
+Axiom may contain some copyrighted material whose use has not been
+authorized by the copyright owners. We believe that this not-for-
+profit, educational use constitutes a fair use of the copyrighted
+material (as provided for in section 107 of the U.S.  Copyright Law).
+
+Notwithstanding the provisions of sections 106 and 106A, the fair use
+of a copyrighted work, including such use by reproduction in copies or
+phonorecords, or by any other means specified by that section, for
+purposes such as criticism, comment, news reporting, teaching
+(including multiple copies for classroom use), scholarship, or
+research, is not an infringement of copyright. In determining whether
+the use made of a work in any particular case is a fair use the
+factors to be considered shall include:
+
+  1. the purpose and character of the use, including whether such use
+     is of a commercial nature or is for nonprofit educational purposes;
+  2. the nature of the copyrighted work;
+  3. the amount and substantiality of the portion used in relation to
+     the copyrighted work as a whole; and
+  4. the effect of the use upon the potential market for or value of
+     the copyrighted work.
+
+The fact that a work is unpublished shall not itself bar a finding of
+fair use if such finding is made upon consideration of all of the
+above factors.
+
+===================================================================
+FAQ 46: Axiom Trademark information
+===================================================================
+The name "Axiom" and the Axiom-included iconic images are common
+law trademarks of this project. The term of service applies to the
+code distributed and compiled versions of code distributed from the
+Axiom websites at 
+  axiom-developer.org
+  savannah.nongnu.org/projects/axiom
+  sourceforge.net/projects/axiom
+  github.com/daly/axiom
+



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More integrals
=======================================================================
diff --git a/changelog b/changelog
index 98ee5e5..509310d 100644
--- a/changelog
+++ b/changelog
@@ -1,3 +1,5 @@
+20080406 tpd src/input/Makefile add integration regression testing
+20080406 tpd src/input/schaum19.input integrals of sin(ax) and cos(ax)
 20080404 tpd faq FAQ 46: Axiom Trademark information
 20080404 tpd faq FAQ 45: Axiom Copyright information
 20080403 tpd src/input/Makefile add integration regression testing
diff --git a/src/input/Makefile.pamphlet b/src/input/Makefile.pamphlet
index dbeb3d7..8170a48 100644
--- a/src/input/Makefile.pamphlet
+++ b/src/input/Makefile.pamphlet
@@ -359,7 +359,7 @@ REGRES= algaggr.regress algbrbf.regress  algfacob.regress alist.regress  \
     schaum5.regress   schaum6.regress  schaum7.regress  schaum8.regress \
     schaum9.regress   schaum10.regress schaum11.regress schaum12.regress \
     schaum13.regress  schaum14.regress schaum15.regress schaum16.regress \
-    schaum17.regress  schaum18.regress \
+    schaum17.regress  schaum18.regress schaum19.regress \
     scherk.regress    scope.regress    seccsc.regress \
     segbind.regress   seg.regress \
     series2.regress   series.regress   sersolve.regress set.regress \
@@ -637,7 +637,7 @@ FILES= ${OUT}/algaggr.input  ${OUT}/algbrbf.input    ${OUT}/algfacob.input \
        ${OUT}/schaum8.input  ${OUT}/schaum9.input    ${OUT}/schaum10.input \
        ${OUT}/schaum11.input ${OUT}/schaum12.input   ${OUT}/schaum13.input \
        ${OUT}/schaum14.input ${OUT}/schaum15.input   ${OUT}/schaum16.input \
-       ${OUT}/schaum17.input ${OUT}/schaum18.input \
+       ${OUT}/schaum17.input ${OUT}/schaum18.input   ${OUT}/schaum19.input \
        ${OUT}/saddle.input \
        ${OUT}/scherk.input   ${OUT}/scope.input      ${OUT}/seccsc.input \
        ${OUT}/segbind.input  ${OUT}/seg.input        ${OUT}/series2.input \
@@ -945,6 +945,7 @@ DOCFILES= \
   ${DOC}/schaum13.input.dvi    ${DOC}/schaum14.input.dvi \
   ${DOC}/schaum15.input.dvi    ${DOC}/schaum16.input.dvi \
   ${DOC}/schaum17.input.dvi    ${DOC}/schaum18.input.dvi \
+  ${DOC}/schaum19.input.dvi \
   ${DOC}/s01eaf.input.dvi      ${DOC}/s13aaf.input.dvi     \
   ${DOC}/s13acf.input.dvi      ${DOC}/s13adf.input.dvi     \
   ${DOC}/s14aaf.input.dvi      ${DOC}/s14abf.input.dvi     \
diff --git a/src/input/schaum19.input.pamphlet b/src/input/schaum19.input.pamphlet
new file mode 100644
index 0000000..37e89ee
--- /dev/null
+++ b/src/input/schaum19.input.pamphlet
@@ -0,0 +1,888 @@
+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/input schaum19.input}
+\author{Timothy Daly}
+\maketitle
+\eject
+\tableofcontents
+\eject
+\section{\cite{1}:14.399~~~~~$\displaystyle
+\int{\sin{ax}\cos{ax}}~dx$}
+$$\int{\sin{ax}\cos{ax}}=
+\frac{\sin^2{ax}}{2a}
+$$
+<<*>>=
+)spool schaum19.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1 of 36
+aa:=integrate(sin(a*x)*cos(a*x),x)
+--R 
+--R
+--R                  2
+--R          cos(a x)
+--R   (1)  - ---------
+--R              2a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.400~~~~~$\displaystyle
+\int{\sin{px}\cos{qx}}~dx$}
+$$\int{\sin{px}\cos{qx}}=
+-\frac{cos(p-q)x}{2(p-q)}-\frac{cos(p+q)x}{2(p+q)}
+$$
+<<*>>=
+)clear all
+
+--S 2 of 36
+aa:=integrate(sin(p*x)*cos(q*x),x)
+--R 
+--R
+--R        q sin(p x)sin(q x) + p cos(p x)cos(q x)
+--R   (1)  ---------------------------------------
+--R                         2    2
+--R                        q  - p
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.401~~~~~$\displaystyle
+\int{\sin^n{ax}\cos{ax}}~dx$ provided $n \ne -1$}
+$$\int{\sin^n{ax}\cos{ax}}=
+\frac{\sin^{n+1}{ax}}{(n+1)a}
+$$
+<<*>>=
+)clear all
+
+--S 3 of 36
+aa:=integrate(sin(a*x)^n*cos(a*x),x)
+--R 
+--R
+--R                  n log(sin(a x))
+--R        sin(a x)%e
+--R   (1)  -------------------------
+--R                 a n + a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.402~~~~~$\displaystyle
+\int{\cos^n{ax}*sin{ax}}~dx$ provided $n \ne -1$}
+$$\int{\cos^n{ax}*sin{ax}}=
+-\frac{\cos^{n+1}{ax}}{(n+1)a}
+$$
+<<*>>=
+)clear all
+
+--S 4 of 36
+aa:=integrate(cos(a*x)^n*sin(a*x),x)
+--R 
+--R
+--R                    n log(cos(a x))
+--R          cos(a x)%e
+--R   (1)  - -------------------------
+--R                   a n + a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.403~~~~~$\displaystyle
+\int{\sin^2{ax}\cos^2{ax}}$}
+$$\int{\sin^2{ax}\cos^2{ax}}=
+\frac{x}{8}-\frac{\sin{4ax}}{32a}
+$$
+<<*>>=
+)clear all
+
+--S 5 of 36
+aa:=integrate(sin(a*x)^2*cos(a*x)^2,x)
+--R 
+--R
+--R                    3
+--R        (- 2cos(a x)  + cos(a x))sin(a x) + a x
+--R   (1)  ---------------------------------------
+--R                           8a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.404~~~~~$\displaystyle
+\int{\frac{dx}{\sin{ax}\cos{ax}}}$}
+$$\int{\frac{1}{\sin{ax}\cos{ax}}}=
+\frac{1}{a}\ln~\tan{ax}
+$$
+<<*>>=
+)clear all
+
+--S 6 of 36
+aa:=integrate(1/(sin(a*x)*cos(a*x)),x)
+--R 
+--R
+--R              sin(a x)              2cos(a x)
+--R        log(------------) - log(- ------------)
+--R            cos(a x) + 1          cos(a x) + 1
+--R   (1)  ---------------------------------------
+--R                           a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.405~~~~~$\displaystyle
+\int{\frac{dx}{\sin^2{ax}\cos{ax}}}$}
+$$\int{\frac{1}{\sin^2{ax}\cos{ax}}}=
+\frac{1}{a}\ln~\tan\left(\frac{\pi}{4}+\frac{ax}{2}\right)-\frac{1}{a\sin{ax}}
+$$
+<<*>>=
+)clear all
+
+--S 7 of 36
+aa:=integrate(1/(sin(a*x)^2*cos(a*x)),x)
+--R 
+--R
+--R   (1)
+--R                   sin(a x) + cos(a x) + 1
+--R       sin(a x)log(-----------------------)
+--R                         cos(a x) + 1
+--R     + 
+--R                     sin(a x) - cos(a x) - 1
+--R       - sin(a x)log(-----------------------) - 1
+--R                           cos(a x) + 1
+--R  /
+--R     a sin(a x)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.406~~~~~$\displaystyle
+\int{\frac{dx}{\sin{ax}\cos^2{ax}}}$}
+$$\int{\frac{1}{\sin{ax}\cos^2{ax}}}=
+\frac{1}{a}\ln~\tan\frac{ax}{2}+\frac{1}{a\cos{ax}}
+$$
+<<*>>=
+)clear all
+
+--S 8 of 36
+aa:=integrate(1/(sin(a*x)*cos(a*x)^2),x)
+--R 
+--R
+--R                      sin(a x)
+--R        cos(a x)log(------------) + cos(a x) + 1
+--R                    cos(a x) + 1
+--R   (1)  ----------------------------------------
+--R                       a cos(a x)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.407~~~~~$\displaystyle
+\int{\frac{dx}{\sin^2{ax}\cos^2{ax}}}$}
+$$\int{\frac{1}{\sin^2{ax}\cos^2{ax}}}=
+-\frac{2\cot{2ax}}{a}
+$$
+<<*>>=
+)clear all
+
+--S 9 of 36
+aa:=integrate(1/(sin(a*x)^2*cos(a*x)^2),x)
+--R 
+--R
+--R                    2
+--R         - 2cos(a x)  + 1
+--R   (1)  ------------------
+--R        a cos(a x)sin(a x)
+--R                                          Type: Union(Expression Integer,...)
+--E
+@
+
+\section{\cite{1}:14.408~~~~~$\displaystyle
+\int{\frac{\sin^2{ax}}{\cos{ax}}}~dx$}
+$$\int{\frac{\sin^2{ax}}{\cos{ax}}}=
+-\frac{\sin{ax}}{a}+\frac{1}{a}\ln~\tan\left(\frac{ax}{2}+\frac{\pi}{4}\right)
+$$
+<<*>>=
+)clear all
+
+--S 10 of 36
+aa:=integrate(sin(a*x)^2/cos(a*x),x)
+--R 
+--R
+--R            sin(a x) + cos(a x) + 1        sin(a x) - cos(a x) - 1
+--R        log(-----------------------) - log(-----------------------) - sin(a x)
+--R                  cos(a x) + 1                   cos(a x) + 1
+--R   (1)  ----------------------------------------------------------------------
+--R                                           a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.409~~~~~$\displaystyle
+\int{\frac{\cos^2{ax}}{\sin{ax}}}~dx$}
+$$\int{\frac{\cos^2{ax}}{\sin{ax}}}=
+\frac{\cos{ax}}{a}+\frac{1}{a}\ln~\tan{\frac{ax}{2}}
+$$
+<<*>>=
+)clear all
+
+--S 11 of 36
+aa:=integrate(cos(a*x)^2/sin(a*x),x)
+--R 
+--R
+--R              sin(a x)
+--R        log(------------) + cos(a x)
+--R            cos(a x) + 1
+--R   (1)  ----------------------------
+--R                      a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.410~~~~~$\displaystyle
+\int{\frac{dx}{\cos{ax}(1\pm\sin{ax})}}$}
+$$\int{\frac{1}{\cos{ax}(1\pm\sin{ax})}}=
+\mp\frac{1}{2a(1\pm\sin{ax})}
++\frac{1}{2a}\ln~\tan\left(\frac{ax}{2}+\frac{\pi}{4}\right)
+$$
+<<*>>=
+)clear all
+
+--S 12 of 36
+aa:=integrate(1/(cos(a*x)*(1+sin(a*x))),x)
+--R 
+--R
+--R   (1)
+--R                         sin(a x) + cos(a x) + 1
+--R       (sin(a x) + 1)log(-----------------------)
+--R                               cos(a x) + 1
+--R     + 
+--R                           sin(a x) - cos(a x) - 1
+--R       (- sin(a x) - 1)log(-----------------------) + sin(a x)
+--R                                 cos(a x) + 1
+--R  /
+--R     2a sin(a x) + 2a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+)clear all 
+
+--S 13 of 36
+aa:=integrate(1/(cos(a*x)*(1-sin(a*x))),x)
+--R 
+--R
+--R   (1)
+--R                         sin(a x) + cos(a x) + 1
+--R       (sin(a x) - 1)log(-----------------------)
+--R                               cos(a x) + 1
+--R     + 
+--R                           sin(a x) - cos(a x) - 1
+--R       (- sin(a x) + 1)log(-----------------------) - sin(a x)
+--R                                 cos(a x) + 1
+--R  /
+--R     2a sin(a x) - 2a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.411~~~~~$\displaystyle
+\int{\frac{dx}{\sin{ax}(1\pm\cos{ax})}}$}
+$$\int{\frac{1}{\sin{ax}(1\pm\cos{ax})}}=
+\pm\frac{1}{2a(1\pm\cos{ax})}+\frac{1}{2a}\ln~\tan\frac{ax}{2}
+$$
+<<*>>=
+)clear all
+
+--S 14 of 36
+aa:=integrate(1/(sin(a*x)*(1+cos(a*x))),x)
+--R 
+--R
+--R                             sin(a x)
+--R        (2cos(a x) + 2)log(------------) - cos(a x) + 1
+--R                           cos(a x) + 1
+--R   (1)  -----------------------------------------------
+--R                        4a cos(a x) + 4a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+)clear all
+
+--S 15 of 36
+aa:=integrate(1/(sin(a*x)*(1-cos(a*x))),x)
+--R 
+--R
+--R                             sin(a x)
+--R        (2cos(a x) - 2)log(------------) + cos(a x) + 1
+--R                           cos(a x) + 1
+--R   (1)  -----------------------------------------------
+--R                        4a cos(a x) - 4a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.412~~~~~$\displaystyle
+\int{\frac{dx}{\sin{ax}\pm\cos{ax}}}$}
+$$\int{\frac{1}{\sin{ax}\pm\cos{ax}}}=
+\frac{1}{a\sqrt{2}}\ln~\tan\left(\frac{ax}{2}\pm\frac{\pi}{8}\right)
+$$
+<<*>>=
+)clear all
+
+--S 16 of 36
+aa:=integrate(1/(sin(a*x)+cos(a*x)),x)
+--R 
+--R
+--R                    +-+                  +-+                 +-+
+--R         +-+    (- \|2  + 1)sin(a x) + (\|2  - 1)cos(a x) + \|2  - 2
+--R        \|2 log(----------------------------------------------------)
+--R                                 sin(a x) + cos(a x)
+--R   (1)  -------------------------------------------------------------
+--R                                      2a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+)clear all
+
+--S 17 of 36
+aa:=integrate(1/(sin(a*x)-cos(a*x)),x)
+--R 
+--R
+--R                    +-+                    +-+                 +-+
+--R         +-+    (- \|2  + 1)sin(a x) + (- \|2  + 1)cos(a x) - \|2  + 2
+--R        \|2 log(------------------------------------------------------)
+--R                                  sin(a x) - cos(a x)
+--R   (1)  ---------------------------------------------------------------
+--R                                       2a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.413~~~~~$\displaystyle
+\int{\frac{\sin{ax}~dx}{\sin{ax}\pm\cos{ax}}}$}
+$$\int{\frac{\sin{ax}}{\sin{ax}\pm\cos{ax}}}=
+\frac{x}{2}\mp\frac{1}{2a}\ln(\sin{ax}\pm\cos{ax})
+$$
+<<*>>=
+)clear all
+
+--S 18 of 36
+aa:=integrate(sin(a*x)/(sin(a*x)+cos(a*x)),x)
+--R 
+--R
+--R                  2             - 2sin(a x) - 2cos(a x)
+--R        log(------------) - log(-----------------------) + a x
+--R            cos(a x) + 1              cos(a x) + 1
+--R   (1)  ------------------------------------------------------
+--R                                  2a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+)clear all 
+
+--S 19 of 36
+aa:=integrate(sin(a*x)/(sin(a*x)-cos(a*x)),x)
+--R 
+--R
+--R            2sin(a x) - 2cos(a x)              2
+--R        log(---------------------) - log(------------) + a x
+--R                 cos(a x) + 1            cos(a x) + 1
+--R   (1)  ----------------------------------------------------
+--R                                 2a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.414~~~~~$\displaystyle
+\int{\frac{cos{ax}~dx}{\sin{ax}\pm{\cos{ax}}}}$}
+$$\int{\frac{cos{ax}}{\sin{ax}\pm{\cos{ax}}}}=
+\pm\frac{x}{2}+\frac{1}{2a}\ln(sin{ax}\pm\cos{ax})
+$$
+<<*>>=
+)clear all
+
+--S 20 of 36
+aa:=integrate(cos(a*x)/(sin(a*x)+cos(a*x)),x)
+--R 
+--R
+--R                    2             - 2sin(a x) - 2cos(a x)
+--R        - log(------------) + log(-----------------------) + a x
+--R              cos(a x) + 1              cos(a x) + 1
+--R   (1)  --------------------------------------------------------
+--R                                   2a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+)clear all
+
+--S 21 of 36
+aa:=integrate(cos(a*x)/(sin(a*x)-cos(a*x)),x)
+--R 
+--R
+--R            2sin(a x) - 2cos(a x)              2
+--R        log(---------------------) - log(------------) - a x
+--R                 cos(a x) + 1            cos(a x) + 1
+--R   (1)  ----------------------------------------------------
+--R                                 2a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.415~~~~~$\displaystyle
+\int{\frac{\sin{ax}~dx}{p+q\cos{ax}}}$}
+$$\int{\frac{\sin{ax}}{p+q\cos{ax}}}=
+-\frac{1}{aq}\ln(p+q\cos{ax})
+$$
+<<*>>=
+)clear all
+
+--S 22 of 36
+aa:=integrate(sin(a*x)/(p+q*cos(a*x)),x)
+--R 
+--R
+--R                  2             - 2q cos(a x) - 2p
+--R        log(------------) - log(------------------)
+--R            cos(a x) + 1           cos(a x) + 1
+--R   (1)  -------------------------------------------
+--R                            a q
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.416~~~~~$\displaystyle
+\int{\frac{\cos{ax}~dx}{p+q\sin{ax}}}$}
+$$\int{\frac{\cos{ax}}{p+q\sin{ax}}}=
+\frac{1}{aq}\ln(p+q\sin{ax})
+$$
+<<*>>=
+)clear all
+
+--S 23 of 36
+aa:=integrate(cos(a*x)/(p+q*sin(a*x)),x)
+--R 
+--R
+--R            2q sin(a x) + 2p              2
+--R        log(----------------) - log(------------)
+--R              cos(a x) + 1          cos(a x) + 1
+--R   (1)  -----------------------------------------
+--R                           a q
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.417~~~~~$\displaystyle
+\int{\frac{\sin{ax}~dx}{(p+q\cos{ax})^n}}$}
+$$\int{\frac{\sin{ax}}{(p+q\cos{ax})^n}}=
+\frac{1}{aq(n-1)(p+q\cos{ax})^{n-1}}
+$$
+<<*>>=
+)clear all
+
+--S 24 of 36
+aa:=integrate(sin(a*x)/(p+q*cos(a*x))^n,x)
+--R 
+--R
+--R                  q cos(a x) + p
+--R   (1)  ----------------------------------
+--R                     n log(q cos(a x) + p)
+--R        (a n - a)q %e
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.418~~~~~$\displaystyle
+\int{\frac{\cos{ax}~dx}{(p+q\sin{ax})^n}}$}
+$$\int{\frac{\cos{ax}}{(p+q\sin{ax})^n}}=
+\frac{-1}{aq(n-1)(p+q\sin{ax})^{n-1}}
+$$
+<<*>>=
+)clear all
+
+--S 25 of 36
+aa:=integrate(cos(a*x)/(p+q*sin(a*x))^n,x)
+--R 
+--R
+--R                 - q sin(a x) - p
+--R   (1)  ----------------------------------
+--R                     n log(q sin(a x) + p)
+--R        (a n - a)q %e
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.419~~~~~$\displaystyle
+\int{\frac{dx}{p\sin{ax}+q\cos{ax}}}$}
+$$\int{\frac{1}{p\sin{ax}+q\cos{ax}}}=
+\frac{1}{a\sqrt{p^2+q^2}}\ln~\tan\left(\frac{ax+\tan^{-1}(q/p)}{2}\right)
+$$
+<<*>>=
+)clear all
+
+--S 26 of 36
+aa:=integrate(1/(p*sin(a*x)+q*cos(a*x)),x)
+--R 
+--R
+--R   (1)
+--R     log
+--R                                                  +-------+
+--R                             2            2    2  | 2    2
+--R            (p q sin(a x) - p cos(a x) - q  - p )\|q  + p
+--R          + 
+--R                3    2                 2    3               2    3
+--R            (- q  - p q)sin(a x) + (p q  + p )cos(a x) + p q  + p
+--R       /
+--R          p sin(a x) + q cos(a x)
+--R  /
+--R       +-------+
+--R       | 2    2
+--R     a\|q  + p
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.420~~~~~$\displaystyle
+\int{\frac{dx}{p\sin{ax}+q\cos{ax}+r}}$}
+$$\int{\frac{1}{p\sin{ax}+q\cos{ax}+r}}=
+\left\{
+\begin{array}{l}
+\displaystyle
+\frac{2}{a\sqrt{r^2-p^2-q^q}}
+\tan^{-1}\left(\frac{p+(r-q)\tan(ax/2)}{\sqrt{r^2-p^2-a^2}}\right)\\
+\\
+\displaystyle
+\frac{1}{a\sqrt{p^2+q^2-r^2}}\ln\left(
+\frac{p-\sqrt{p^2+q^2-r^2}+(r-q)\tan{(ax/2)}}
+{p+\sqrt{p^2+q^2-r^2}+(r-q)\tan{(ax/2)}}\right)
+\end{array}
+\right.
+$$
+<<*>>=
+)clear all
+
+--S 27 of 36
+aa:=integrate(1/(p*sin(a*x)+q*cos(a*x)+r),x)
+--R 
+--R
+--R   (1)
+--R   [
+--R       log
+--R                                              2          2                   2
+--R                    (p r - p q)sin(a x) + (- r  + q r + p )cos(a x) - q r + q
+--R                  + 
+--R                     2
+--R                    p
+--R             *
+--R                 +--------------+
+--R                 |   2    2    2
+--R                \|- r  + q  + p
+--R            + 
+--R                3      2       2    2      3    2
+--R              (r  - q r  + (- q  - p )r + q  + p q)sin(a x)
+--R            + 
+--R                  2      2    3               2      2    3
+--R              (p r  - p q  - p )cos(a x) + p r  - p q  - p
+--R         /
+--R            p sin(a x) + q cos(a x) + r
+--R    /
+--R         +--------------+
+--R         |   2    2    2
+--R       a\|- r  + q  + p
+--R     ,
+--R                                             +------------+
+--R                                             | 2    2    2
+--R          ((r - q)sin(a x) + p cos(a x) + p)\|r  - q  - p
+--R    2atan(-------------------------------------------------)
+--R                  2    2    2             2    2    2
+--R                (r  - q  - p )cos(a x) + r  - q  - p
+--R    --------------------------------------------------------]
+--R                          +------------+
+--R                          | 2    2    2
+--R                        a\|r  - q  - p
+--R                                     Type: Union(List Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.421~~~~~$\displaystyle
+\int{\frac{dx}{p\sin{ax}+q(1+\cos{ax})}}$}
+$$\int{\frac{1}{p\sin{ax}+q(1+\cos{ax})}}=
+\frac{1}{ap}\ln\left(q+p\tan{\frac{ax}{2}}\right)
+$$
+<<*>>=
+)clear all
+
+--S 28 of 36
+aa:=integrate(1/(p*sin(a*x)+q*(1+cos(a*x))),x)
+--R 
+--R
+--R            p sin(a x) + q cos(a x) + q
+--R        log(---------------------------)
+--R                    cos(a x) + 1
+--R   (1)  --------------------------------
+--R                       a p
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.422~~~~~$\displaystyle
+\int{\frac{dx}{p\sin{ax}+q\cos{ax}\pm\sqrt{p^2+q^2}}}$}
+$$\int{\frac{1}{p\sin{ax}+q\cos{ax}\pm\sqrt{p^2+q^2}}}=
+\frac{-1}{a\sqrt{p^2+q^2}}
+\tan\left(\frac{\pi}{4}\mp\frac{ax+\tan^{-1}{(q/p)}}{2}\right)
+$$
+<<*>>=
+)clear all
+
+--S 29 of 36
+aa:=integrate(1/(p*sin(a*x)+q*cos(a*x)+sqrt(p^2+q^2)),x)
+--R 
+--R
+--R   (1)
+--R                                                                 +-------+
+--R            5      2 3      4                5      2 3      4   | 2    2
+--R       ((64q  + 64p q  + 12p q)cos(a x) + 64q  + 64p q  + 12p q)\|q  + p
+--R     + 
+--R             6      2 4      4 2     6               6      2 4      4 2     6
+--R       (- 64q  - 96p q  - 36p q  - 2p )cos(a x) - 64q  - 96p q  - 36p q  - 2p
+--R  /
+--R                 6        2 4        4 2      6
+--R           (64a q  + 80a p q  + 24a p q  + a p )sin(a x)
+--R         + 
+--R                   5        3 3       5                    5        3 3       5
+--R         (- 32a p q  - 32a p q  - 6a p q)cos(a x) - 32a p q  - 32a p q  - 6a p q
+--R      *
+--R          +-------+
+--R          | 2    2
+--R         \|q  + p
+--R     + 
+--R               7         2 5        4 3       6
+--R       (- 64a q  - 112a p q  - 56a p q  - 7a p q)sin(a x)
+--R     + 
+--R               6        3 4        5 2      7                   6        3 4
+--R       (32a p q  + 48a p q  + 18a p q  + a p )cos(a x) + 32a p q  + 48a p q
+--R     + 
+--R            5 2      7
+--R       18a p q  + a p
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+)clear all
+
+--S 30 of 36
+aa:=integrate(1/(p*sin(a*x)+q*cos(a*x)-sqrt(p^2+q^2)),x)
+--R 
+--R
+--R   (1)
+--R                                                                 +-------+
+--R            5      2 3      4                5      2 3      4   | 2    2
+--R       ((64q  + 64p q  + 12p q)cos(a x) + 64q  + 64p q  + 12p q)\|q  + p
+--R     + 
+--R           6      2 4      4 2     6               6      2 4      4 2     6
+--R       (64q  + 96p q  + 36p q  + 2p )cos(a x) + 64q  + 96p q  + 36p q  + 2p
+--R  /
+--R                 6        2 4        4 2      6
+--R           (64a q  + 80a p q  + 24a p q  + a p )sin(a x)
+--R         + 
+--R                   5        3 3       5                    5        3 3       5
+--R         (- 32a p q  - 32a p q  - 6a p q)cos(a x) - 32a p q  - 32a p q  - 6a p q
+--R      *
+--R          +-------+
+--R          | 2    2
+--R         \|q  + p
+--R     + 
+--R             7         2 5        4 3       6
+--R       (64a q  + 112a p q  + 56a p q  + 7a p q)sin(a x)
+--R     + 
+--R                 6        3 4        5 2      7                   6        3 4
+--R       (- 32a p q  - 48a p q  - 18a p q  - a p )cos(a x) - 32a p q  - 48a p q
+--R     + 
+--R              5 2      7
+--R       - 18a p q  - a p
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.423~~~~~$\displaystyle
+\int{\frac{dx}{p^2\sin^2{ax}+q^2\cos^2{ax}}}$}
+$$\int{\frac{1}{p^2\sin^2{ax}+q^2\cos^2{ax}}}=
+\frac{1}{apq}\tan^{-1}\left(\frac{p\tan{ax}}{q}\right)
+$$
+<<*>>=
+)clear all
+
+--S 31 of 36
+aa:=integrate(1/(p^2*sin(a*x)^2+q^2*cos(a*x)^2),x)
+--R 
+--R
+--R                   2     2              2
+--R                ((q  - 2p )cos(a x) - 2p )sin(a x)            q sin(a x)
+--R        - atan(-----------------------------------) + atan(----------------)
+--R                           2                               2p cos(a x) + 2p
+--R               p q cos(a x)  + 2p q cos(a x) + p q
+--R   (1)  --------------------------------------------------------------------
+--R                                        a p q
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.424~~~~~$\displaystyle
+\int{\frac{dx}{p^2\sin^2{ax}-q^2\cos^2{ax}}}$}
+$$\int{\frac{1}{p^2\sin^2{ax}-q^2\cos^2{ax}}}=
+\frac{1}{2apq}\ln\left(\frac{p\tan{ax}-q}{p\tan{ax}+q}\right)
+$$
+<<*>>=
+)clear all
+
+--S 32 of 36
+aa:=integrate(1/(p^2*sin(a*x)^2-q^2*cos(a*x)^2),x)
+--R 
+--R
+--R            2p sin(a x) - 2q cos(a x)        - 2p sin(a x) - 2q cos(a x)
+--R        log(-------------------------) - log(---------------------------)
+--R                   cos(a x) + 1                      cos(a x) + 1
+--R   (1)  -----------------------------------------------------------------
+--R                                      2a p q
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.425~~~~~$\displaystyle
+\int{\sin^m{ax}\cos^n{ax}}~dx$}
+$$\int{\sin^m{ax}\cos^n{ax}}=
+\left\{
+\begin{array}{l}
+\displaystyle
+-\frac{\sin^{m-1}{ax}\cos^{n+1}ax}{a(m+n)}
++\frac{m-1}{m+n}\int{\sin^{m-2}{ax}\cos^n{ax}}\\
+\\
+\displaystyle
+\frac{\sin^{m+1}{ax}\cos^{n-1}{ax}}{a(m+n)}
++\frac{n-1}{m+n}\int{\sin^m{ax}\cos^{n-2}{ax}}
+\end{array}
+\right.
+$$
+<<*>>=
+)clear all
+
+--S 33 of 36
+aa:=integrate(sin(a*x)^m*cos(a*x)^n,x)
+--R 
+--R
+--R           x
+--R         ++           n         m
+--I   (1)   |   cos(%H a) sin(%H a) d%H
+--R        ++
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.426~~~~~$\displaystyle
+\int{\frac{\sin^m{ax}}{\cos^n{ax}}}~dx$}
+$$\int{\frac{\sin^m{ax}}{\cos^n{ax}}}=
+\left\{
+\begin{array}{l}
+\displaystyle
+\frac{\sin^{m-1}{ax}}{a(n-1)\cos^{n-1}{ax}}
+-\frac{m-1}{n-1}\int{\frac{\sin^{m-2}{ax}}{\cos^{n-2}{ax}}}\\
+\\
+\displaystyle
+\frac{\sin^{m+1}{ax}}{a(n-1)\cos^{n-1}{ax}}
+-\frac{m-n+2}{n-1}\int{\frac{\sin^m{ax}}{\cos^{n-2}{ax}}}\\
+\\
+\displaystyle
+\frac{-\sin^{m-1}{ax}}{a(m-n)\cos^{n-1}{ax}}
++\frac{m-1}{m-n}\int{\frac{\sin^{m-2}{ax}}{\cos^n{ax}}}
+\end{array}
+\right.
+$$
+<<*>>=
+)clear all
+
+--S 34 of 36
+aa:=integrate(sin(a*x)^m/cos(a*x)^n,x)
+--R 
+--R
+--R           x          m
+--I         ++  sin(%H a)
+--I   (1)   |   ---------- d%H
+--R        ++            n
+--I             cos(%H a)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.427~~~~~$\displaystyle
+\int{\frac{\cos^m{ax}}{\sin^n{ax}}}~dx$}
+$$\int{\frac{\cos^m{ax}}{\sin^n{ax}}}=
+\left\{
+\begin{array}{l}
+\displaystyle
+\frac{-\cos^{m-1}{ax}}{a(n-1)\sin^{n-1}{ax}}
+-\frac{m-1}{n-1}\int{\frac{\cos^{m-2}{ax}}{\sin^{n-2}{ax}}}\\
+\\
+\displaystyle
+\frac{-\cos^{m+1}{ax}}{a(n-1)\sin^{n-1}{ax}}
+-\frac{m-n+2}{n-1}\int{\frac{\cos^m{ax}}{\sin^{n-2}{ax}}}\\
+\\
+\displaystyle
+\frac{\cos^{m-1}{ax}}{a(m-n)\sin^{n-1}{ax}}
++\frac{m-1}{m-n}\int{\frac{\cos^{m-2}{ax}}{\sin^n{ax}}}
+\end{array}
+\right.
+$$
+<<*>>=
+)clear all
+
+--S 35 of 36
+aa:=integrate(cos(a*x)^m/sin(a*x)^n,x)
+--R 
+--R
+--R           x          m
+--I         ++  cos(%H a)
+--I   (1)   |   ---------- d%H
+--R        ++            n
+--I             sin(%H a)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.428~~~~~$\displaystyle
+\int{\frac{dx}{\sin^m{ax}\cos^n{ax}}}$}
+$$\int{\frac{1}{\sin^m{ax}\cos^n{ax}}}
+\left\{
+\begin{array}{l}
+\displaystyle
+\frac{1}{a(n-1)\sin^{m-1}{ax}\cos^{n-1}{ax}}
++\frac{m+n-2}{n-1}\int{\frac{1}{\sin^m{ax}\cos^{n-2}{ax}}}\\
+\\
+\displaystyle
+\frac{-1}{a(m-1)\sin^{m-1}{ax}\cos^{n-1}{ax}}
++\frac{m+n-2}{m-1}\int{\frac{1}{\sin^{m-2}{ax}\cos^n{ax}}}
+\end{array}
+\right.
+$$
+<<*>>=
+)clear all
+
+--S 36 of 36
+aa:=integrate(1/(sin(a*x)^m*cos(a*x)^n),x)
+--R 
+--R
+--R           x
+--R         ++            1
+--I   (1)   |   -------------------- d%H
+--R        ++            n         m
+--I             cos(%H a) sin(%H a)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+)spool
+)lisp (bye)
+@
+
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} Spiegel, Murray R.
+{\sl Mathematical Handbook of Formulas and Tables}\\
+Schaum's Outline Series McGraw-Hill 1968 pp78-80
+\end{thebibliography}
+\end{document}



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In response to observations by Waldek and Martin various cleanups
were made to mapleok.input.pamphlet
========================================================================
diff --git a/changelog b/changelog
index 509310d..a244a50 100644
--- a/changelog
+++ b/changelog
@@ -1,3 +1,4 @@
+20080408 tpd src/input/mapleok.input fix I->%i, reorganize
 20080406 tpd src/input/Makefile add integration regression testing
 20080406 tpd src/input/schaum19.input integrals of sin(ax) and cos(ax)
 20080404 tpd faq FAQ 46: Axiom Trademark information
diff --git a/src/input/mapleok.input.pamphlet b/src/input/mapleok.input.pamphlet
index 1fb777d..a470496 100644
--- a/src/input/mapleok.input.pamphlet
+++ b/src/input/mapleok.input.pamphlet
@@ -19,7 +19,7 @@
 )set message auto off
 )clear all
 )set break resume
---S 1 of 267
+--S 1 of 224
 in1012a:=integrate(log(abs(z^3-1))/(1+z)^2, z= 0..%plusInfinity,"noPole")
 --R 
 --R
@@ -30,43 +30,27 @@ in1012a:=integrate(log(abs(z^3-1))/(1+z)^2, z= 0..%plusInfinity,"noPole")
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
 --E 1
 
---S 2 of 267
-in101a:=integrate((sqrt(z)^I)^I, z= 0..1,"noPole")
+--S 2 of 224
+in101a:=integrate((sqrt(z)^%i)^%i, z= 0..1,"noPole")
 --R 
 --R
---R           2
---R   (2)  ------
---R         2
---R        I  + 2
---R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
+--R   (2)  2
+--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
 --E 2
 
---S 3 of 267
-in106a:=integrate(((I+z)^I)^I, z= 0..1,"noPole")
---R 
---R
---R                  2                  2
---R                 I log(I + 1)       I log(I)
---R        (I + 1)%e             - I %e
---R   (3)  ------------------------------------
---R                        2
---R                       I  + 1
---R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 3
-
---S 4 of 267
+--S 3 of 224
 in108a:=integrate(sqrt((1 + cos(z))*(1 + sin(z))),z=0..%plusInfinity,"noPole")
 --R 
 --R
---R   (4)   + infinity
+--R   (3)   + infinity
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 4
+--E 3
 
---S 5 of 267
+--S 4 of 224
 in119a:=integrate(log(1/z+sqrt(1+1/z)), z=0..1,"noPole")
 --R 
 --R
---R   (5)
+--R   (4)
 --R              +-+              +-+                 +-+
 --R       3log(2\|2  + 3) + 2log(\|2  + 1) - 3log(- 2\|2  + 3)
 --R     + 
@@ -78,129 +62,67 @@ in119a:=integrate(log(1/z+sqrt(1+1/z)), z=0..1,"noPole")
 --R  /
 --R     4
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 5
+--E 4
 
---S 6 of 267
+--S 5 of 224
 in120a:=integrate(1/(1+1/z^6), z=0..%plusInfinity)
 --R 
 --R
---R   (6)   + infinity
---R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 6
-
---S 7 of 267
-in1029a:=integrate((I*z/(I*z+1))^(1/2), z= 0..%plusInfinity,"noPole")
---R 
---R
---R   (7)   + infinity
+--R   (5)   + infinity
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 7
+--E 5
 
---S 8 of 267
-in1030a:=integrate(I*z/(I*z+1), z= 0..%plusInfinity,"noPole")
+--S 6 of 224
+in1030a:=integrate(%i*z/(%i*z+1), z= 0..%plusInfinity,"noPole")
 --R 
 --R
---R   (8)   + infinity
---R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 8
+--R   (6)   + infinity
+--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
+--E 6
 
---S 9 of 267
+--S 7 of 224
 in1066a:=integrate(acoth(z)*real(z), z= 0..1,"noPole")
 --R 
 --R
 --R        1
---R   (9)  -
+--R   (7)  -
 --R        2
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 9
+--E 7
 
---S 10 of 267
+--S 8 of 224
 in1067a:=integrate(acoth(z)*z^(1/2), z= 0..1,"noPole")
 --R 
 --R
---R         - 2log(2) - %pi + 8
---R   (10)  -------------------
---R                  6
+--R        - 2log(2) - %pi + 8
+--R   (8)  -------------------
+--R                 6
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 10
+--E 8
 
---S 11 of 267
+--S 9 of 224
 in1076a:=integrate(sin(z)*(1-cos(z)/(1-sin(z)^2)^(1/2))^2, z= 0..1,"noPole")
 --R 
 --R
---R   (11)  - 4cos(1) + 4
+--R   (9)  - 4cos(1) + 4
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 11
+--E 9
 
---S 12 of 267
+--S 10 of 224
 in1084a:=integrate(atan(sin(z))+atan(1/sin(z)), z= 0..1,"noPole")
 --R 
 --R
 --R           %pi
---R   (12)  - ---
+--R   (10)  - ---
 --R            2
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 12
-
---S 13 of 267
-in1107a:=integrate(-log(z)/(-1+z^(1/2))^3, z= 0..1/2*I,"noPole")
---R 
---R
---R   (13)
---R                                            +-+
---R                  +-+              +-+     \|I
---R       ((2I + 12)\|I  + (- 6I - 4)\|2 )log(----)
---R                                            +-+
---R                                           \|2
---R     + 
---R                                             +-+           +-+
---R                  +-+            +-+     - 4\|I  + (I + 2)\|2
---R       ((- I - 6)\|I  + (3I + 2)\|2 )log(---------------------)
---R                                                   +-+
---R                                                 2\|2
---R     + 
---R                2                                  2
---R               I             +-+           +-+    I        +-+
---R       (- 3log(--) + 2I + 4)\|I  + (I + 1)\|2 log(--) - 4I\|2
---R                4                                  4
---R  /
---R             +-+              +-+
---R     (I + 6)\|I  + (- 3I - 2)\|2
---R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 13
-
---S 14 of 267
-in1108a:=integrate(log(z)/(-1+z^(1/2))^3, z= 0..1/2*I,"noPole")
---R 
---R
---R   (14)
---R                                            +-+
---R                    +-+            +-+     \|I
---R       ((- 2I - 12)\|I  + (6I + 4)\|2 )log(----)
---R                                            +-+
---R                                           \|2
---R     + 
---R                                             +-+           +-+
---R                +-+              +-+     - 4\|I  + (I + 2)\|2
---R       ((I + 6)\|I  + (- 3I - 2)\|2 )log(---------------------)
---R                                                   +-+
---R                                                 2\|2
---R     + 
---R              2                                    2
---R             I             +-+             +-+    I        +-+
---R       (3log(--) - 2I - 4)\|I  + (- I - 1)\|2 log(--) + 4I\|2
---R              4                                    4
---R  /
---R             +-+              +-+
---R     (I + 6)\|I  + (- 3I - 2)\|2
---R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 14
+--E 10
 
---S 15 of 267
+--S 11 of 224
 in1112a:=integrate((1-1/z)^(1/2), z= %pi..2*%pi,"noPole")
 --R 
 --R
---R   (15)
+--R   (11)
 --R               +--------+              +-------+
 --R               |2%pi - 1               |%pi - 1
 --R       - 2log( |--------  + 1) + 2log( |-------  + 1)
@@ -220,198 +142,130 @@ in1112a:=integrate((1-1/z)^(1/2), z= %pi..2*%pi,"noPole")
 --R  /
 --R     4
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 15
+--E 11
 
---S 16 of 267
-in1114a:=integrate(-z-(1/2*2^(1/2)+1/2*I*2^(1/2))*z^(1/2), z= 1..%plusInfinity,"noPole")
+--S 12 of 224
+in1114a:=integrate(-z-(1/2*2^(1/2)+1/2*%i*2^(1/2))*z^(1/2), z= 1..%plusInfinity,"noPole")
 --R 
 --R
---R   (16)  - infinity
---R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 16
+--R   (12)  - infinity
+--R   Type: Union(f1: OrderedCompletion Expression Complex Fraction Integer,...)
+--E 12
 
---S 17 of 267
-in1118:=integrate(acot(z), z= 0..1/2*I)
+--S 13 of 224
+in1118:=integrate(acot(z), z= 0..1/2*%i)
 --R 
 --R
---R               2
---R              I  + 4             4I
---R         2log(------) + I atan(------)
---R                 4              2
---R                               I  - 4
---R   (17)  -----------------------------
---R                       4
---R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 17
+--R         1     3    1     1
+--R   (13)  - log(-) - - log(-)
+--R         2     4    8     9
+--R   Type: Union(f1: OrderedCompletion Expression Complex Fraction Integer,...)
+--E 13
 
---S 18 of 267
+--S 14 of 224
 in1120a:=integrate((z^2)^(1/2), z= 1..2,"noPole")
 --R 
 --R
 --R         3
---R   (18)  -
+--R   (14)  -
 --R         2
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 18
-
---S 19 of 267
-in1130a:=integrate(3^log(z), z= -I..I,"noPole")
---R 
---R
---R             log(3)log(I)       log(3)log(- I)
---R         I %e             + I %e
---R   (19)  -------------------------------------
---R                       log(3) + 1
---R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 19
+--E 14
 
---S 20 of 267
-in1149:=integrate(imag(z)*z^(1/6), z= -I..I)
+--S 15 of 224
+in1130a:=integrate(3^log(z), z= -%i..%i,"noPole")
 --R 
 --R
---R   (20)  0
---R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 20
+--R              log(%i)log(3)        log(- %i)log(3)
+--R         %i %e              + %i %e
+--R   (15)  -----------------------------------------
+--R                         log(3) + 1
+--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
+--E 15
 
---S 21 of 267
+--S 16 of 224
 in1149:=integrate(imag(z)*z^(1/6), z= -%i..%i)
 --R 
 --R
---R   (21)  0
+--R   (16)  0
 --R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
---E 21
-
---S 22 of 267
-in1150a:=integrate(1/z^(1/2), z= -I..I,"noPole")
---R 
---R
---R           +-+     +---+
---R   (22)  2\|I  - 2\|- I
---R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 22
+--E 16
 
---S 23 of 267
-in1150c:=integrate(1/z^(1/2), z= -%i..%i,"noPole")
+--S 17 of 224
+in1150a:=integrate(1/z^(1/2), z= -%i..%i,"noPole")
 --R 
 --R
 --R           +--+     +----+
---R   (23)  2\|%i  - 2\|- %i
+--R   (17)  2\|%i  - 2\|- %i
 --R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
---E 23
-
---S 24 of 267
-in1161:=integrate(hermiteH(1, z), z= -I..I)
---R 
---R
---R   (24)  0
---R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 24
+--E 17
 
---S 25 of 267
+--S 18 of 224
 in1161a:=integrate(hermiteH(1, z), z= -%i..%i)
 --R 
 --R
---R   (25)  0
+--R   (18)  0
 --R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
---E 25
-
---S 26 of 267 used to work
-in1160:=integrate(HermiteH(2, z), z= -%i..%i)
---R 
---R   There are no library operations named HermiteH 
---R      Use HyperDoc Browse or issue
---R                              )what op HermiteH
---R      to learn if there is any operation containing " HermiteH " in its
---R      name.
---R 
---RDaly Bug
---R   Cannot find a definition or applicable library operation named 
---R      HermiteH with argument type(s) 
---R                               PositiveInteger
---R                                 Variable z
---R      
---R      Perhaps you should use "@" to indicate the required return type, 
---R      or "$" to specify which version of the function you need.
---E 26
--- 
---     20%i
---   - ----
---       3
---         Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
+--E 18
 
---S 27 of 267
-in1162:=integrate(laguerreL(1, z), z= -I..I)
+--S 19 of 224
+in1160:=integrate(hermiteH(2, z), z= -%i..%i)
 --R 
 --R
---R   (26)  2I
---R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 27
+--R           20%i
+--R   (19)  - ----
+--R             3
+--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
+--E 19
 
---S 28 of 267
+--S 20 of 224
 in1162:=integrate(laguerreL(1, z), z= -%i..%i)
 --R 
 --R
---R   (27)  2%i
+--R   (20)  2%i
 --R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
---E 28
-
---S 29 of 267
-in1163:=integrate(legendreP(3, z), z= -I..I)
---R 
---R
---R   (28)  0
---R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 29
+--E 20
 
---S 30 of 267
+--S 21 of 224
 in1163:=integrate(legendreP(3, z), z= -%i..%i)
 --R 
 --R
---R   (29)  0
+--R   (21)  0
 --R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
---E 30
-
---S 31 of 267
-in1164:=integrate(legendreP(2, z), z= -I..I)
---R 
---R
---R          3
---R   (30)  I  - I
---R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 31
+--E 21
 
---S 32 of 267
+--S 22 of 224
 in1164:=integrate(legendreP(2, z), z= -%i..%i)
 --R 
 --R
---R   (31)  - 2%i
+--R   (22)  - 2%i
 --R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
---E 32
+--E 22
 
---S 33 of 267
+--S 23 of 224
 in1167a:=integrate((z^2)^(1/6), z= -3..-1,"noPole")
 --R 
 --R
 --R            3+---+    3+---+
 --R         - 3\|- 1  + 9\|- 3
---R   (32)  -------------------
+--R   (23)  -------------------
 --R                  4
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 33
+--E 23
 
---S 34 of 267
+--S 24 of 224
 in1180:=integrate(z^(1/3)/(z^2+1), z= 0..10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000!
000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000)
 --R 
 --R
---R   (33)  potentialPole
+--R   (24)  potentialPole
 --R                                         Type: Union(pole: potentialPole,...)
---E 34
+--E 24
 
---S 35 of 267
+--S 25 of 224
 in1180:=integrate(z^(1/3)/(z^2+1), z= 0..10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000!
000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000,"noPole")
 --R 
 --R
---R   (34)
+--R   (25)
 --R         3
 --R      *
 --R         log
@@ -637,75 +491,75 @@ in1180:=integrate(z^(1/3)/(z^2+1), z= 0..100000000000000000000000000000000000000
 --R  /
 --R     24
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 35
+--E 25
 
---S 36 of 267
-in1183a:=integrate(csc(z), z= 1-I..1+I,"noPole")
+--S 26 of 224
+in1183a:=integrate(csc(z), z= 1-%i..1+%i,"noPole")
 --R 
 --R
---R   (35)
---R                          2                                    2
---R                sin(I + 1)                           sin(I - 1)
---R   log(-----------------------------) - log(-----------------------------)
---R                 2                                    2
---R       cos(I + 1)  + 2cos(I + 1) + 1        cos(I - 1)  + 2cos(I - 1) + 1
---R   -----------------------------------------------------------------------
---R                                      2
---R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 36
+--R   (26)
+--R                            2                                      2
+--R                 sin(1 + %i)                            sin(1 - %i)
+--R   log(-------------------------------) - log(-------------------------------)
+--R                  2                                      2
+--R       cos(1 + %i)  + 2cos(1 + %i) + 1        cos(1 - %i)  + 2cos(1 - %i) + 1
+--R   ---------------------------------------------------------------------------
+--R                                        2
+--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
+--E 26
 
---S 37 of 267
+--S 27 of 224
 in1185a:=integrate((z+1)^(1/2)/(1+z^4), z= 0..1,"noPole")
 --R 
 --R
---R   (36)
+--R   (27)
 --R         ROOT
 --R                 +-----------------------------------------+
 --R                 |         2                          2          +-+
---I                \|- 96%%BC1  - 64%%BC0 %%BC1 - 96%%BC0  - 1  - 4\|2 %%BC1
+--I                \|- 96%%BQ1  - 64%%BQ0 %%BQ1 - 96%%BQ0  - 1  - 4\|2 %%BQ1
 --R              + 
 --R                    +-+
---I                - 4\|2 %%BC0
+--I                - 4\|2 %%BQ0
 --R           /
 --R                +-+
 --R              2\|2
 --R      *
 --R         log
 --R                              +-+            +-+             +-+           +-+
---I                      ((24576\|2 %%BC0 - 768\|2 )%%BC1 - 768\|2 %%BC0 - 48\|2 )
+--I                      ((24576\|2 %%BQ0 - 768\|2 )%%BQ1 - 768\|2 %%BQ0 - 48\|2 )
 --R                   *
 --R                       +-----------------------------------------+
 --R                       |         2                          2
---I                      \|- 96%%BC1  - 64%%BC0 %%BC1 - 96%%BC0  - 1
+--I                      \|- 96%%BQ1  - 64%%BQ0 %%BQ1 - 96%%BQ0  - 1
 --R                  + 
 --R                                             2               2
---I                    (196608%%BC0 - 6144)%%BC1  + (196608%%BC0  + 384)%%BC1
+--I                    (196608%%BQ0 - 6144)%%BQ1  + (196608%%BQ0  + 384)%%BQ1
 --R                  + 
 --R                               2
---I                    - 6144%%BC0  + 384%%BC0 + 48
+--I                    - 6144%%BQ0  + 384%%BQ0 + 48
 --R               *
 --R                  ROOT
 --R                          +-----------------------------------------+
 --R                          |         2                          2
---I                         \|- 96%%BC1  - 64%%BC0 %%BC1 - 96%%BC0  - 1
+--I                         \|- 96%%BQ1  - 64%%BQ0 %%BQ1 - 96%%BQ0  - 1
 --R                       + 
 --R                             +-+          +-+
---I                         - 4\|2 %%BC1 - 4\|2 %%BC0
+--I                         - 4\|2 %%BQ1 - 4\|2 %%BQ0
 --R                    /
 --R                         +-+
 --R                       2\|2
 --R              + 
---I                  ((- 3072%%BC0 + 384)%%BC1 + 384%%BC0 - 12)
+--I                  ((- 3072%%BQ0 + 384)%%BQ1 + 384%%BQ0 - 12)
 --R               *
 --R                   +-----------------------------------------+
 --R                   |         2                          2
---I                  \|- 96%%BC1  - 64%%BC0 %%BC1 - 96%%BC0  - 1
+--I                  \|- 96%%BQ1  - 64%%BQ0 %%BQ1 - 96%%BQ0  - 1
 --R              + 
 --R                         +-+             +-+      2
---I                (- 12288\|2 %%BC0 + 1536\|2 )%%BC1
+--I                (- 12288\|2 %%BQ0 + 1536\|2 )%%BQ1
 --R              + 
 --R                         +-+     2      +-+              +-+     2      +-+
---I                (- 12288\|2 %%BC0  + 48\|2 )%%BC1 + 1536\|2 %%BC0  + 48\|2 %%BC0
+--I                (- 12288\|2 %%BQ0  + 48\|2 )%%BQ1 + 1536\|2 %%BQ0  + 48\|2 %%BQ0
 --R              + 
 --R                   +-+
 --R                60\|2
@@ -717,55 +571,55 @@ in1185a:=integrate((z+1)^(1/2)/(1+z^4), z= 0..1,"noPole")
 --R            ROOT
 --R                    +-----------------------------------------+
 --R                    |         2                          2          +-+
---I                   \|- 96%%BC1  - 64%%BC0 %%BC1 - 96%%BC0  - 1  - 4\|2 %%BC1
+--I                   \|- 96%%BQ1  - 64%%BQ0 %%BQ1 - 96%%BQ0  - 1  - 4\|2 %%BQ1
 --R                 + 
 --R                       +-+
---I                   - 4\|2 %%BC0
+--I                   - 4\|2 %%BQ0
 --R              /
 --R                   +-+
 --R                 2\|2
 --R         *
 --R            log
---I                         ((24576%%BC0 - 768)%%BC1 - 768%%BC0 - 48)
+--I                         ((24576%%BQ0 - 768)%%BQ1 - 768%%BQ0 - 48)
 --R                      *
 --R                          +-----------------------------------------+
 --R                          |         2                          2
---I                         \|- 96%%BC1  - 64%%BC0 %%BC1 - 96%%BC0  - 1
+--I                         \|- 96%%BQ1  - 64%%BQ0 %%BQ1 - 96%%BQ0  - 1
 --R                     + 
 --R                              +-+             +-+      2
---I                       (98304\|2 %%BC0 - 3072\|2 )%%BC1
+--I                       (98304\|2 %%BQ0 - 3072\|2 )%%BQ1
 --R                     + 
 --R                              +-+     2       +-+              +-+     2
---I                       (98304\|2 %%BC0  + 192\|2 )%%BC1 - 3072\|2 %%BC0
+--I                       (98304\|2 %%BQ0  + 192\|2 )%%BQ1 - 3072\|2 %%BQ0
 --R                     + 
 --R                           +-+           +-+
---I                       192\|2 %%BC0 + 24\|2
+--I                       192\|2 %%BQ0 + 24\|2
 --R                  *
 --R                     ROOT
 --R                             +-----------------------------------------+
 --R                             |         2                          2
---I                            \|- 96%%BC1  - 64%%BC0 %%BC1 - 96%%BC0  - 1
+--I                            \|- 96%%BQ1  - 64%%BQ0 %%BQ1 - 96%%BQ0  - 1
 --R                          + 
 --R                                +-+          +-+
---I                            - 4\|2 %%BC1 - 4\|2 %%BC0
+--I                            - 4\|2 %%BQ1 - 4\|2 %%BQ0
 --R                       /
 --R                            +-+
 --R                          2\|2
 --R                 + 
---I                     ((- 3072%%BC0 + 384)%%BC1 + 384%%BC0 - 12)
+--I                     ((- 3072%%BQ0 + 384)%%BQ1 + 384%%BQ0 - 12)
 --R                  *
 --R                      +-----------------------------------------+
 --R                      |         2                          2
---I                     \|- 96%%BC1  - 64%%BC0 %%BC1 - 96%%BC0  - 1
+--I                     \|- 96%%BQ1  - 64%%BQ0 %%BQ1 - 96%%BQ0  - 1
 --R                 + 
 --R                            +-+             +-+      2
---I                   (- 12288\|2 %%BC0 + 1536\|2 )%%BC1
+--I                   (- 12288\|2 %%BQ0 + 1536\|2 )%%BQ1
 --R                 + 
 --R                            +-+     2      +-+              +-+     2
---I                   (- 12288\|2 %%BC0  + 48\|2 )%%BC1 + 1536\|2 %%BC0
+--I                   (- 12288\|2 %%BQ0  + 48\|2 )%%BQ1 + 1536\|2 %%BQ0
 --R                 + 
 --R                      +-+           +-+
---I                   48\|2 %%BC0 + 42\|2
+--I                   48\|2 %%BQ0 + 42\|2
 --R              /
 --R                  +-+
 --R                 \|2
@@ -774,56 +628,56 @@ in1185a:=integrate((z+1)^(1/2)/(1+z^4), z= 0..1,"noPole")
 --R            ROOT
 --R                      +-----------------------------------------+
 --R                      |         2                          2          +-+
---I                   - \|- 96%%BC1  - 64%%BC0 %%BC1 - 96%%BC0  - 1  - 4\|2 %%BC1
+--I                   - \|- 96%%BQ1  - 64%%BQ0 %%BQ1 - 96%%BQ0  - 1  - 4\|2 %%BQ1
 --R                 + 
 --R                       +-+
---I                   - 4\|2 %%BC0
+--I                   - 4\|2 %%BQ0
 --R              /
 --R                   +-+
 --R                 2\|2
 --R         *
 --R            log
 --R                                    +-+            +-+             +-+
---I                             (24576\|2 %%BC0 - 768\|2 )%%BC1 - 768\|2 %%BC0
+--I                             (24576\|2 %%BQ0 - 768\|2 )%%BQ1 - 768\|2 %%BQ0
 --R                           + 
 --R                                  +-+
 --R                             - 48\|2
 --R                      *
 --R                          +-----------------------------------------+
 --R                          |         2                          2
---I                         \|- 96%%BC1  - 64%%BC0 %%BC1 - 96%%BC0  - 1
+--I                         \|- 96%%BQ1  - 64%%BQ0 %%BQ1 - 96%%BQ0  - 1
 --R                     + 
 --R                                                  2
---I                       (- 196608%%BC0 + 6144)%%BC1
+--I                       (- 196608%%BQ0 + 6144)%%BQ1
 --R                     + 
 --R                                     2                        2
---I                       (- 196608%%BC0  - 384)%%BC1 + 6144%%BC0  - 384%%BC0 - 48
+--I                       (- 196608%%BQ0  - 384)%%BQ1 + 6144%%BQ0  - 384%%BQ0 - 48
 --R                  *
 --R                     ROOT
 --R                               +-----------------------------------------+
 --R                               |         2                          2
---I                            - \|- 96%%BC1  - 64%%BC0 %%BC1 - 96%%BC0  - 1
+--I                            - \|- 96%%BQ1  - 64%%BQ0 %%BQ1 - 96%%BQ0  - 1
 --R                          + 
 --R                                +-+          +-+
---I                            - 4\|2 %%BC1 - 4\|2 %%BC0
+--I                            - 4\|2 %%BQ1 - 4\|2 %%BQ0
 --R                       /
 --R                            +-+
 --R                          2\|2
 --R                 + 
---I                     ((3072%%BC0 - 384)%%BC1 - 384%%BC0 + 12)
+--I                     ((3072%%BQ0 - 384)%%BQ1 - 384%%BQ0 + 12)
 --R                  *
 --R                      +-----------------------------------------+
 --R                      |         2                          2
---I                     \|- 96%%BC1  - 64%%BC0 %%BC1 - 96%%BC0  - 1
+--I                     \|- 96%%BQ1  - 64%%BQ0 %%BQ1 - 96%%BQ0  - 1
 --R                 + 
 --R                            +-+             +-+      2
---I                   (- 12288\|2 %%BC0 + 1536\|2 )%%BC1
+--I                   (- 12288\|2 %%BQ0 + 1536\|2 )%%BQ1
 --R                 + 
 --R                            +-+     2      +-+              +-+     2
---I                   (- 12288\|2 %%BC0  + 48\|2 )%%BC1 + 1536\|2 %%BC0
+--I                   (- 12288\|2 %%BQ0  + 48\|2 )%%BQ1 + 1536\|2 %%BQ0
 --R                 + 
 --R                      +-+           +-+
---I                   48\|2 %%BC0 + 60\|2
+--I                   48\|2 %%BQ0 + 60\|2
 --R              /
 --R                  +-+
 --R                 \|2
@@ -831,52 +685,52 @@ in1185a:=integrate((z+1)^(1/2)/(1+z^4), z= 0..1,"noPole")
 --R         ROOT
 --R                   +-----------------------------------------+
 --R                   |         2                          2          +-+
---I                - \|- 96%%BC1  - 64%%BC0 %%BC1 - 96%%BC0  - 1  - 4\|2 %%BC1
+--I                - \|- 96%%BQ1  - 64%%BQ0 %%BQ1 - 96%%BQ0  - 1  - 4\|2 %%BQ1
 --R              + 
 --R                    +-+
---I                - 4\|2 %%BC0
+--I                - 4\|2 %%BQ0
 --R           /
 --R                +-+
 --R              2\|2
 --R      *
 --R         log
---I                      ((24576%%BC0 - 768)%%BC1 - 768%%BC0 - 48)
+--I                      ((24576%%BQ0 - 768)%%BQ1 - 768%%BQ0 - 48)
 --R                   *
 --R                       +-----------------------------------------+
 --R                       |         2                          2
---I                      \|- 96%%BC1  - 64%%BC0 %%BC1 - 96%%BC0  - 1
+--I                      \|- 96%%BQ1  - 64%%BQ0 %%BQ1 - 96%%BQ0  - 1
 --R                  + 
 --R                             +-+             +-+      2
---I                    (- 98304\|2 %%BC0 + 3072\|2 )%%BC1
+--I                    (- 98304\|2 %%BQ0 + 3072\|2 )%%BQ1
 --R                  + 
 --R                             +-+     2       +-+              +-+     2
---I                    (- 98304\|2 %%BC0  - 192\|2 )%%BC1 + 3072\|2 %%BC0
+--I                    (- 98304\|2 %%BQ0  - 192\|2 )%%BQ1 + 3072\|2 %%BQ0
 --R                  + 
 --R                          +-+           +-+
---I                    - 192\|2 %%BC0 - 24\|2
+--I                    - 192\|2 %%BQ0 - 24\|2
 --R               *
 --R                  ROOT
 --R                            +-----------------------------------------+
 --R                            |         2                          2
---I                         - \|- 96%%BC1  - 64%%BC0 %%BC1 - 96%%BC0  - 1
+--I                         - \|- 96%%BQ1  - 64%%BQ0 %%BQ1 - 96%%BQ0  - 1
 --R                       + 
 --R                             +-+          +-+
---I                         - 4\|2 %%BC1 - 4\|2 %%BC0
+--I                         - 4\|2 %%BQ1 - 4\|2 %%BQ0
 --R                    /
 --R                         +-+
 --R                       2\|2
 --R              + 
---I                  ((3072%%BC0 - 384)%%BC1 - 384%%BC0 + 12)
+--I                  ((3072%%BQ0 - 384)%%BQ1 - 384%%BQ0 + 12)
 --R               *
 --R                   +-----------------------------------------+
 --R                   |         2                          2
---I                  \|- 96%%BC1  - 64%%BC0 %%BC1 - 96%%BC0  - 1
+--I                  \|- 96%%BQ1  - 64%%BQ0 %%BQ1 - 96%%BQ0  - 1
 --R              + 
 --R                         +-+             +-+      2
---I                (- 12288\|2 %%BC0 + 1536\|2 )%%BC1
+--I                (- 12288\|2 %%BQ0 + 1536\|2 )%%BQ1
 --R              + 
 --R                         +-+     2      +-+              +-+     2      +-+
---I                (- 12288\|2 %%BC0  + 48\|2 )%%BC1 + 1536\|2 %%BC0  + 48\|2 %%BC0
+--I                (- 12288\|2 %%BQ0  + 48\|2 )%%BQ1 + 1536\|2 %%BQ0  + 48\|2 %%BQ0
 --R              + 
 --R                   +-+
 --R                42\|2
@@ -888,55 +742,55 @@ in1185a:=integrate((z+1)^(1/2)/(1+z^4), z= 0..1,"noPole")
 --R            ROOT
 --R                      +-----------------------------------------+
 --R                      |         2                          2          +-+
---I                   - \|- 96%%BC1  - 64%%BC0 %%BC1 - 96%%BC0  - 1  - 4\|2 %%BC1
+--I                   - \|- 96%%BQ1  - 64%%BQ0 %%BQ1 - 96%%BQ0  - 1  - 4\|2 %%BQ1
 --R                 + 
 --R                       +-+
---I                   - 4\|2 %%BC0
+--I                   - 4\|2 %%BQ0
 --R              /
 --R                   +-+
 --R                 2\|2
 --R         *
 --R            log
---I                         ((- 24576%%BC0 + 768)%%BC1 + 768%%BC0 + 48)
+--I                         ((- 24576%%BQ0 + 768)%%BQ1 + 768%%BQ0 + 48)
 --R                      *
 --R                          +-----------------------------------------+
 --R                          |         2                          2
---I                         \|- 96%%BC1  - 64%%BC0 %%BC1 - 96%%BC0  - 1
+--I                         \|- 96%%BQ1  - 64%%BQ0 %%BQ1 - 96%%BQ0  - 1
 --R                     + 
 --R                              +-+             +-+      2
---I                       (98304\|2 %%BC0 - 3072\|2 )%%BC1
+--I                       (98304\|2 %%BQ0 - 3072\|2 )%%BQ1
 --R                     + 
 --R                              +-+     2       +-+              +-+     2
---I                       (98304\|2 %%BC0  + 192\|2 )%%BC1 - 3072\|2 %%BC0
+--I                       (98304\|2 %%BQ0  + 192\|2 )%%BQ1 - 3072\|2 %%BQ0
 --R                     + 
 --R                           +-+           +-+
---I                       192\|2 %%BC0 + 24\|2
+--I                       192\|2 %%BQ0 + 24\|2
 --R                  *
 --R                     ROOT
 --R                               +-----------------------------------------+
 --R                               |         2                          2
---I                            - \|- 96%%BC1  - 64%%BC0 %%BC1 - 96%%BC0  - 1
+--I                            - \|- 96%%BQ1  - 64%%BQ0 %%BQ1 - 96%%BQ0  - 1
 --R                          + 
 --R                                +-+          +-+
---I                            - 4\|2 %%BC1 - 4\|2 %%BC0
+--I                            - 4\|2 %%BQ1 - 4\|2 %%BQ0
 --R                       /
 --R                            +-+
 --R                          2\|2
 --R                 + 
---I                     ((3072%%BC0 - 384)%%BC1 - 384%%BC0 + 12)
+--I                     ((3072%%BQ0 - 384)%%BQ1 - 384%%BQ0 + 12)
 --R                  *
 --R                      +-----------------------------------------+
 --R                      |         2                          2
---I                     \|- 96%%BC1  - 64%%BC0 %%BC1 - 96%%BC0  - 1
+--I                     \|- 96%%BQ1  - 64%%BQ0 %%BQ1 - 96%%BQ0  - 1
 --R                 + 
 --R                            +-+             +-+      2
---I                   (- 12288\|2 %%BC0 + 1536\|2 )%%BC1
+--I                   (- 12288\|2 %%BQ0 + 1536\|2 )%%BQ1
 --R                 + 
 --R                            +-+     2      +-+              +-+     2
---I                   (- 12288\|2 %%BC0  + 48\|2 )%%BC1 + 1536\|2 %%BC0
+--I                   (- 12288\|2 %%BQ0  + 48\|2 )%%BQ1 + 1536\|2 %%BQ0
 --R                 + 
 --R                      +-+           +-+
---I                   48\|2 %%BC0 + 42\|2
+--I                   48\|2 %%BQ0 + 42\|2
 --R              /
 --R                  +-+
 --R                 \|2
@@ -944,53 +798,53 @@ in1185a:=integrate((z+1)^(1/2)/(1+z^4), z= 0..1,"noPole")
 --R         ROOT
 --R                   +-----------------------------------------+
 --R                   |         2                          2          +-+
---I                - \|- 96%%BC1  - 64%%BC0 %%BC1 - 96%%BC0  - 1  - 4\|2 %%BC1
+--I                - \|- 96%%BQ1  - 64%%BQ0 %%BQ1 - 96%%BQ0  - 1  - 4\|2 %%BQ1
 --R              + 
 --R                    +-+
---I                - 4\|2 %%BC0
+--I                - 4\|2 %%BQ0
 --R           /
 --R                +-+
 --R              2\|2
 --R      *
 --R         log
 --R                                   +-+            +-+             +-+
---I                          (- 24576\|2 %%BC0 + 768\|2 )%%BC1 + 768\|2 %%BC0
+--I                          (- 24576\|2 %%BQ0 + 768\|2 )%%BQ1 + 768\|2 %%BQ0
 --R                        + 
 --R                             +-+
 --R                          48\|2
 --R                   *
 --R                       +-----------------------------------------+
 --R                       |         2                          2
---I                      \|- 96%%BC1  - 64%%BC0 %%BC1 - 96%%BC0  - 1
+--I                      \|- 96%%BQ1  - 64%%BQ0 %%BQ1 - 96%%BQ0  - 1
 --R                  + 
 --R                                             2               2
---I                    (196608%%BC0 - 6144)%%BC1  + (196608%%BC0  + 384)%%BC1
+--I                    (196608%%BQ0 - 6144)%%BQ1  + (196608%%BQ0  + 384)%%BQ1
 --R                  + 
 --R                               2
---I                    - 6144%%BC0  + 384%%BC0 + 48
+--I                    - 6144%%BQ0  + 384%%BQ0 + 48
 --R               *
 --R                  ROOT
 --R                            +-----------------------------------------+
 --R                            |         2                          2
---I                         - \|- 96%%BC1  - 64%%BC0 %%BC1 - 96%%BC0  - 1
+--I                         - \|- 96%%BQ1  - 64%%BQ0 %%BQ1 - 96%%BQ0  - 1
 --R                       + 
 --R                             +-+          +-+
---I                         - 4\|2 %%BC1 - 4\|2 %%BC0
+--I                         - 4\|2 %%BQ1 - 4\|2 %%BQ0
 --R                    /
 --R                         +-+
 --R                       2\|2
 --R              + 
---I                  ((3072%%BC0 - 384)%%BC1 - 384%%BC0 + 12)
+--I                  ((3072%%BQ0 - 384)%%BQ1 - 384%%BQ0 + 12)
 --R               *
 --R                   +-----------------------------------------+
 --R                   |         2                          2
---I                  \|- 96%%BC1  - 64%%BC0 %%BC1 - 96%%BC0  - 1
+--I                  \|- 96%%BQ1  - 64%%BQ0 %%BQ1 - 96%%BQ0  - 1
 --R              + 
 --R                         +-+             +-+      2
---I                (- 12288\|2 %%BC0 + 1536\|2 )%%BC1
+--I                (- 12288\|2 %%BQ0 + 1536\|2 )%%BQ1
 --R              + 
 --R                         +-+     2      +-+              +-+     2      +-+
---I                (- 12288\|2 %%BC0  + 48\|2 )%%BC1 + 1536\|2 %%BC0  + 48\|2 %%BC0
+--I                (- 12288\|2 %%BQ0  + 48\|2 )%%BQ1 + 1536\|2 %%BQ0  + 48\|2 %%BQ0
 --R              + 
 --R                   +-+
 --R                60\|2
@@ -1001,52 +855,52 @@ in1185a:=integrate((z+1)^(1/2)/(1+z^4), z= 0..1,"noPole")
 --R         ROOT
 --R                 +-----------------------------------------+
 --R                 |         2                          2          +-+
---I                \|- 96%%BC1  - 64%%BC0 %%BC1 - 96%%BC0  - 1  - 4\|2 %%BC1
+--I                \|- 96%%BQ1  - 64%%BQ0 %%BQ1 - 96%%BQ0  - 1  - 4\|2 %%BQ1
 --R              + 
 --R                    +-+
---I                - 4\|2 %%BC0
+--I                - 4\|2 %%BQ0
 --R           /
 --R                +-+
 --R              2\|2
 --R      *
 --R         log
---I                      ((- 24576%%BC0 + 768)%%BC1 + 768%%BC0 + 48)
+--I                      ((- 24576%%BQ0 + 768)%%BQ1 + 768%%BQ0 + 48)
 --R                   *
 --R                       +-----------------------------------------+
 --R                       |         2                          2
---I                      \|- 96%%BC1  - 64%%BC0 %%BC1 - 96%%BC0  - 1
+--I                      \|- 96%%BQ1  - 64%%BQ0 %%BQ1 - 96%%BQ0  - 1
 --R                  + 
 --R                             +-+             +-+      2
---I                    (- 98304\|2 %%BC0 + 3072\|2 )%%BC1
+--I                    (- 98304\|2 %%BQ0 + 3072\|2 )%%BQ1
 --R                  + 
 --R                             +-+     2       +-+              +-+     2
---I                    (- 98304\|2 %%BC0  - 192\|2 )%%BC1 + 3072\|2 %%BC0
+--I                    (- 98304\|2 %%BQ0  - 192\|2 )%%BQ1 + 3072\|2 %%BQ0
 --R                  + 
 --R                          +-+           +-+
---I                    - 192\|2 %%BC0 - 24\|2
+--I                    - 192\|2 %%BQ0 - 24\|2
 --R               *
 --R                  ROOT
 --R                          +-----------------------------------------+
 --R                          |         2                          2
---I                         \|- 96%%BC1  - 64%%BC0 %%BC1 - 96%%BC0  - 1
+--I                         \|- 96%%BQ1  - 64%%BQ0 %%BQ1 - 96%%BQ0  - 1
 --R                       + 
 --R                             +-+          +-+
---I                         - 4\|2 %%BC1 - 4\|2 %%BC0
+--I                         - 4\|2 %%BQ1 - 4\|2 %%BQ0
 --R                    /
 --R                         +-+
 --R                       2\|2
 --R              + 
---I                  ((- 3072%%BC0 + 384)%%BC1 + 384%%BC0 - 12)
+--I                  ((- 3072%%BQ0 + 384)%%BQ1 + 384%%BQ0 - 12)
 --R               *
 --R                   +-----------------------------------------+
 --R                   |         2                          2
---I                  \|- 96%%BC1  - 64%%BC0 %%BC1 - 96%%BC0  - 1
+--I                  \|- 96%%BQ1  - 64%%BQ0 %%BQ1 - 96%%BQ0  - 1
 --R              + 
 --R                         +-+             +-+      2
---I                (- 12288\|2 %%BC0 + 1536\|2 )%%BC1
+--I                (- 12288\|2 %%BQ0 + 1536\|2 )%%BQ1
 --R              + 
 --R                         +-+     2      +-+              +-+     2      +-+
---I                (- 12288\|2 %%BC0  + 48\|2 )%%BC1 + 1536\|2 %%BC0  + 48\|2 %%BC0
+--I                (- 12288\|2 %%BQ0  + 48\|2 )%%BQ1 + 1536\|2 %%BQ0  + 48\|2 %%BQ0
 --R              + 
 --R                   +-+
 --R                42\|2
@@ -1058,199 +912,199 @@ in1185a:=integrate((z+1)^(1/2)/(1+z^4), z= 0..1,"noPole")
 --R            ROOT
 --R                    +-----------------------------------------+
 --R                    |         2                          2          +-+
---I                   \|- 96%%BC1  - 64%%BC0 %%BC1 - 96%%BC0  - 1  - 4\|2 %%BC1
+--I                   \|- 96%%BQ1  - 64%%BQ0 %%BQ1 - 96%%BQ0  - 1  - 4\|2 %%BQ1
 --R                 + 
 --R                       +-+
---I                   - 4\|2 %%BC0
+--I                   - 4\|2 %%BQ0
 --R              /
 --R                   +-+
 --R                 2\|2
 --R         *
 --R            log
 --R                                    +-+            +-+             +-+
---I                           (- 24576\|2 %%BC0 + 768\|2 )%%BC1 + 768\|2 %%BC0
+--I                           (- 24576\|2 %%BQ0 + 768\|2 )%%BQ1 + 768\|2 %%BQ0
 --R                         + 
 --R                              +-+
 --R                           48\|2
 --R                      *
 --R                          +-----------------------------------------+
 --R                          |         2                          2
---I                         \|- 96%%BC1  - 64%%BC0 %%BC1 - 96%%BC0  - 1
+--I                         \|- 96%%BQ1  - 64%%BQ0 %%BQ1 - 96%%BQ0  - 1
 --R                     + 
 --R                                                  2
---I                       (- 196608%%BC0 + 6144)%%BC1
+--I                       (- 196608%%BQ0 + 6144)%%BQ1
 --R                     + 
 --R                                     2                        2
---I                       (- 196608%%BC0  - 384)%%BC1 + 6144%%BC0  - 384%%BC0 - 48
+--I                       (- 196608%%BQ0  - 384)%%BQ1 + 6144%%BQ0  - 384%%BQ0 - 48
 --R                  *
 --R                     ROOT
 --R                             +-----------------------------------------+
 --R                             |         2                          2
---I                            \|- 96%%BC1  - 64%%BC0 %%BC1 - 96%%BC0  - 1
+--I                            \|- 96%%BQ1  - 64%%BQ0 %%BQ1 - 96%%BQ0  - 1
 --R                          + 
 --R                                +-+          +-+
---I                            - 4\|2 %%BC1 - 4\|2 %%BC0
+--I                            - 4\|2 %%BQ1 - 4\|2 %%BQ0
 --R                       /
 --R                            +-+
 --R                          2\|2
 --R                 + 
---I                     ((- 3072%%BC0 + 384)%%BC1 + 384%%BC0 - 12)
+--I                     ((- 3072%%BQ0 + 384)%%BQ1 + 384%%BQ0 - 12)
 --R                  *
 --R                      +-----------------------------------------+
 --R                      |         2                          2
---I                     \|- 96%%BC1  - 64%%BC0 %%BC1 - 96%%BC0  - 1
+--I                     \|- 96%%BQ1  - 64%%BQ0 %%BQ1 - 96%%BQ0  - 1
 --R                 + 
 --R                            +-+             +-+      2
---I                   (- 12288\|2 %%BC0 + 1536\|2 )%%BC1
+--I                   (- 12288\|2 %%BQ0 + 1536\|2 )%%BQ1
 --R                 + 
 --R                            +-+     2      +-+              +-+     2
---I                   (- 12288\|2 %%BC0  + 48\|2 )%%BC1 + 1536\|2 %%BC0
+--I                   (- 12288\|2 %%BQ0  + 48\|2 )%%BQ1 + 1536\|2 %%BQ0
 --R                 + 
 --R                      +-+           +-+
---I                   48\|2 %%BC0 + 60\|2
+--I                   48\|2 %%BQ0 + 60\|2
 --R              /
 --R                  +-+
 --R                 \|2
 --R     + 
 --R       -
 --R             +------+
---I            \|4%%BC1
+--I            \|4%%BQ1
 --R         *
 --R            log
 --R                            +-+             +-+      2
---I                     (98304\|2 %%BC0 - 3072\|2 )%%BC1
+--I                     (98304\|2 %%BQ0 - 3072\|2 )%%BQ1
 --R                   + 
 --R                            +-+     2       +-+               +-+     3
---I                     (98304\|2 %%BC0  + 192\|2 )%%BC1 + 98304\|2 %%BC0
+--I                     (98304\|2 %%BQ0  + 192\|2 )%%BQ1 + 98304\|2 %%BQ0
 --R                   + 
 --R                         +-+           +-+
---I                     768\|2 %%BC0 - 36\|2
+--I                     768\|2 %%BQ0 - 36\|2
 --R                *
 --R                    +------+
---I                   \|4%%BC1
+--I                   \|4%%BQ1
 --R               + 
 --R                                         2              2
---I                 (12288%%BC0 - 1536)%%BC1  + (12288%%BC0  - 48)%%BC1
+--I                 (12288%%BQ0 - 1536)%%BQ1  + (12288%%BQ0  - 48)%%BQ1
 --R               + 
 --R                           3
---I                 12288%%BC0  + 96%%BC0 + 18
+--I                 12288%%BQ0  + 96%%BQ0 + 18
 --R     + 
 --R          +------+
---I         \|4%%BC1
+--I         \|4%%BQ1
 --R      *
 --R         log
 --R                                          2              2
---I                  (98304%%BC0 - 3072)%%BC1  + (98304%%BC0  + 192)%%BC1
+--I                  (98304%%BQ0 - 3072)%%BQ1  + (98304%%BQ0  + 192)%%BQ1
 --R                + 
 --R                            3
---I                  98304%%BC0  + 768%%BC0 - 36
+--I                  98304%%BQ0  + 768%%BQ0 - 36
 --R             *
 --R                 +------+
---I                \|4%%BC1
+--I                \|4%%BQ1
 --R            + 
 --R                                      2              2                        3
---I              (12288%%BC0 - 1536)%%BC1  + (12288%%BC0  - 48)%%BC1 + 12288%%BC0
+--I              (12288%%BQ0 - 1536)%%BQ1  + (12288%%BQ0  - 48)%%BQ1 + 12288%%BQ0
 --R            + 
---I              96%%BC0 + 9
+--I              96%%BQ0 + 9
 --R     + 
 --R       -
 --R             +------+
---I            \|4%%BC1
+--I            \|4%%BQ1
 --R         *
 --R            log
 --R                                               2                2
---I                     (- 98304%%BC0 + 3072)%%BC1  + (- 98304%%BC0  - 192)%%BC1
+--I                     (- 98304%%BQ0 + 3072)%%BQ1  + (- 98304%%BQ0  - 192)%%BQ1
 --R                   + 
 --R                                 3
---I                     - 98304%%BC0  - 768%%BC0 + 36
+--I                     - 98304%%BQ0  - 768%%BQ0 + 36
 --R                *
 --R                    +------+
---I                   \|4%%BC1
+--I                   \|4%%BQ1
 --R               + 
 --R                                         2              2
---I                 (12288%%BC0 - 1536)%%BC1  + (12288%%BC0  - 48)%%BC1
+--I                 (12288%%BQ0 - 1536)%%BQ1  + (12288%%BQ0  - 48)%%BQ1
 --R               + 
 --R                           3
---I                 12288%%BC0  + 96%%BC0 + 9
+--I                 12288%%BQ0  + 96%%BQ0 + 9
 --R     + 
 --R          +------+
---I         \|4%%BC1
+--I         \|4%%BQ1
 --R      *
 --R         log
 --R                           +-+             +-+      2
---I                  (- 98304\|2 %%BC0 + 3072\|2 )%%BC1
+--I                  (- 98304\|2 %%BQ0 + 3072\|2 )%%BQ1
 --R                + 
 --R                           +-+     2       +-+               +-+     3
---I                  (- 98304\|2 %%BC0  - 192\|2 )%%BC1 - 98304\|2 %%BC0
+--I                  (- 98304\|2 %%BQ0  - 192\|2 )%%BQ1 - 98304\|2 %%BQ0
 --R                + 
 --R                        +-+           +-+
---I                  - 768\|2 %%BC0 + 36\|2
+--I                  - 768\|2 %%BQ0 + 36\|2
 --R             *
 --R                 +------+
---I                \|4%%BC1
+--I                \|4%%BQ1
 --R            + 
 --R                                      2              2                        3
---I              (12288%%BC0 - 1536)%%BC1  + (12288%%BC0  - 48)%%BC1 + 12288%%BC0
+--I              (12288%%BQ0 - 1536)%%BQ1  + (12288%%BQ0  - 48)%%BQ1 + 12288%%BQ0
 --R            + 
---I              96%%BC0 + 18
+--I              96%%BQ0 + 18
 --R     + 
 --R          +------+
---I         \|4%%BC0
+--I         \|4%%BQ0
 --R      *
 --R         log
 --R                       +-+     3        +-+     2       +-+           +-+
---I                (98304\|2 %%BC0  + 3072\|2 %%BC0  + 576\|2 %%BC0 - 60\|2 )
+--I                (98304\|2 %%BQ0  + 3072\|2 %%BQ0  + 576\|2 %%BQ0 - 60\|2 )
 --R             *
 --R                 +------+
---I                \|4%%BC0
+--I                \|4%%BQ0
 --R            + 
 --R                          3            2
---I              - 12288%%BC0  - 1536%%BC0  - 144%%BC0 + 30
+--I              - 12288%%BQ0  - 1536%%BQ0  - 144%%BQ0 + 30
 --R     + 
 --R       -
 --R             +------+
---I            \|4%%BC0
+--I            \|4%%BQ0
 --R         *
 --R            log
 --R                            3            2                  +------+
---I                 (98304%%BC0  + 3072%%BC0  + 576%%BC0 - 60)\|4%%BC0
+--I                 (98304%%BQ0  + 3072%%BQ0  + 576%%BQ0 - 60)\|4%%BQ0
 --R               + 
 --R                             3            2
---I                 - 12288%%BC0  - 1536%%BC0  - 144%%BC0 + 21
+--I                 - 12288%%BQ0  - 1536%%BQ0  - 144%%BQ0 + 21
 --R     + 
 --R          +------+
---I         \|4%%BC0
+--I         \|4%%BQ0
 --R      *
 --R         log
 --R                           3            2                  +------+
---I              (- 98304%%BC0  - 3072%%BC0  - 576%%BC0 + 60)\|4%%BC0
+--I              (- 98304%%BQ0  - 3072%%BQ0  - 576%%BQ0 + 60)\|4%%BQ0
 --R            + 
 --R                          3            2
---I              - 12288%%BC0  - 1536%%BC0  - 144%%BC0 + 21
+--I              - 12288%%BQ0  - 1536%%BQ0  - 144%%BQ0 + 21
 --R     + 
 --R       -
 --R             +------+
---I            \|4%%BC0
+--I            \|4%%BQ0
 --R         *
 --R            log
 --R                            +-+     3        +-+     2       +-+           +-+
---I                   (- 98304\|2 %%BC0  - 3072\|2 %%BC0  - 576\|2 %%BC0 + 60\|2 )
+--I                   (- 98304\|2 %%BQ0  - 3072\|2 %%BQ0  - 576\|2 %%BQ0 + 60\|2 )
 --R                *
 --R                    +------+
---I                   \|4%%BC0
+--I                   \|4%%BQ0
 --R               + 
 --R                             3            2
---I                 - 12288%%BC0  - 1536%%BC0  - 144%%BC0 + 30
+--I                 - 12288%%BQ0  - 1536%%BQ0  - 144%%BQ0 + 30
 --R  /
 --R     4
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 37
+--E 27
 
---S 38 of 267
+--S 28 of 224
 in1186a:=integrate((z^2+z)^(1/2)/(1+z^2)^2, z= 0..1,"noPole")
 --R 
 --R
---R   (37)
+--R   (28)
 --R             +-+      4+-+    %pi
 --R         (17\|2  - 24)\|2 cos(---)
 --R                               8
@@ -1416,13 +1270,13 @@ in1186a:=integrate((z^2+z)^(1/2)/(1+z^2)^2, z= 0..1,"noPole")
 --R         +-+
 --R     384\|2  - 544
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 38
+--E 28
 
---S 39 of 267
+--S 29 of 224
 in1190a:=integrate(sin(z)^2*tan(z)^(1/2), z= 0..1,"noPole")
 --R 
 --R
---R   (38)
+--R   (29)
 --R                                                                   +------+
 --R                     3                             4            2  |sin(1)
 --R           ((96cos(1)  + 24cos(1))sin(1) - 96cos(1)  + 120cos(1) ) |------
@@ -1566,13 +1420,13 @@ in1190a:=integrate(sin(z)^2*tan(z)^(1/2), z= 0..1,"noPole")
 --R                                      4             2
 --R       - 1024cos(1)sin(1) + 2048cos(1)  - 2048cos(1)  - 64
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 39
+--E 29
 
---S 40 of 267
+--S 30 of 224
 in1191a:=integrate(sin(z)^2/tan(z)^(1/2), z= 0..1,"noPole")
 --R 
 --R
---R   (39)
+--R   (30)
 --R                                                                   +------+
 --R                       3                            4           2  |sin(1)
 --R           ((- 32cos(1)  - 8cos(1))sin(1) + 32cos(1)  - 40cos(1) ) |------
@@ -1711,29 +1565,29 @@ in1191a:=integrate(sin(z)^2/tan(z)^(1/2), z= 0..1,"noPole")
 --R                                      4             2
 --R       - 1024cos(1)sin(1) + 2048cos(1)  - 2048cos(1)  - 64
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 40
+--E 30
 
---S 41 of 267
+--S 31 of 224
 in1193a:=integrate(-sin(z)^2*cot(z-1), z= 0..1,"noPole")
 --R 
 --R
---R   (40)   + infinity
+--R   (31)   + infinity
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 41
+--E 31
 
---S 42 of 267
+--S 32 of 224
 in1207:=integrate(sin(z)*cos(z)*tan(z)^(1/2), z= 0..1)
 --R 
 --R
---R   (41)  potentialPole
+--R   (32)  potentialPole
 --R                                         Type: Union(pole: potentialPole,...)
---E 42
+--E 32
 
---S 43 of 267
+--S 33 of 224
 in1207a:=integrate(sin(z)*cos(z)*tan(z)^(1/2), z= 0..1,"noPole")
 --R 
 --R
---R   (42)
+--R   (33)
 --R                                                                   +------+
 --R                       3                            4           2  |sin(1)
 --R           ((- 32cos(1)  - 8cos(1))sin(1) + 32cos(1)  - 40cos(1) ) |------
@@ -1872,21 +1726,21 @@ in1207a:=integrate(sin(z)*cos(z)*tan(z)^(1/2), z= 0..1,"noPole")
 --R                                      4             2
 --R       - 1024cos(1)sin(1) + 2048cos(1)  - 2048cos(1)  - 64
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 43
+--E 33
 
---S 44 of 267
+--S 34 of 224
 in1210a:=integrate(-sin(z)*cos(z)*cot(z-1), z= 0..1,"noPole")
 --R 
 --R
---R   (43)   + infinity
+--R   (34)   + infinity
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 44
+--E 34
 
---S 45 of 267
+--S 35 of 224
 in1214a:=integrate(-sin(z)*tan(z)*csc(z-1), z= 0..1,"noPole")
 --R 
 --R
---R   (44)
+--R   (35)
 --R              1 2    1 2
 --R         4cos(-) sin(-)
 --R              2      2
@@ -1935,13 +1789,13 @@ in1214a:=integrate(-sin(z)*tan(z)*csc(z-1), z= 0..1,"noPole")
 --R     2sin(-)  - 2cos(-)
 --R          2          2
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 45
+--E 35
 
---S 46 of 267
+--S 36 of 224
 in1217a:=integrate(sin(z)*sec(z)*tan(z)^(1/2), z= 0..1,"noPole")
 --R 
 --R
---R   (45)
+--R   (36)
 --R                  +------+
 --R                  |sin(1)                        +-+
 --R         (2cos(1) |------  + (- sin(1) - cos(1))\|2 )
@@ -2039,13 +1893,13 @@ in1217a:=integrate(sin(z)*sec(z)*tan(z)^(1/2), z= 0..1,"noPole")
 --R     16cos(1)\|2  |------  - 16sin(1) - 16cos(1)
 --R                 \|cos(1)
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 46
+--E 36
 
---S 47 of 267
+--S 37 of 224
 in1218a:=integrate(sin(z)*sec(z)/tan(z)^(1/2), z= 0..1,"noPole")
 --R 
 --R
---R   (46)
+--R   (37)
 --R           +-+
 --R         2\|2
 --R      *
@@ -2100,32 +1954,21 @@ in1218a:=integrate(sin(z)*sec(z)/tan(z)^(1/2), z= 0..1,"noPole")
 --R  /
 --R     16
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 47
+--E 37
 
---S 48 of 267
+--S 38 of 224
 in1a:=integrate(log(abs(z^2-1))/(1+z)^2, z= 0..%plusInfinity,"noPole")
 --R 
 --R
---R   (47)  1
+--R   (38)  1
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 48
-
---S 49 of 267
-in13:=integrate(cos(z)^2*sin(z)^n, z)
---R 
---R
---R            z
---R          ++         2       n
---I   (48)   |   cos(%K) sin(%K) d%K
---R         ++
---R                                          Type: Union(Expression Integer,...)
---E 49
+--E 38
 
---S 50 of 267
+--S 39 of 224
 in15ab:=integrate(log(sqrt(z)+z^5), z=0..a,"noPole")
 --R 
 --R
---R   (49)
+--R   (39)
 --R              %pi
 --R         6cos(---)
 --R               9
@@ -2295,66 +2138,58 @@ in15ab:=integrate(log(sqrt(z)+z^5), z=0..a,"noPole")
 --R  /
 --R     12
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 50
+--E 39
 
---S 51 of 267
+--S 40 of 224
 in20a:=integrate(log(sin(z)^2+cos(z)^2), z= 0..1,"noPole")
 --R 
 --R
---R   (50)  0
+--R   (40)  0
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 51
+--E 40
 
---S 52 of 267
+--S 41 of 224
 in126a:=integrate(atan(1/cot(z)), z= 0..2*%pi,"noPole")
 --R 
 --R
 --R             2
---R   (51)  2%pi
+--R   (41)  2%pi
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 52
+--E 41
 
---S 53 of 267
+--S 42 of 224
 in128a:=integrate(atan(sqrt(1-cos(z)^2)/(1+cos(z))), z= 0..1,"noPole")
 --R 
 --R
 --R         1
---R   (52)  -
+--R   (42)  -
 --R         4
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 53
-
---S 54 of 267
-in134:=integrate(log(exp(z)), z= -I..I)
---R 
---R
---R   (53)  0
---R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 54
+--E 42
 
---S 55 of 267
+--S 43 of 224
 in134a:=integrate(log(exp(z)), z= -%i..%i)
 --R 
 --R
---R   (54)  0
+--R   (43)  0
 --R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
---E 55
+--E 43
 
---S 56 of 267
+--S 44 of 224
 in1221a:=integrate(sin(z)*csc(z)*acoth(1/z), z= 0..1,"noPole")
 --R 
 --R
 --R         log(4)
---R   (55)  ------
+--R   (44)  ------
 --R            2
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 56
+--E 44
 
---S 57 of 267
+--S 45 of 224
 in1228a:=integrate(sin(z)*csc(z)*tan(z)^(1/2), z= 0..1,"noPole")
 --R 
 --R
---R   (56)
+--R   (45)
 --R           +-+
 --R         2\|2
 --R      *
@@ -2409,23 +2244,23 @@ in1228a:=integrate(sin(z)*csc(z)*tan(z)^(1/2), z= 0..1,"noPole")
 --R  /
 --R     16
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 57
+--E 45
 
---S 58 of 267
+--S 46 of 224
 in1241a:=integrate(sin(z)*csc(z)*acoth(1/z), z= 0..1,"noPole")
 --R 
 --R
 --R         log(4)
---R   (57)  ------
+--R   (46)  ------
 --R            2
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 58
+--E 46
 
---S 59 of 267
+--S 47 of 224
 in1248a:=integrate(sin(z)*csc(z)*tan(z)^(1/2), z= 0..1,"noPole")
 --R 
 --R
---R   (58)
+--R   (47)
 --R           +-+
 --R         2\|2
 --R      *
@@ -2480,13 +2315,13 @@ in1248a:=integrate(sin(z)*csc(z)*tan(z)^(1/2), z= 0..1,"noPole")
 --R  /
 --R     16
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 59
+--E 47
 
---S 60 of 267
+--S 48 of 224
 in1261a:=integrate(1/(sin(z)+cos(2*z)), z= -1..1,"noPole")
 --R 
 --R
---R   (59)
+--R   (48)
 --R                  2         2
 --R         (- sin(1)  + cos(1)  + 2cos(1) + 1)
 --R      *
@@ -2529,119 +2364,111 @@ in1261a:=integrate(1/(sin(z)+cos(2*z)), z= -1..1,"noPole")
 --R             2          2                +-+
 --R     (3sin(1)  - 3cos(1)  - 6cos(1) - 3)\|3
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 60
-
---S 61 of 267
-in1273a:=integrate((1/(z-I))^(1/2), z= 0..%plusInfinity,"noPole")
---R 
---R
---R   (60)   + infinity
---R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 61
+--E 48
 
---S 62 of 267
-in1274a:=integrate(1/(1/(z-I))^(1/2), z= 0..%plusInfinity,"noPole")
+--S 49 of 224
+in1273a:=integrate((1/(z-%i))^(1/2), z= 0..%plusInfinity,"noPole")
 --R 
 --R
---R   (61)   + infinity
---R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 62
+--R   (49)   + infinity
+--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
+--E 49
 
---S 63 of 267
-in1278a:=integrate((1+1/(I*z)^(1/2))^(1/2), z= 0..%plusInfinity,"noPole")
+--S 50 of 224
+in1274a:=integrate(1/(1/(z-%i))^(1/2), z= 0..%plusInfinity,"noPole")
 --R 
 --R
---R   (62)   + infinity
---R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 63
+--R   (50)   + infinity
+--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
+--E 50
 
---S 64 of 267
+--S 51 of 224
 in1284a:=integrate(log(1+2^(1/2)/z^(1/4)-1/z^(1/2)), z= 0..%plusInfinity,"noPole")
 --R 
 --R
---R   (63)   + infinity
+--R   (51)   + infinity
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 64
+--E 51
 
---S 65  of 267
+--S 52 of 224
 in1314a:=integrate(log(1-z)*atanh(z^(1/2)), z= 0..1,"noPole")
 --R 
 --R
 --R         log(16) - 6
---R   (64)  -----------
+--R   (52)  -----------
 --R              2
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 65
+--E 52
 
---S 66 of 267
-in1359a:=integrate((I*z)^(1/2)*(-I*z)^(1/2), z= %minusInfinity..%plusInfinity,"noPole")
+--S 53 of 224
+in1359a:=integrate((%i*z)^(1/2)*(-%i*z)^(1/2), z= %minusInfinity..%plusInfinity,"noPole")
 --R 
 --R
---R   (65)   + infinity
---R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 66
+--R   (53)   + infinity
+--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
+--E 53
 
---S 67 of 267
+--S 54 of 224
 in1376a:=integrate(z*acoth(z^(1/2)), z= 0..1,"noPole")
 --R 
 --R
 --R         2
---R   (66)  -
+--R   (54)  -
 --R         3
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 67
+--E 54
 
---S 68 of 267
+--S 55 of 224
 in1377a:=integrate(z*acoth(1-z), z= 0..1,"noPole")
 --R 
 --R
 --R         log(4) - 1
---R   (67)  ----------
+--R   (55)  ----------
 --R              2
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 68
+--E 55
 
---S 69 of 267
+--S 56 of 224
 in1378a:=integrate(z*acoth(1-(1-z)^(1/2)), z= 0..1,"noPole")
 --R 
 --R
 --R         - 3log(4) + 5
---R   (68)  -------------
+--R   (56)  -------------
 --R               3
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 69
+--E 56
 
---S 70 of 267
+--S 57 of 224
 in1392a:=integrate(acoth(z^(1/2)), z= 0..1,"noPole")
 --R 
 --R
---R   (69)  1
+--R   (57)  1
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 70
+--E 57
 
---S 71 of 267
+--S 58 of 224
 in1397a:=integrate(1/(-1+z^(1/2))^(1/2), z= 1..2,"noPole")
 --R 
 --R
 --R                     +--------+
 --R            +-+      | +-+
 --R         (4\|2  + 8)\|\|2  - 1
---R   (70)  ----------------------
+--R   (58)  ----------------------
 --R                    3
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 71
+--E 58
 
---S 72 of 267
+--S 59 of 224
 in1398a:=integrate(acoth(1/z), z= 1..2,"noPole")
 --R 
 --R
 --R         3log(9) - 2log(4)
---R   (71)  -----------------
+--R   (59)  -----------------
 --R                 4
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 72
+--E 59
 
---S 73 of 267
+--S 60 of 224
 in1399a:=integrate(acoth(1/z^(1/2)), z= 1..2,"noPole")
 --R 
 --R
@@ -2650,16 +2477,16 @@ in1399a:=integrate(acoth(1/z^(1/2)), z= 1..2,"noPole")
 --R         log(-----------) + 4\|2  - 4
 --R                +-+
 --R              2\|2  - 3
---R   (72)  ----------------------------
+--R   (60)  ----------------------------
 --R                       4
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 73
+--E 60
 
---S 74 of 267
+--S 61 of 224
 in143a:=integrate(sqrt(1+z)/(1+z^2), z= 0..1,"noPole")
 --R 
 --R
---R   (73)
+--R   (61)
 --R         4+-+    %pi
 --R         \|2 cos(---)
 --R                  8
@@ -2758,928 +2585,1256 @@ in143a:=integrate(sqrt(1+z)/(1+z^2), z= 0..1,"noPole")
 --R  /
 --R     4
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 74
+--E 61
 
---S 75 of 267
-in144:=integrate(1, z= I*infinity..%plusInfinity)
+--S 62 of 224
+in144:=integrate(1, z= %i*infinity..%plusInfinity)
 --R 
 --R
---R   (74)   + infinity
---R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 75
+--R   (62)   + infinity
+--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
+--E 62
 
---S 76 of 267
-in146a:=integrate(csc(z), z= 1-I..1+I,"noPole")
+--S 63 of 224
+in146a:=integrate(csc(z), z= 1-%i..1+%i,"noPole")
 --R 
 --R
---R   (75)
---R                          2                                    2
---R                sin(I + 1)                           sin(I - 1)
---R   log(-----------------------------) - log(-----------------------------)
---R                 2                                    2
---R       cos(I + 1)  + 2cos(I + 1) + 1        cos(I - 1)  + 2cos(I - 1) + 1
---R   -----------------------------------------------------------------------
---R                                      2
---R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 76
+--R   (63)
+--R                            2                                      2
+--R                 sin(1 + %i)                            sin(1 - %i)
+--R   log(-------------------------------) - log(-------------------------------)
+--R                  2                                      2
+--R       cos(1 + %i)  + 2cos(1 + %i) + 1        cos(1 - %i)  + 2cos(1 - %i) + 1
+--R   ---------------------------------------------------------------------------
+--R                                        2
+--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
+--E 63
 
---S 77 of 267
+--S 64 of 224
 in148:=integrate(min(1,z), z= 0..2)
 --R 
 --R
---R   (76)  2
+--R   (64)  2
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 77
+--E 64
 
---S 78 of 267
+--S 65 of 224
 in156a:=integrate(z^(2/3), z= 1..10,"noPole")
 --R 
 --R
 --R           3+--+2
 --R         30\|10   - 3
---R   (77)  ------------
+--R   (65)  ------------
 --R               5
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 78
-
---S 79 of 267
-in159a:=integrate(log(z)/z^2, z= -I..-1,"noPole")
---R 
---R
---R                2
---R         - log(I ) + 2I - 2
---R   (78)  ------------------
---R                 2I
---R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 79
-
---S 80 of 267
-in160:=integrate((-z^2-z)^sin(z), z)
---R 
---R
---R            z
---I          ++       2      sin(%K)
---I   (79)   |   (- %K  - %K)       d%K
---R         ++
---R                                          Type: Union(Expression Integer,...)
---E 80
-
---S 81 of 267
-in1425a:=integrate(-(z^2+I*z+3)/(z^2+I*z+2), z= 0..%plusInfinity,"noPole")
---R 
---R
---R   (80)  [- infinity,- infinity]
---R               Type: Union(f2: List OrderedCompletion Expression Integer,...)
---E 81
-
---S 82 of 267
-in1426a:=integrate(-I/(1+I*z^3)*z^3, z= 0..%plusInfinity,"noPole")
---R 
---R
---R   (81)  - infinity
---R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 82
-
---S 83 of 267
-in1428a:=integrate(-I/(1+I*z)*z, z= 0..%plusInfinity,"noPole")
---R 
---R
---R   (82)  - infinity
---R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 83
+--E 65
 
---S 84 of 267
-in1432:=integrate(-(z+I)*(-1+1/(z+I)), z= 0..%plusInfinity)
+--S 66 of 224
+in1425a:=integrate(-(z^2+%i*z+3)/(z^2+%i*z+2), z= 0..%plusInfinity,"noPole")
 --R 
 --R
---R   (83)   + infinity
---R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 84
+--R   (66)  - infinity
+--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
+--E 66
 
---S 85 of 267
-in1433a:=integrate(-1/((I*z)^(1/2)-1)*(-2+(I*z)^(1/2)), z= 0..%plusInfinity,"noPole")
+--S 67 of 224
+in1426a:=integrate(-%i/(1+%i*z^3)*z^3, z= 0..%plusInfinity,"noPole")
 --R 
 --R
---R   (84)  - infinity
---R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 85
+--R   (67)  - infinity
+--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
+--E 67
 
---S 86 of 267
-in1434a:=integrate(-(1+(I*z)^(1/2))/(I*z)^(1/2), z= 0..%plusInfinity,"noPole")
+--S 68 of 224
+in1428a:=integrate(-%i/(1+%i*z)*z, z= 0..%plusInfinity,"noPole")
 --R 
 --R
---R   (85)  - infinity
---R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 86
+--R   (68)  - infinity
+--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
+--E 68
 
---S 87 of 267
-in1435a:=integrate(-1/(1+(I*z)^(1/2))*(I*z)^(1/2), z= 0..%plusInfinity,"noPole")
+--S 69 of 224
+in1432:=integrate(-(z+%i)*(-1+1/(z+%i)), z= 0..%plusInfinity)
 --R 
 --R
---R   (86)  - infinity
---R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 87
+--R   (69)   + infinity
+--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
+--E 69
 
---S 88 of 267
-in1436a:=integrate(-((I*z)^(1/2)-1)/(-2+(I*z)^(1/2)), z= 0..%plusInfinity,"noPole")
+--S 70 of 224
+in1434a:=integrate(-(1+(%i*z)^(1/2))/(%i*z)^(1/2), z= 0..%plusInfinity,"noPole")
 --R 
 --R
---R   (87)  - infinity
---R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 88
+--R   (70)  - infinity
+--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
+--E 70
 
---S 89 of 267
-in1440a:=integrate((1-(I*z)^(1/2))/(I*z)^(1/2), z= 0..%plusInfinity,"noPole")
+--S 71 of 224
+in1440a:=integrate((1-(%i*z)^(1/2))/(%i*z)^(1/2), z= 0..%plusInfinity,"noPole")
 --R 
 --R
---R   (88)  - infinity
---R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 89
+--R   (71)  - infinity
+--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
+--E 71
 
---S 90 of 267
-in1460:=integrate(z^2+I*z+3, z= 0..%plusInfinity)
+--S 72 of 224
+in1460:=integrate(z^2+%i*z+3, z= 0..%plusInfinity)
 --R 
 --R
---R   (89)   + infinity
---R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 90
+--R   (72)   + infinity
+--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
+--E 72
 
---S 91 of 267
-in1463a:=integrate(1-(I*z)^(1/2)/(1-I*z), z= 0..%plusInfinity,"noPole")
+--S 73 of 224
+in1464a:=integrate(1+1/(%i*z)^(1/2), z= 0..%plusInfinity,"noPole")
 --R 
 --R
---R   (90)   + infinity
---R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 91
+--R   (73)   + infinity
+--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
+--E 73
 
---S 92 of 267
-in1464a:=integrate(1+1/(I*z)^(1/2), z= 0..%plusInfinity,"noPole")
+--S 74 of 224
+in2045:=integrate(atan(1/tan(z)), z= 0..2*%pi,"noPole")
 --R 
 --R
---R   (91)   + infinity
+--R               2
+--R   (74)  - 3%pi
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 92
-
---S 93 of 267 used to work
-in2045:=integrate(atan(1/tan(z)), z= 0..2*Pi)
---R 
---R   There are 34 exposed and 23 unexposed library operations named * 
---R      having 2 argument(s) but none was determined to be applicable. 
---R      Use HyperDoc Browse, or issue
---R                                )display op *
---R      to learn more about the available operations. Perhaps 
---R      package-calling the operation or using coercions on the arguments
---R      will allow you to apply the operation.
---R 
---RDaly Bug
---R   Cannot find a definition or applicable library operation named * 
---R      with argument type(s) 
---R                               PositiveInteger
---R                                   Domain
---R      
---R      Perhaps you should use "@" to indicate the required return type, 
---R      or "$" to specify which version of the function you need.
---E 93
---
---        2  
---  - 3%pi
---                  Type: Union(f1: OrderedCompletion Expression Integer,...)
+--E 74
 
---S 94 of 267
+--S 75 of 224
 in1502a:=integrate(log(z)^2*log(-z), z= 0..%plusInfinity,"noPole")
 --R 
 --R
---R   (92)   + infinity
+--R   (75)   + infinity
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 94
-
---S 94 of 267
-in1512a:=integrate(log(z)*(1/(z-I))^(1/2), z= 1..%plusInfinity,"noPole")
---R 
---R
---R   (93)  [ + infinity, + infinity]
---R               Type: Union(f2: List OrderedCompletion Expression Integer,...)
---E 94
+--E 75
 
---S 96 of 267
-in1513a:=integrate(log(z)*(1/(z+I))^(1/2), z= 1..%plusInfinity,"noPole")
+--S 76 of 224
+in1512a:=integrate(log(z)*(1/(z-%i))^(1/2), z= 1..%plusInfinity,"noPole")
 --R 
 --R
---R   (94)  [ + infinity, + infinity]
---R               Type: Union(f2: List OrderedCompletion Expression Integer,...)
---E 96
+--R   (76)  [ + infinity, + infinity]
+--R       Type: Union(f2: List OrderedCompletion Expression Complex Integer,...)
+--E 76
 
---S 97 of 267
-in1514a:=integrate(log(z)/(I/(z-I))^(1/2), z= 1..%plusInfinity,"noPole")
+--S 77 of 224
+in1513a:=integrate(log(z)*(1/(z+%i))^(1/2), z= 1..%plusInfinity,"noPole")
 --R 
 --R
---R   (95)   + infinity
---R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 97
+--R   (77)  [ + infinity, + infinity]
+--R       Type: Union(f2: List OrderedCompletion Expression Complex Integer,...)
+--E 77
 
---S 98 of 267
-in1563a:=integrate(log(1-z^3)*(I*z)^(1/2), z= 0..1,"noPole")
+--S 78 of 224
+in1514a:=integrate(log(z)/(%i/(z-%i))^(1/2), z= 1..%plusInfinity,"noPole")
 --R 
 --R
---R                  2
---R               16I          2                +-+
---R          (log(----) - log(I ) + log(9) - 4)\|I
---R                 9
---R   (96)  [--------------------------------------,- infinity]
---R                             3
---R               Type: Union(f2: List OrderedCompletion Expression Integer,...)
---E 98
+--R   (78)   + infinity
+--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
+--E 78
 
---S 99 of 267
+--S 79 of 224
 in161:=integrate((-z^2)^(1/3), z)
 --R 
 --R
 --R            +----+
 --R           3|   2
 --R         3z\|- z
---R   (97)  ---------
+--R   (79)  ---------
 --R             5
 --R                                          Type: Union(Expression Integer,...)
---E 99
-
---S 100 of 267
-in163:=integrate(log(z)*abs(exp(z)/z), z)
---R 
---R
---I            z              %K
---R          ++             %e
---I   (98)   |   log(%K)abs(----)d%K
---I         ++               %K
---R                                          Type: Union(Expression Integer,...)
---E 100
-
---S 101 of 267
-in166:=integrate((1+z)^z, z)
---R 
---R
---R            z
---I          ++          %K
---I   (99)   |   (%K + 1)  d%K
---R         ++
---R                                          Type: Union(Expression Integer,...)
---E 101
+--E 79
 
---S 102 of 267
+--S 80 of 224
 in179:=integrate(1/(1+(3*z+1)^2), z)
 --R 
 --R
---R          atan(3z + 1)
---R   (100)  ------------
---R                3
+--R         atan(3z + 1)
+--R   (80)  ------------
+--R               3
 --R                                          Type: Union(Expression Integer,...)
---E 102
+--E 80
 
---S 103 of 267
-in1636a:=integrate(-z/(z-1)/(1/(z-I))^(1/2), z= 0..1,"noPole")
+--S 81 of 224
+in1636a:=integrate(-z/(z-1)/(1/(z-%i))^(1/2), z= 0..1,"noPole")
 --R 
 --R
---R   (101)
+--R   (81)
 --R   [ + infinity,
 --R
---R                         +-------+                    +---+
---R           +-----+      \|- I + 1       +-----+      \|- I
---R         6\|I - 1 log(- ----------) - 6\|I - 1 atan(--------)
---R                           +-----+                   +-----+
---R                         2\|I - 1                   \|I - 1
+--R                               +------+                           +----+
+--R           +---------+        \|1 - %i        +---------+       2\|- %i
+--R         3\|- 4 + 4%i log(- ------------) - 3\|- 4 + 4%i atan(------------)
+--R                             +---------+                       +---------+
+--R                            \|- 4 + 4%i                       \|- 4 + 4%i
 --R       + 
---R                  +-------+              +---+
---R         (2I - 8)\|- I + 1  + (- 2I + 6)\|- I
+--R                     +------+             +----+
+--R         (- 8 + 2%i)\|1 - %i  + (6 - 2%i)\|- %i
 --R    /
 --R       3
 --R     ]
---R               Type: Union(f2: List OrderedCompletion Expression Integer,...)
---E 103
-
---S 104 of 267
-in1638a:=integrate(-z/(z-1)/(1-I*z)^(1/2), z= 0..1,"noPole")
---R 
---R
---R   (102)
---R   [ + infinity,
---R
---R                     +-------+ +-----+             +-----+
---R                    \|- I + 1 \|I - 1             \|I - 1
---R         - 2I log(- ------------------) + 2I atan(--------)
---R                          2I - 2                    I - 1
---R       + 
---R            +-------+      +-----+
---R         (2\|- I + 1  - 2)\|I - 1
---R    /
---R         +-----+
---R       I\|I - 1
---R     ]
---R               Type: Union(f2: List OrderedCompletion Expression Integer,...)
---E 104
+--R       Type: Union(f2: List OrderedCompletion Expression Complex Integer,...)
+--E 81
 
---S 105 of 267
-in1639a:=integrate(-z/(z-1)/(1-I*z^2)^(1/2), z= 0..1,"noPole")
+--S 82 of 224
+in1639a:=integrate(-z/(z-1)/(1-%i*z^2)^(1/2), z= 0..1,"noPole")
 --R 
 --R
---R   (103)
---R   [ + infinity,
---R
---R            +-----+
---R           \|I - 1
---R        *
---R           log
---R                      2       +---+     2       +-------+        2       +---+
---R                  ((2I  - 4I)\|- I  + 4I  - 2I)\|- I + 1  + (- 4I  + 4I)\|- I
---R                + 
---R                    3     2
---R                  2I  - 5I  + 2I
---R             /
---R                  +-------+
---R                2\|- I + 1  + I - 2
---R       + 
---R                        +-------+          +-----+                 +-----+
---R           +---+    (- \|- I + 1  - I + 1)\|I - 1       +---+     \|I - 1
---R         4\|- I log(------------------------------) + 4\|- I atan(--------)
---R                               +-------+                            I - 1
---R                      (2I - 2)\|- I + 1  - 2I + 2
---R       + 
---R                    +-----+
---R         - log(- I)\|I - 1
---R    /
---R         +---+ +-----+
---R       2\|- I \|I - 1
---R     ,
---R     + infinity,
---R
---R                      +-------+          +-----+
---R           +-+    (- \|- I + 1  - I + 1)\|I - 1
---R         2\|I log(------------------------------)
---R                             +-------+
---R                    (2I - 2)\|- I + 1  - 2I + 2
---R       + 
---R                         +-------+      +-+               +-----+
---R           +-----+     (\|- I + 1  - 1)\|I       +-+     \|I - 1
---R         2\|I - 1 atan(--------------------) + 2\|I atan(--------)
---R                                 I                         I - 1
---R    /
---R        +-----+ +-+
---R       \|I - 1 \|I
---R     ]
---R               Type: Union(f2: List OrderedCompletion Expression Integer,...)
---E 105
+--R   (82)
+--R          +------------------------+
+--R          |          +-+     +----+
+--R          |(1 + 3%i)\|2  + 2\|- %i
+--R          |------------------------
+--R          |           +-+
+--R         \|          \|2
+--R      *
+--R         log
+--R                        +------+         +-+               +----+ +------+
+--R                    (16\|1 - %i  - 16%i)\|2  + (48 - 16%i)\|- %i \|1 - %i
+--R                  + 
+--R                                  +----+
+--R                    (- 16 + 16%i)\|- %i
+--R               *
+--R                   +------------------------+
+--R                   |          +-+     +----+
+--R                   |(1 + 3%i)\|2  + 2\|- %i
+--R                   |------------------------
+--R                   |           +-+
+--R                  \|          \|2
+--R              + 
+--R                      +------+              +-+               +----+ +------+
+--R                (- 32\|1 - %i  + 64 - 64%i)\|2  + (32 + 32%i)\|- %i \|1 - %i
+--R           /
+--R               +-+
+--R              \|2
+--R     + 
+--R       -
+--R             +------------------------+
+--R             |          +-+     +----+
+--R             |(1 + 3%i)\|2  + 2\|- %i
+--R             |------------------------
+--R             |           +-+
+--R            \|          \|2
+--R         *
+--R            log
+--R                                                 +------------------------+
+--R                                                 |          +-+     +----+
+--R                                +-+      +----+  |(1 + 3%i)\|2  + 2\|- %i
+--R                   ((16 - 16%i)\|2  + 32\|- %i ) |------------------------
+--R                                                 |           +-+
+--R                                                \|          \|2
+--R                 + 
+--R                               +-+               +----+
+--R                   (32 - 32%i)\|2  + (32 + 32%i)\|- %i
+--R              /
+--R                  +-+
+--R                 \|2
+--R     + 
+--R          +------------------------+
+--R          |          +-+     +----+
+--R          |(1 + 3%i)\|2  - 2\|- %i
+--R          |------------------------
+--R          |           +-+
+--R         \|          \|2
+--R      *
+--R         log
+--R                        +------+         +-+                 +----+ +------+
+--R                    (16\|1 - %i  - 16%i)\|2  + (- 48 + 16%i)\|- %i \|1 - %i
+--R                  + 
+--R                                +----+
+--R                    (16 - 16%i)\|- %i
+--R               *
+--R                   +------------------------+
+--R                   |          +-+     +----+
+--R                   |(1 + 3%i)\|2  - 2\|- %i
+--R                   |------------------------
+--R                   |           +-+
+--R                  \|          \|2
+--R              + 
+--R                      +------+              +-+                 +----+ +------+
+--R                (- 32\|1 - %i  + 64 - 64%i)\|2  + (- 32 - 32%i)\|- %i \|1 - %i
+--R           /
+--R               +-+
+--R              \|2
+--R     + 
+--R       -
+--R             +------------------------+
+--R             |          +-+     +----+
+--R             |(1 + 3%i)\|2  - 2\|- %i
+--R             |------------------------
+--R             |           +-+
+--R            \|          \|2
+--R         *
+--R            log
+--R                                                 +------------------------+
+--R                                                 |          +-+     +----+
+--R                                +-+      +----+  |(1 + 3%i)\|2  - 2\|- %i
+--R                   ((16 - 16%i)\|2  - 32\|- %i ) |------------------------
+--R                                                 |           +-+
+--R                                                \|          \|2
+--R                 + 
+--R                               +-+                 +----+
+--R                   (32 - 32%i)\|2  + (- 32 - 32%i)\|- %i
+--R              /
+--R                  +-+
+--R                 \|2
+--R     + 
+--R          +------------------------+
+--R          |          +-+     +----+
+--R          |(1 + 3%i)\|2  - 2\|- %i
+--R          |------------------------
+--R          |           +-+
+--R         \|          \|2
+--R      *
+--R         log
+--R                                                +------------------------+
+--R                                                |          +-+     +----+
+--R                               +-+      +----+  |(1 + 3%i)\|2  - 2\|- %i
+--R                ((- 16 + 16%i)\|2  + 32\|- %i ) |------------------------
+--R                                                |           +-+
+--R                                               \|          \|2
+--R              + 
+--R                            +-+                 +----+
+--R                (32 - 32%i)\|2  + (- 32 - 32%i)\|- %i
+--R           /
+--R               +-+
+--R              \|2
+--R     + 
+--R       -
+--R             +------------------------+
+--R             |          +-+     +----+
+--R             |(1 + 3%i)\|2  - 2\|- %i
+--R             |------------------------
+--R             |           +-+
+--R            \|          \|2
+--R         *
+--R            log
+--R                             +------+         +-+               +----+ +------+
+--R                       (- 16\|1 - %i  + 16%i)\|2  + (48 - 16%i)\|- %i \|1 - %i
+--R                     + 
+--R                                     +----+
+--R                       (- 16 + 16%i)\|- %i
+--R                  *
+--R                      +------------------------+
+--R                      |          +-+     +----+
+--R                      |(1 + 3%i)\|2  - 2\|- %i
+--R                      |------------------------
+--R                      |           +-+
+--R                     \|          \|2
+--R                 + 
+--R                       +------+              +-+                 +----+ +------+
+--R                 (- 32\|1 - %i  + 64 - 64%i)\|2  + (- 32 - 32%i)\|- %i \|1 - %i
+--R              /
+--R                  +-+
+--R                 \|2
+--R     + 
+--R          +------------------------+
+--R          |          +-+     +----+
+--R          |(1 + 3%i)\|2  + 2\|- %i
+--R          |------------------------
+--R          |           +-+
+--R         \|          \|2
+--R      *
+--R         log
+--R                                                +------------------------+
+--R                                                |          +-+     +----+
+--R                               +-+      +----+  |(1 + 3%i)\|2  + 2\|- %i
+--R                ((- 16 + 16%i)\|2  - 32\|- %i ) |------------------------
+--R                                                |           +-+
+--R                                               \|          \|2
+--R              + 
+--R                            +-+               +----+
+--R                (32 - 32%i)\|2  + (32 + 32%i)\|- %i
+--R           /
+--R               +-+
+--R              \|2
+--R     + 
+--R       -
+--R             +------------------------+
+--R             |          +-+     +----+
+--R             |(1 + 3%i)\|2  + 2\|- %i
+--R             |------------------------
+--R             |           +-+
+--R            \|          \|2
+--R         *
+--R            log
+--R                             +------+         +-+
+--R                       (- 16\|1 - %i  + 16%i)\|2
+--R                     + 
+--R                                     +----+ +------+               +----+
+--R                       (- 48 + 16%i)\|- %i \|1 - %i  + (16 - 16%i)\|- %i
+--R                  *
+--R                      +------------------------+
+--R                      |          +-+     +----+
+--R                      |(1 + 3%i)\|2  + 2\|- %i
+--R                      |------------------------
+--R                      |           +-+
+--R                     \|          \|2
+--R                 + 
+--R                       +------+              +-+               +----+ +------+
+--R                 (- 32\|1 - %i  + 64 - 64%i)\|2  + (32 + 32%i)\|- %i \|1 - %i
+--R              /
+--R                  +-+
+--R                 \|2
+--R  /
+--R     4
+--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
+--E 82
 
---S 106 of 267
-in1712a:=integrate(-log(-z)*(-I*z)^(1/2), z= 0..1,"noPole")
+--S 83 of 224
+in1712a:=integrate(-log(-z)*(-%i*z)^(1/2), z= 0..1,"noPole")
 --R 
 --R
---R            +---+
---R          4\|- I
---R   (104)  -------
+--R           +----+
+--R         4\|- %i
+--R   (83)  --------
 --R             9
---R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 106
-
---S 107 of 267
-in1720a:=integrate(-z^2/(z^2-1)*(1/(z-I))^(1/2), z= 0..1,"noPole")
---R 
---R
---R   (105)
---R   [ + infinity,
---R
---R            +-----+         2            +-------+ +---+     3      2
---R         - \|I - 1 log((- 8I  - 12I - 4)\|- I - 1 \|- I  - 8I  - 16I  - 9I - 1)
---R       + 
---R          +-----+         2       +-------+ +-------+     3     2
---R         \|I - 1 log((- 2I  - 2I)\|- I - 1 \|- I + 1  - 2I  - 2I  + I + 1)
---R       + 
---R                             +-------+ +-----+
---R             +-------+      \|- I + 1 \|I - 1
---R         - 4\|- I - 1 log(- ------------------)
---R                                  2I - 2
---R       + 
---R                          +---+ +-----+
---R           +-------+     \|- I \|I - 1
---R         4\|- I - 1 atan(--------------)
---R                              I - 1
---R       + 
---R              +-------+ +-------+     +-------+ +---+  +-----+
---R         (- 8\|- I - 1 \|- I + 1  + 8\|- I - 1 \|- I )\|I - 1
---R    /
---R         +-------+ +-----+
---R       4\|- I - 1 \|I - 1
---R     ,
---R     + infinity,
---R
---R                          +-------+ +-----+                  +-------+ +-----+
---R            +-----+      \|- I + 1 \|I - 1      +-----+     \|- I + 1 \|I + 1
---R         - \|I + 1 log(- ------------------) + \|I - 1 atan(------------------)
---R                               2I - 2                              I + 1
---R       + 
---R                         +---+ +-----+                  +---+ +-----+
---R            +-----+     \|- I \|I + 1      +-----+     \|- I \|I - 1
---R         - \|I - 1 atan(--------------) + \|I + 1 atan(--------------)
---R                             I + 1                          I - 1
---R       + 
---R              +-------+     +---+  +-----+ +-----+
---R         (- 2\|- I + 1  + 2\|- I )\|I - 1 \|I + 1
---R    /
---R        +-----+ +-----+
---R       \|I - 1 \|I + 1
---R     ]
---R               Type: Union(f2: List OrderedCompletion Expression Integer,...)
---E 107
+--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
+--E 83
 
---S 108 of 267
-in1721a:=integrate(-z^2/(z^2-1)/(1/(z-I))^(1/2), z= 0..1,"noPole")
---R 
---R
---R   (106)
---R   [ + infinity,  + infinity,
---R
---R           +-------+       +-------+ +-------+     2
---R         3\|- I - 1 log(2I\|- I - 1 \|- I + 1  + 2I  - 1)
---R       + 
---R             +-------+             +-------+ +---+     2
---R         - 3\|- I - 1 log((8I + 4)\|- I - 1 \|- I  + 8I  + 8I + 1)
---R       + 
---R                          +-------+                     +---+
---R            +-----+      \|- I + 1        +-----+      \|- I
---R         12\|I - 1 log(- ----------) - 12\|I - 1 atan(--------)
---R                            +-----+                    +-----+
---R                          2\|I - 1                    \|I - 1
---R       + 
---R                  +-------+      +---+
---R         (8I - 8)\|- I + 1  - 8I\|- I
---R    /
---R       12
---R     ,
---R
---R                         +-------+                    +---+
---R           +-----+      \|- I + 1       +-----+      \|- I
---R         3\|I - 1 log(- ----------) - 3\|I - 1 atan(--------)
---R                           +-----+                   +-----+
---R                         2\|I - 1                   \|I - 1
---R       + 
---R                          +-------+                    +---+
---R             +-----+     \|- I + 1       +-----+      \|- I
---R         - 3\|I + 1 atan(----------) + 3\|I + 1 atan(--------)
---R                           +-----+                    +-----+
---R                          \|I + 1                    \|I + 1
---R       + 
---R                  +-------+      +---+
---R         (2I - 2)\|- I + 1  - 2I\|- I
---R    /
---R       3
---R     ]
---R               Type: Union(f2: List OrderedCompletion Expression Integer,...)
---E 108
+--S 84 of 224
+in1720a:=integrate(-z^2/(z^2-1)*(1/(z-%i))^(1/2), z= 0..1,"noPole")
+--R 
+--R
+--R   (84)
+--R            +------+              +------+
+--R            |   1                 |   1    +------+
+--R       - %i |------ log((2 - 2%i) |------ \|1 - %i  - 2%i)
+--R           \|1 + %i              \|1 + %i
+--R     + 
+--R        +------+              +------+
+--R        |  %i                 |  %i    +------+
+--R        |------ log((2 - 2%i) |------ \|1 - %i  + 2 - 2%i)
+--R       \|1 + %i              \|1 + %i
+--R     + 
+--R          +------+                     +------+
+--R          |   1                 +----+ |   1
+--R       %i |------ log((2 - 2%i)\|- %i  |------  - 1 - 2%i)
+--R         \|1 + %i                     \|1 + %i
+--R     + 
+--R          +------+              +------+
+--R          |  %i                 |  %i    +----+
+--R       -  |------ log((2 - 2%i) |------ \|- %i  + 1 - 2%i)
+--R         \|1 + %i              \|1 + %i
+--R     + 
+--R        +------+                +------+
+--R        |  %i                   |  %i    +----+
+--R        |------ log((- 2 + 2%i) |------ \|- %i  + 1 - 2%i)
+--R       \|1 + %i                \|1 + %i
+--R     + 
+--R            +------+                       +------+
+--R            |   1                   +----+ |   1
+--R       - %i |------ log((- 2 + 2%i)\|- %i  |------  - 1 - 2%i)
+--R           \|1 + %i                       \|1 + %i
+--R     + 
+--R          +------+                +------+
+--R          |  %i                   |  %i    +------+
+--R       -  |------ log((- 2 + 2%i) |------ \|1 - %i  + 2 - 2%i)
+--R         \|1 + %i                \|1 + %i
+--R     + 
+--R        +------+                +------+
+--R        |   1                   |   1    +------+            +------+     +----+
+--R     %i |------ log((- 2 + 2%i) |------ \|1 - %i  - 2%i) - 8\|1 - %i  + 8\|- %i
+--R       \|1 + %i                \|1 + %i
+--R  /
+--R     4
+--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
+--E 84
 
---S 109 of 267
-in1723a:=integrate(-z^2/(z^2-1)*(1+I/z)^(1/2), z= 0..1,"noPole")
+--S 85 of 224
+in1721a:=integrate(-z^2/(z^2-1)/(1/(z-%i))^(1/2), z= 0..1,"noPole")
 --R 
 --R
---R   (107)
---R   [ + infinity,  + infinity,
---R
---R                                                                     +-----+
---R                   +-----+                +-+      +-------+        \|I + 1
---R         - 2I log(\|I + 1  + 1) + 2I log(\|I ) + 4\|- I - 1 log(- -----------)
---R                                                                    +-------+
---R                                                                  2\|- I - 1
---R       + 
---R                   +-----+
---R         I log(- 2\|I + 1  + I + 2)
---R       + 
---R          +-------+        +-------+ +-----+    2          +-----+
---R         \|- I + 1 log(- 2\|- I + 1 \|I + 1  - I  + 2) - 4\|I + 1
---R       + 
---R                2  +-------+        +-------+
---R         - log(I )\|- I + 1  - 2%pi\|- I - 1  - I log(I)
---R    /
---R       4
---R     ,
---R
---R                                                                     +-----+
---R                   +-----+                +-+      +-------+        \|I + 1
---R         - 2I log(\|I + 1  + 1) + 2I log(\|I ) + 4\|- I - 1 log(- -----------)
---R                                                                    +-------+
---R                                                                  2\|- I - 1
---R       + 
---R                                                     +-----+
---R                   +-----+              +-----+     \|I - 1       +-----+
---R         I log(- 2\|I + 1  + I + 2) + 4\|I - 1 atan(--------) - 4\|I + 1
---R                                                     +-----+
---R                                                    \|I + 1
---R       + 
---R                +-------+
---R         - 2%pi\|- I - 1  - I log(I)
---R    /
---R       4
---R     ]
---R               Type: Union(f2: List OrderedCompletion Expression Integer,...)
---E 109
+--R   (85)   + infinity
+--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
+--E 85
 
---S 110 of 267
-in1724a:=integrate(-z^2/(z^2-1)*(1-(I*z)^(1/2))^(1/2), z= 0..1,"noPole")
+--S 86 of 224
+in1723a:=integrate(-z^2/(z^2-1)*(1+%i/z)^(1/2), z= 0..1,"noPole")
 --R 
 --R
---R                            +----------+
---R             +-+            |   +-+
---R          (4\|I  - 12I + 8)\|- \|I  + 1  - 8
---R   (108)  ----------------------------------
---R                          15I
---R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 110
+--R   (86)   + infinity
+--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
+--E 86
 
---S 111 of 267
+--S 87 of 224
 in1731:=integrate(-log(1-z^2)*atanh(z), z= 0..1)
 --R 
 --R
---R                  2
---R          - log(4)  + 4log(4)
---R   (109)  -------------------
---R                   4
+--R                 2
+--R         - log(4)  + 4log(4)
+--R   (87)  -------------------
+--R                  4
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 111
+--E 87
 
---S 112 of 267
+--S 88 of 224
 in1793a:=integrate((1-z^(1/2))^(1/2)*acoth(z^(1/2)), z= 0..1,"noPole")
 --R 
 --R
---R              +-+       +-+
---R          - 2\|2 log(12\|2  + 17) + 16
---R   (110)  ----------------------------
---R                       15
+--R             +-+       +-+
+--R         - 2\|2 log(12\|2  + 17) + 16
+--R   (88)  ----------------------------
+--R                      15
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 112
+--E 88
 
---S 113 of 267
+--S 89 of 224
 in1794a:=integrate((1-z^(1/2))^(1/2)*acoth(1-z^(1/2)), z= 0..1,"noPole")
 --R 
 --R
---R          - 4log(2) - 8%pi + 32
---R   (111)  ---------------------
---R                    15
+--R         - 4log(2) - 8%pi + 32
+--R   (89)  ---------------------
+--R                   15
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 113
+--E 89
 
---S 114 of 267
+--S 90 of 224
 in1796a:=integrate((1+(1-z)^(1/2))^(1/2), z= 0..1,"noPole")
 --R 
 --R
---R            +-+
---R          8\|2  + 8
---R   (112)  ---------
---R              15
---R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 114
-
---S 115 of 267
-in183:=integrate(1/z, z= I..2*I)
---R 
---R
---R                2         2
---R          log(4I ) - log(I )
---R   (113)  ------------------
---R                   2
+--R           +-+
+--R         8\|2  + 8
+--R   (90)  ---------
+--R             15
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 115
+--E 90
 
---S 116 of 267
-in184:=integrate(exp(I*z), z= I..2*I)
+--S 91 of 224
+in184:=integrate(exp(%i*z), z= %i..2*%i)
 --R 
 --R
---R              2      2
---R            2I      I
---R          %e    - %e
---R   (114)  ------------
---R                I
---R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 116
+--R              2
+--R         %i %e  - %i %e
+--R   (91)  --------------
+--R                  2
+--R             %e %e
+--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
+--E 91
 
---S 117 of 267
+--S 92 of 224
 in184a:=integrate(exp(%i*z), z= %i..2*%i)
 --R 
 --R
---R               2
---R          %i %e  - %i %e
---R   (115)  --------------
---R                   2
---R              %e %e
+--R              2
+--R         %i %e  - %i %e
+--R   (92)  --------------
+--R                  2
+--R             %e %e
 --R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
---E 117
+--E 92
 
---S 118 of 267
-in187a:=integrate(2^log(z), z= -I..I,"noPole")
+--S 93 of 224
+in187a:=integrate(2^log(z), z= -%i..%i,"noPole")
 --R 
 --R
---R              log(2)log(I)       log(2)log(- I)
---R          I %e             + I %e
---R   (116)  -------------------------------------
---R                        log(2) + 1
---R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 118
+--R              log(%i)log(2)        log(- %i)log(2)
+--R         %i %e              + %i %e
+--R   (93)  -----------------------------------------
+--R                         log(2) + 1
+--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
+--E 93
 
---S 119 of 267
+--S 94 of 224
 in187a:=integrate(2^log(z), z= -%i..%i,"noPole")
 --R 
 --R
---R               log(%i)log(2)        log(- %i)log(2)
---R          %i %e              + %i %e
---R   (117)  -----------------------------------------
---R                          log(2) + 1
+--R              log(%i)log(2)        log(- %i)log(2)
+--R         %i %e              + %i %e
+--R   (94)  -----------------------------------------
+--R                         log(2) + 1
 --R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
---E 119
+--E 94
 
---S 120 of 267
+--S 95 of 224
 in194a:=integrate(sqrt(z^2), z= 1..2,"noPole")
 --R 
 --R
---R          3
---R   (118)  -
---R          2
+--R         3
+--R   (95)  -
+--R         2
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 120
+--E 95
 
---S 121 of 267
-in1854a:=integrate(1/(z-1)/(1/(z-I))^(1/2), z= 0..1,"noPole")
+--S 96 of 224
+in1854a:=integrate(1/(z-1)/(1/(z-%i))^(1/2), z= 0..1,"noPole")
 --R 
 --R
---R   (119)
---R   [- infinity,
+--R   (96)
+--R   [ + infinity,
 --R
---R                         +-------+                    +---+
---R           +-----+      \|- I + 1       +-----+      \|- I        +-------+
---R       - 2\|I - 1 log(- ----------) + 2\|I - 1 atan(--------) + 2\|- I + 1
---R                           +-----+                   +-----+
---R                         2\|I - 1                   \|I - 1
+--R                              +------+                          +----+
+--R          +---------+        \|1 - %i       +---------+       2\|- %i
+--R       - \|- 4 + 4%i log(- ------------) + \|- 4 + 4%i atan(------------)
+--R                            +---------+                      +---------+
+--R                           \|- 4 + 4%i                      \|- 4 + 4%i
 --R     + 
---R           +---+
---R       - 2\|- I
+--R         +------+     +----+
+--R       2\|1 - %i  - 2\|- %i
 --R     ]
---R               Type: Union(f2: List OrderedCompletion Expression Integer,...)
---E 121
+--R       Type: Union(f2: List OrderedCompletion Expression Complex Integer,...)
+--E 96
 
---S 122 of 267
-in1856a:=integrate(1/(z-1)/(1-I*z)^(1/2), z= 0..1,"noPole")
+--S 97 of 224
+in1856a:=integrate(1/(z-1)/(1-%i*z)^(1/2), z= 0..1,"noPole")
 --R 
 --R
---R                              +-------+ +-----+           +-----+
---R                             \|- I + 1 \|I - 1           \|I - 1
---R                      2log(- ------------------) - 2atan(--------)
---R                                   2I - 2                  I - 1
---R   (120)  [- infinity,--------------------------------------------]
---R                                         +-----+
---R                                        \|I - 1
---R               Type: Union(f2: List OrderedCompletion Expression Integer,...)
---E 122
+--R   (97)
+--R   [ + infinity,
+--R                                +------+
+--R       +---------+           %i\|1 - %i          +---------+        1 + %i
+--R    - \|- 2 - 2%i log(- --------------------) + \|- 2 - 2%i atan(------------)]
+--R                                 +---------+                      +---------+
+--R                        (1 + %i)\|- 2 - 2%i                      \|- 2 - 2%i
+--R       Type: Union(f2: List OrderedCompletion Expression Complex Integer,...)
+--E 97
 
---S 123 of 267 used to work
-in1859a:=integrate(1/(z^2-1)*(1+1/z^3)^(1/2), z= 0..1,"noPole")
---R 
---R
---R   (121)  "failed"
---R                                                Type: Union(fail: failed,...)
---E 123
---
---             +-------------------+
---             |        2
---         (- \|- 3%%EM0  - 2 + 6%i  - %%EM0)
---      *
---         log
---                                +--+                                 +--+
---                    ((8 + 72%i)\|%i  + 10 + 8%i)%%EM0 + (- 2 - 18%i)\|%i  + 2
---                  + 
---                    18%i
---             *
---                 +-------------------+
---                 |        2
---                \|- 3%%EM0  - 2 + 6%i
---            + 
---                            +--+                 2
---              ((- 8 - 72%i)\|%i  - 10 - 8%i)%%EM0
---            + 
---                            +--+                                  +--+
---              ((- 2 - 18%i)\|%i  + 2 + 18%i)%%EM0 + (- 128 - 4%i)\|%i  - 68
---            + 
---              - 120%i
---     + 
---           +-------------------+
---           |        2
---         (\|- 3%%EM0  - 2 + 6%i  + %%EM0)
---      *
---         log
---                                           +-------------------+
---                                           |        2
---              ((10 + 8%i)%%EM0 + 2 + 18%i)\|- 3%%EM0  - 2 + 6%i
---            + 
---                               2
---              (- 10 - 8%i)%%EM0  + (2 + 18%i)%%EM0 - 50 - 40%i
---     + 
---             +-------------------+
---             |        2
---         (- \|- 3%%EM0  - 2 + 6%i  + %%EM0)
---      *
---         log
---                                             +-------------------+
---                                             |        2
---              ((- 10 - 8%i)%%EM0 - 2 - 18%i)\|- 3%%EM0  - 2 + 6%i
---            + 
---                               2
---              (- 10 - 8%i)%%EM0  + (2 + 18%i)%%EM0 - 50 - 40%i
---     + 
---           +-------------------+
---           |        2
---         (\|- 3%%EM0  - 2 + 6%i  - %%EM0)
---      *
---         log
---                                  +--+                               +--+
---                    ((- 8 - 72%i)\|%i  - 10 - 8%i)%%EM0 + (2 + 18%i)\|%i  - 2
---                  + 
---                    - 18%i
---             *
---                 +-------------------+
---                 |        2
---                \|- 3%%EM0  - 2 + 6%i
---            + 
---                            +--+                 2
---              ((- 8 - 72%i)\|%i  - 10 - 8%i)%%EM0
---            + 
---                            +--+                                  +--+
---              ((- 2 - 18%i)\|%i  + 2 + 18%i)%%EM0 + (- 128 - 4%i)\|%i  - 68
---            + 
---              - 120%i
---     + 
---         2%%EM0
---      *
---         log
---                          +--+                 2
---              ((72 - 8%i)\|%i  + 8 - 10%i)%%EM0
---            + 
---                         +--+                                +--+
---             ((18 - 2%i)\|%i  - 18 + 2%i)%%EM0 + (22 - 48%i)\|%i  - 71 + 17%i
---     + 
---                                   2
---       - 2%%EM0 log((8 - 10%i)%%EM0  + (- 18 + 2%i)%%EM0 - 31 + 8%i)
---  /
---     4
---            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
-
---S 124 of 267
-in1863a:=integrate(1/(z^2-1)*(1/(z-I))^(1/2), z= 0..1,"noPole")
---R 
---R
---R   (122)
---R   [- infinity,
---R
---R          +-----+       2       +-------+ +-------+     3     2
---R         \|I - 1 log((2I  + 2I)\|- I - 1 \|- I + 1  - 2I  - 2I  + I + 1)
---R       + 
---R            +-----+       2            +-------+ +---+     3      2
---R         - \|I - 1 log((8I  + 12I + 4)\|- I - 1 \|- I  - 8I  - 16I  - 9I - 1)
---R       + 
---R                           +-------+ +-----+                     +---+ +-----+
---R           +-------+      \|- I + 1 \|I - 1       +-------+     \|- I \|I - 1
---R         4\|- I - 1 log(- ------------------) - 4\|- I - 1 atan(--------------)
---R                                2I - 2                               I - 1
---R    /
---R         +-------+ +-----+
---R       4\|- I - 1 \|I - 1
---R     ,
---R    - infinity,
---R
---R                        +-------+ +-----+                  +-------+ +-----+
---R          +-----+      \|- I + 1 \|I - 1      +-----+     \|- I + 1 \|I + 1
---R         \|I + 1 log(- ------------------) - \|I - 1 atan(------------------)
---R                             2I - 2                              I + 1
---R       + 
---R                       +---+ +-----+                  +---+ +-----+
---R          +-----+     \|- I \|I + 1      +-----+     \|- I \|I - 1
---R         \|I - 1 atan(--------------) - \|I + 1 atan(--------------)
---R                           I + 1                          I - 1
---R    /
---R        +-----+ +-----+
---R       \|I - 1 \|I + 1
---R     ]
---R               Type: Union(f2: List OrderedCompletion Expression Integer,...)
---E 124
+--S 98 of 224
+in1863a:=integrate(1/(z^2-1)*(1/(z-%i))^(1/2), z= 0..1,"noPole")
+--R 
+--R
+--R   (98)
+--R          +------+              +------+
+--R          |   1                 |   1    +------+
+--R       %i |------ log((2 - 2%i) |------ \|1 - %i  - 2%i)
+--R         \|1 + %i              \|1 + %i
+--R     + 
+--R          +------+              +------+
+--R          |  %i                 |  %i    +------+
+--R       -  |------ log((2 - 2%i) |------ \|1 - %i  + 2 - 2%i)
+--R         \|1 + %i              \|1 + %i
+--R     + 
+--R            +------+                     +------+
+--R            |   1                 +----+ |   1
+--R       - %i |------ log((2 - 2%i)\|- %i  |------  - 1 - 2%i)
+--R           \|1 + %i                     \|1 + %i
+--R     + 
+--R        +------+              +------+
+--R        |  %i                 |  %i    +----+
+--R        |------ log((2 - 2%i) |------ \|- %i  + 1 - 2%i)
+--R       \|1 + %i              \|1 + %i
+--R     + 
+--R          +------+                +------+
+--R          |  %i                   |  %i    +----+
+--R       -  |------ log((- 2 + 2%i) |------ \|- %i  + 1 - 2%i)
+--R         \|1 + %i                \|1 + %i
+--R     + 
+--R          +------+                       +------+
+--R          |   1                   +----+ |   1
+--R       %i |------ log((- 2 + 2%i)\|- %i  |------  - 1 - 2%i)
+--R         \|1 + %i                       \|1 + %i
+--R     + 
+--R        +------+                +------+
+--R        |  %i                   |  %i    +------+
+--R        |------ log((- 2 + 2%i) |------ \|1 - %i  + 2 - 2%i)
+--R       \|1 + %i                \|1 + %i
+--R     + 
+--R            +------+                +------+
+--R            |   1                   |   1    +------+
+--R       - %i |------ log((- 2 + 2%i) |------ \|1 - %i  - 2%i)
+--R           \|1 + %i                \|1 + %i
+--R  /
+--R     4
+--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
+--E 98
 
---S 125 of 267
+--S 99 of 224
 in1864a:=integrate(1/(z^2-1)*((1+z)/(z-1))^(1/3), z= 0..1,"noPole")
 --R 
 --R
---R   (123)   + infinity
+--R   (99)   + infinity
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 125
-
---S 126 of 267
-in1866a:=integrate(1/(z^2-1)*(1-I/z)^(1/2), z= 0..1,"noPole")
---R 
---R
---R   (124)
---R   [- infinity,
---R
---R                                                                       +-----+
---R          +-----+      +-------+ +-----+    2          +-----+        \|I - 1
---R         \|I + 1 log(2\|- I + 1 \|I + 1  - I  + 2) + 4\|I - 1 log(- -----------)
---R                                                                      +-------+
---R                                                                    2\|- I + 1
---R       + 
---R                2  +-----+
---R         - log(I )\|I + 1
---R    /
---R       4
---R     ,
---R    - infinity,
---R                      +-----+                      +-------+
---R      +-----+        \|I - 1        +-------+     \|- I + 1         +-------+
---R    2\|I - 1 log(- -----------) + 2\|- I - 1 atan(----------) - %pi\|- I - 1
---R                     +-------+                     +-------+
---R                   2\|- I + 1                     \|- I - 1
---R    -------------------------------------------------------------------------]
---R                                        2
---R               Type: Union(f2: List OrderedCompletion Expression Integer,...)
---E 126
-
---S 127 of 267
-in1867a:=integrate(1/(z^2-1)*(1-(I*z)^(1/2))^(1/2), z= 0..1,"noPole")
---R 
---R
---R   (125)  0
---R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 127
+--E 99
 
---S 128 of 267
-in1869a:=integrate(1/(z^2-1)*(1-1/(I*z)^(1/2))^(1/2), z= 0..1,"noPole")
+--S 100 of 224
+in1866a:=integrate(1/(z^2-1)*(1-%i/z)^(1/2), z= 0..1,"noPole")
 --R 
 --R
---R   (126)  0
---R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 128
+--R   (100)  - infinity
+--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
+--E 100
 
---S 129 of 267
-in1870a:=integrate(1/(z^2-1)/(1+(I*z)^(1/2))^(1/2), z= 0..1,"noPole")
+--S 101 of 224
+in1870a:=integrate(1/(z^2-1)/(1+(%i*z)^(1/2))^(1/2), z= 0..1,"noPole")
 --R 
 --R
---R   (127)  0
---R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 129
+--R   (101)
+--R       -
+--R             +-------------------+
+--R             |    +---------+
+--R             |    |  +-+
+--R             |    |3\|2  + 4
+--R             |4%i |---------  + 1
+--R             |    |     +-+
+--R            \|   \|  16\|2
+--R         *
+--R            log
+--R                                    +---------+
+--R                                    |  +-+                 +---------+
+--R                          +-+       |3\|2  + 4        +-+  | +--+
+--R                     ((48\|2  - 64) |---------  - 4%i\|2 )\|\|%i  + 1
+--R                                    |     +-+
+--R                                   \|  16\|2
+--R                  *
+--R                      +-------------------+
+--R                      |    +---------+
+--R                      |    |  +-+
+--R                      |    |3\|2  + 4
+--R                      |4%i |---------  + 1
+--R                      |    |     +-+
+--R                     \|   \|  16\|2
+--R                 + 
+--R                                       +---------+
+--R                                       |  +-+
+--R                           +-+         |3\|2  + 4       +--+      +-+
+--R                   (- 16%i\|2  + 16%i) |---------  + (4\|%i  + 8)\|2  - 4
+--R                                       |     +-+
+--R                                      \|  16\|2
+--R              /
+--R                  +-+
+--R                 \|2
+--R     + 
+--R          +-------------------+
+--R          |    +---------+
+--R          |    |  +-+
+--R          |    |3\|2  + 4
+--R          |4%i |---------  + 1
+--R          |    |     +-+
+--R         \|   \|  16\|2
+--R      *
+--R         log
+--R                                                      +-------------------+
+--R                               +---------+            |    +---------+
+--R                               |  +-+                 |    |  +-+
+--R                     +-+       |3\|2  + 4        +-+  |    |3\|2  + 4
+--R                ((48\|2  - 64) |---------  - 4%i\|2 ) |4%i |---------  + 1
+--R                               |     +-+              |    |     +-+
+--R                              \|  16\|2              \|   \|  16\|2
+--R              + 
+--R                                    +---------+
+--R                                    |  +-+
+--R                        +-+         |3\|2  + 4      +-+
+--R                (- 16%i\|2  + 16%i) |---------  + 8\|2  - 4
+--R                                    |     +-+
+--R                                   \|  16\|2
+--R           /
+--R               +-+
+--R              \|2
+--R     + 
+--R       -
+--R             +-------------------+
+--R             |  +-----------+
+--R             |  |    +-+
+--R             |  |- 3\|2  + 4
+--R             |4 |-----------  + 1
+--R             |  |      +-+
+--R            \| \|   16\|2
+--R         *
+--R            log
+--R                                        +-----------+
+--R                                        |    +-+                 +---------+
+--R                            +-+         |- 3\|2  + 4        +-+  | +--+
+--R                     ((48%i\|2  + 64%i) |-----------  + 4%i\|2 )\|\|%i  + 1
+--R                                        |      +-+
+--R                                       \|   16\|2
+--R                  *
+--R                      +-------------------+
+--R                      |  +-----------+
+--R                      |  |    +-+
+--R                      |  |- 3\|2  + 4
+--R                      |4 |-----------  + 1
+--R                      |  |      +-+
+--R                     \| \|   16\|2
+--R                 + 
+--R                                   +-----------+
+--R                                   |    +-+
+--R                         +-+       |- 3\|2  + 4       +--+      +-+
+--R                   (- 16\|2  - 16) |-----------  + (4\|%i  + 8)\|2  + 4
+--R                                   |      +-+
+--R                                  \|   16\|2
+--R              /
+--R                  +-+
+--R                 \|2
+--R     + 
+--R          +-------------------+
+--R          |  +-----------+
+--R          |  |    +-+
+--R          |  |- 3\|2  + 4
+--R          |4 |-----------  + 1
+--R          |  |      +-+
+--R         \| \|   16\|2
+--R      *
+--R         log
+--R                                     +-----------+
+--R                                     |    +-+
+--R                         +-+         |- 3\|2  + 4        +-+
+--R                  ((48%i\|2  + 64%i) |-----------  + 4%i\|2 )
+--R                                     |      +-+
+--R                                    \|   16\|2
+--R               *
+--R                   +-------------------+
+--R                   |  +-----------+
+--R                   |  |    +-+
+--R                   |  |- 3\|2  + 4
+--R                   |4 |-----------  + 1
+--R                   |  |      +-+
+--R                  \| \|   16\|2
+--R              + 
+--R                                +-----------+
+--R                                |    +-+
+--R                      +-+       |- 3\|2  + 4      +-+
+--R                (- 16\|2  - 16) |-----------  + 8\|2  + 4
+--R                                |      +-+
+--R                               \|   16\|2
+--R           /
+--R               +-+
+--R              \|2
+--R     + 
+--R          +---------------------+
+--R          |    +-----------+
+--R          |    |    +-+
+--R          |    |- 3\|2  + 4
+--R          |- 4 |-----------  + 1
+--R          |    |      +-+
+--R         \|   \|   16\|2
+--R      *
+--R         log
+--R                                     +-----------+
+--R                                     |    +-+                 +---------+
+--R                         +-+         |- 3\|2  + 4        +-+  | +--+
+--R                  ((48%i\|2  + 64%i) |-----------  - 4%i\|2 )\|\|%i  + 1
+--R                                     |      +-+
+--R                                    \|   16\|2
+--R               *
+--R                   +---------------------+
+--R                   |    +-----------+
+--R                   |    |    +-+
+--R                   |    |- 3\|2  + 4
+--R                   |- 4 |-----------  + 1
+--R                   |    |      +-+
+--R                  \|   \|   16\|2
+--R              + 
+--R                              +-----------+
+--R                              |    +-+
+--R                    +-+       |- 3\|2  + 4       +--+      +-+
+--R                (16\|2  + 16) |-----------  + (4\|%i  + 8)\|2  + 4
+--R                              |      +-+
+--R                             \|   16\|2
+--R           /
+--R               +-+
+--R              \|2
+--R     + 
+--R       -
+--R             +---------------------+
+--R             |    +-----------+
+--R             |    |    +-+
+--R             |    |- 3\|2  + 4
+--R             |- 4 |-----------  + 1
+--R             |    |      +-+
+--R            \|   \|   16\|2
+--R         *
+--R            log
+--R                                        +-----------+
+--R                                        |    +-+
+--R                            +-+         |- 3\|2  + 4        +-+
+--R                     ((48%i\|2  + 64%i) |-----------  - 4%i\|2 )
+--R                                        |      +-+
+--R                                       \|   16\|2
+--R                  *
+--R                      +---------------------+
+--R                      |    +-----------+
+--R                      |    |    +-+
+--R                      |    |- 3\|2  + 4
+--R                      |- 4 |-----------  + 1
+--R                      |    |      +-+
+--R                     \|   \|   16\|2
+--R                 + 
+--R                                 +-----------+
+--R                                 |    +-+
+--R                       +-+       |- 3\|2  + 4      +-+
+--R                   (16\|2  + 16) |-----------  + 8\|2  + 4
+--R                                 |      +-+
+--R                                \|   16\|2
+--R              /
+--R                  +-+
+--R                 \|2
+--R     + 
+--R          +---------------------+
+--R          |      +---------+
+--R          |      |  +-+
+--R          |      |3\|2  + 4
+--R          |- 4%i |---------  + 1
+--R          |      |     +-+
+--R         \|     \|  16\|2
+--R      *
+--R         log
+--R                                 +---------+
+--R                                 |  +-+                 +---------+
+--R                       +-+       |3\|2  + 4        +-+  | +--+
+--R                  ((48\|2  - 64) |---------  + 4%i\|2 )\|\|%i  + 1
+--R                                 |     +-+
+--R                                \|  16\|2
+--R               *
+--R                   +---------------------+
+--R                   |      +---------+
+--R                   |      |  +-+
+--R                   |      |3\|2  + 4
+--R                   |- 4%i |---------  + 1
+--R                   |      |     +-+
+--R                  \|     \|  16\|2
+--R              + 
+--R                                  +---------+
+--R                                  |  +-+
+--R                      +-+         |3\|2  + 4       +--+      +-+
+--R                (16%i\|2  - 16%i) |---------  + (4\|%i  + 8)\|2  - 4
+--R                                  |     +-+
+--R                                 \|  16\|2
+--R           /
+--R               +-+
+--R              \|2
+--R     + 
+--R       -
+--R             +---------------------+
+--R             |      +---------+
+--R             |      |  +-+
+--R             |      |3\|2  + 4
+--R             |- 4%i |---------  + 1
+--R             |      |     +-+
+--R            \|     \|  16\|2
+--R         *
+--R            log
+--R                                                         +---------------------+
+--R                                  +---------+            |      +---------+
+--R                                  |  +-+                 |      |  +-+
+--R                        +-+       |3\|2  + 4        +-+  |      |3\|2  + 4
+--R                   ((48\|2  - 64) |---------  + 4%i\|2 ) |- 4%i |---------  + 1
+--R                                  |     +-+              |      |     +-+
+--R                                 \|  16\|2              \|     \|  16\|2
+--R                 + 
+--R                                     +---------+
+--R                                     |  +-+
+--R                         +-+         |3\|2  + 4      +-+
+--R                   (16%i\|2  - 16%i) |---------  + 8\|2  - 4
+--R                                     |     +-+
+--R                                    \|  16\|2
+--R              /
+--R                  +-+
+--R                 \|2
+--R     + 
+--R          +---------------------+
+--R          |      +---------+
+--R          |      |  +-+
+--R          |      |3\|2  + 4
+--R          |- 4%i |---------  + 1
+--R          |      |     +-+
+--R         \|     \|  16\|2
+--R      *
+--R         log
+--R                                                        +---------------------+
+--R                                 +---------+            |      +---------+
+--R                                 |  +-+                 |      |  +-+
+--R                       +-+       |3\|2  + 4        +-+  |      |3\|2  + 4
+--R                ((- 48\|2  + 64) |---------  - 4%i\|2 ) |- 4%i |---------  + 1
+--R                                 |     +-+              |      |     +-+
+--R                                \|  16\|2              \|     \|  16\|2
+--R              + 
+--R                                  +---------+
+--R                                  |  +-+
+--R                      +-+         |3\|2  + 4      +-+
+--R                (16%i\|2  - 16%i) |---------  + 8\|2  - 4
+--R                                  |     +-+
+--R                                 \|  16\|2
+--R           /
+--R               +-+
+--R              \|2
+--R     + 
+--R       -
+--R             +---------------------+
+--R             |      +---------+
+--R             |      |  +-+
+--R             |      |3\|2  + 4
+--R             |- 4%i |---------  + 1
+--R             |      |     +-+
+--R            \|     \|  16\|2
+--R         *
+--R            log
+--R                                      +---------+
+--R                                      |  +-+                 +---------+
+--R                            +-+       |3\|2  + 4        +-+  | +--+
+--R                     ((- 48\|2  + 64) |---------  - 4%i\|2 )\|\|%i  + 1
+--R                                      |     +-+
+--R                                     \|  16\|2
+--R                  *
+--R                      +---------------------+
+--R                      |      +---------+
+--R                      |      |  +-+
+--R                      |      |3\|2  + 4
+--R                      |- 4%i |---------  + 1
+--R                      |      |     +-+
+--R                     \|     \|  16\|2
+--R                 + 
+--R                                     +---------+
+--R                                     |  +-+
+--R                         +-+         |3\|2  + 4       +--+      +-+
+--R                   (16%i\|2  - 16%i) |---------  + (4\|%i  + 8)\|2  - 4
+--R                                     |     +-+
+--R                                    \|  16\|2
+--R              /
+--R                  +-+
+--R                 \|2
+--R     + 
+--R          +---------------------+
+--R          |    +-----------+
+--R          |    |    +-+
+--R          |    |- 3\|2  + 4
+--R          |- 4 |-----------  + 1
+--R          |    |      +-+
+--R         \|   \|   16\|2
+--R      *
+--R         log
+--R                                       +-----------+
+--R                                       |    +-+
+--R                           +-+         |- 3\|2  + 4        +-+
+--R                  ((- 48%i\|2  - 64%i) |-----------  + 4%i\|2 )
+--R                                       |      +-+
+--R                                      \|   16\|2
+--R               *
+--R                   +---------------------+
+--R                   |    +-----------+
+--R                   |    |    +-+
+--R                   |    |- 3\|2  + 4
+--R                   |- 4 |-----------  + 1
+--R                   |    |      +-+
+--R                  \|   \|   16\|2
+--R              + 
+--R                              +-----------+
+--R                              |    +-+
+--R                    +-+       |- 3\|2  + 4      +-+
+--R                (16\|2  + 16) |-----------  + 8\|2  + 4
+--R                              |      +-+
+--R                             \|   16\|2
+--R           /
+--R               +-+
+--R              \|2
+--R     + 
+--R       -
+--R             +---------------------+
+--R             |    +-----------+
+--R             |    |    +-+
+--R             |    |- 3\|2  + 4
+--R             |- 4 |-----------  + 1
+--R             |    |      +-+
+--R            \|   \|   16\|2
+--R         *
+--R            log
+--R                                          +-----------+
+--R                                          |    +-+                 +---------+
+--R                              +-+         |- 3\|2  + 4        +-+  | +--+
+--R                     ((- 48%i\|2  - 64%i) |-----------  + 4%i\|2 )\|\|%i  + 1
+--R                                          |      +-+
+--R                                         \|   16\|2
+--R                  *
+--R                      +---------------------+
+--R                      |    +-----------+
+--R                      |    |    +-+
+--R                      |    |- 3\|2  + 4
+--R                      |- 4 |-----------  + 1
+--R                      |    |      +-+
+--R                     \|   \|   16\|2
+--R                 + 
+--R                                 +-----------+
+--R                                 |    +-+
+--R                       +-+       |- 3\|2  + 4       +--+      +-+
+--R                   (16\|2  + 16) |-----------  + (4\|%i  + 8)\|2  + 4
+--R                                 |      +-+
+--R                                \|   16\|2
+--R              /
+--R                  +-+
+--R                 \|2
+--R     + 
+--R       -
+--R             +-------------------+
+--R             |  +-----------+
+--R             |  |    +-+
+--R             |  |- 3\|2  + 4
+--R             |4 |-----------  + 1
+--R             |  |      +-+
+--R            \| \|   16\|2
+--R         *
+--R            log
+--R                                          +-----------+
+--R                                          |    +-+
+--R                              +-+         |- 3\|2  + 4        +-+
+--R                     ((- 48%i\|2  - 64%i) |-----------  - 4%i\|2 )
+--R                                          |      +-+
+--R                                         \|   16\|2
+--R                  *
+--R                      +-------------------+
+--R                      |  +-----------+
+--R                      |  |    +-+
+--R                      |  |- 3\|2  + 4
+--R                      |4 |-----------  + 1
+--R                      |  |      +-+
+--R                     \| \|   16\|2
+--R                 + 
+--R                                   +-----------+
+--R                                   |    +-+
+--R                         +-+       |- 3\|2  + 4      +-+
+--R                   (- 16\|2  - 16) |-----------  + 8\|2  + 4
+--R                                   |      +-+
+--R                                  \|   16\|2
+--R              /
+--R                  +-+
+--R                 \|2
+--R     + 
+--R          +-------------------+
+--R          |  +-----------+
+--R          |  |    +-+
+--R          |  |- 3\|2  + 4
+--R          |4 |-----------  + 1
+--R          |  |      +-+
+--R         \| \|   16\|2
+--R      *
+--R         log
+--R                                       +-----------+
+--R                                       |    +-+                 +---------+
+--R                           +-+         |- 3\|2  + 4        +-+  | +--+
+--R                  ((- 48%i\|2  - 64%i) |-----------  - 4%i\|2 )\|\|%i  + 1
+--R                                       |      +-+
+--R                                      \|   16\|2
+--R               *
+--R                   +-------------------+
+--R                   |  +-----------+
+--R                   |  |    +-+
+--R                   |  |- 3\|2  + 4
+--R                   |4 |-----------  + 1
+--R                   |  |      +-+
+--R                  \| \|   16\|2
+--R              + 
+--R                                +-----------+
+--R                                |    +-+
+--R                      +-+       |- 3\|2  + 4       +--+      +-+
+--R                (- 16\|2  - 16) |-----------  + (4\|%i  + 8)\|2  + 4
+--R                                |      +-+
+--R                               \|   16\|2
+--R           /
+--R               +-+
+--R              \|2
+--R     + 
+--R       -
+--R             +-------------------+
+--R             |    +---------+
+--R             |    |  +-+
+--R             |    |3\|2  + 4
+--R             |4%i |---------  + 1
+--R             |    |     +-+
+--R            \|   \|  16\|2
+--R         *
+--R            log
+--R                                                           +-------------------+
+--R                                    +---------+            |    +---------+
+--R                                    |  +-+                 |    |  +-+
+--R                          +-+       |3\|2  + 4        +-+  |    |3\|2  + 4
+--R                   ((- 48\|2  + 64) |---------  + 4%i\|2 ) |4%i |---------  + 1
+--R                                    |     +-+              |    |     +-+
+--R                                   \|  16\|2              \|   \|  16\|2
+--R                 + 
+--R                                       +---------+
+--R                                       |  +-+
+--R                           +-+         |3\|2  + 4      +-+
+--R                   (- 16%i\|2  + 16%i) |---------  + 8\|2  - 4
+--R                                       |     +-+
+--R                                      \|  16\|2
+--R              /
+--R                  +-+
+--R                 \|2
+--R     + 
+--R          +-------------------+
+--R          |    +---------+
+--R          |    |  +-+
+--R          |    |3\|2  + 4
+--R          |4%i |---------  + 1
+--R          |    |     +-+
+--R         \|   \|  16\|2
+--R      *
+--R         log
+--R                                   +---------+
+--R                                   |  +-+                 +---------+
+--R                         +-+       |3\|2  + 4        +-+  | +--+
+--R                  ((- 48\|2  + 64) |---------  + 4%i\|2 )\|\|%i  + 1
+--R                                   |     +-+
+--R                                  \|  16\|2
+--R               *
+--R                   +-------------------+
+--R                   |    +---------+
+--R                   |    |  +-+
+--R                   |    |3\|2  + 4
+--R                   |4%i |---------  + 1
+--R                   |    |     +-+
+--R                  \|   \|  16\|2
+--R              + 
+--R                                    +---------+
+--R                                    |  +-+
+--R                        +-+         |3\|2  + 4       +--+      +-+
+--R                (- 16%i\|2  + 16%i) |---------  + (4\|%i  + 8)\|2  - 4
+--R                                    |     +-+
+--R                                   \|  16\|2
+--R           /
+--R               +-+
+--R              \|2
+--R  /
+--R       +-+
+--R     4\|2
+--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
+--E 101
 
--S 130
-in1872a:=integrate(1/(z^2-1)/(I/(z+I))^(1/2), z= 0..1,"noPole")
+--S 102 of 224
+in1872a:=integrate(1/(z^2-1)/(%i/(z+%i))^(1/2), z= 0..1,"noPole")
 --R 
 --R
---R   (128)
---R   [ + infinity,  + infinity,
---R
---R          +-----+               +-----+ +-----+
---R          |I - 1        2       |I - 1  |  I        2
---R          |----- log((2I  + 2I) |-----  |-----  + 2I  - 1)
---R         \|  I                 \|  I   \|I + 1
---R       + 
---R            +-----+               +-----+
---R            |I - 1        2       |I - 1      2
---R         -  |----- log((8I  - 4I) |-----  + 8I  - 8I + 1)
---R           \|  I                 \|  I
---R       + 
---R                                     +-----+
---R                                     |  I
---R              +-------+    (- I - 1) |-----       +-------+
---R              |- I - 1              \|I + 1       |- I - 1         I + 1
---R         - 4  |------- log(----------------- + 4  |------- atan(-----------)
---R             \|   I              +-------+       \|   I           +-------+
---R                                 |- I - 1                         |- I - 1
---R                              2I |-------                       I |-------
---R                                \|   I                           \|   I
---R    /
---R       4
---R     ,
---R
---R                                 +-----+                           +-----+
---R                                 |  I                              |  I
---R          +-------+    (- I - 1) |-----      +-------+     (I - 1) |-----
---R          |- I - 1              \|I + 1      |- I + 1             \|I + 1
---R       -  |------- log(-----------------) +  |------- atan(---------------)
---R         \|   I              +-------+      \|   I             +-------+
---R                             |- I - 1                          |- I + 1
---R                          2I |-------                        I |-------
---R                            \|   I                            \|   I
---R     + 
---R        +-------+                     +-------+
---R        |- I - 1         I + 1        |- I + 1         I - 1
---R        |------- atan(-----------) -  |------- atan(-----------)
---R       \|   I           +-------+    \|   I           +-------+
---R                        |- I - 1                      |- I + 1
---R                      I |-------                    I |-------
---R                       \|   I                        \|   I
---R     ]
---R               Type: Union(f2: List OrderedCompletion Expression Integer,...)
---E 130
+--R   (102)
+--R                              +------+
+--R        +------+              |  %i    +------+
+--R       \|1 + %i log((2 + 2%i) |------ \|1 + %i  + 2%i)
+--R                             \|1 + %i
+--R     + 
+--R          +------+              +------+
+--R       - \|1 + %i log((2 + 2%i)\|1 + %i  + 1 + 3%i)
+--R     + 
+--R                              +------+
+--R        +------+              |  %i    +------+
+--R       \|1 - %i log((2 - 2%i) |------ \|1 - %i  - 2 + 2%i)
+--R                             \|1 + %i
+--R     + 
+--R          +------+              +------+
+--R       - \|1 - %i log((2 - 2%i)\|1 - %i  - 1 + 3%i)
+--R     + 
+--R        +------+                +------+
+--R       \|1 - %i log((- 2 + 2%i)\|1 - %i  - 1 + 3%i)
+--R     + 
+--R                                  +------+
+--R          +------+                |  %i    +------+
+--R       - \|1 - %i log((- 2 + 2%i) |------ \|1 - %i  - 2 + 2%i)
+--R                                 \|1 + %i
+--R     + 
+--R        +------+                +------+
+--R       \|1 + %i log((- 2 - 2%i)\|1 + %i  + 1 + 3%i)
+--R     + 
+--R                                  +------+
+--R          +------+                |  %i    +------+
+--R       - \|1 + %i log((- 2 - 2%i) |------ \|1 + %i  + 2%i)
+--R                                 \|1 + %i
+--R  /
+--R     4
+--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
+--E 102
 
---S 131 of 267
+--S 103 of 224
 in1933a:=integrate(atan(z)/z/(z*(1+z))^(1/2), z= 0..1,"noPole")
 --R 
 --R
---R   (129)
+--R   (103)
 --R           +-+     4+-+    %pi
 --R         (\|2  - 1)\|2 cos(---)
 --R                            8
@@ -3779,71 +3934,69 @@ in1933a:=integrate(atan(z)/z/(z*(1+z))^(1/2), z= 0..1,"noPole")
 --R       +-+
 --R     2\|2  - 2
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 131
+--E 103
 
---S 132 of 267
+--S 104 of 224
 in1945a:=integrate(acoth((1-z)/(1+z)), z= 0..1,"noPole")
 --R 
 --R
 --R          1
---R   (130)  -
+--R   (104)  -
 --R          2
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 132
+--E 104
 
---S 133 of 267
+--S 105 of 224
 in1946a:=integrate(acoth((1-z)/(1+z))*z, z= 0..1,"noPole")
 --R 
 --R
 --R          1
---R   (131)  -
+--R   (105)  -
 --R          8
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 133
+--E 105
 
---S 134 of 267
+--S 106 of 224
 in1947a:=integrate(acoth((1-z)/(1+z))*z^(1/2), z= 0..1,"noPole")
 --R 
 --R
 --R          2
---R   (132)  -
+--R   (106)  -
 --R          9
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 134
+--E 106
 
---S 135 of 267
+--S 107 of 224
 in1950a:=integrate(acoth((1-z)/(1+z))/(1-z)^(1/2), z= 0..1,"noPole")
 --R 
 --R
 --R          - log(4) - 2log(2) + 4
---R   (133)  ----------------------
+--R   (107)  ----------------------
 --R                     2
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 135
+--E 107
 
---S 136 of 267
-in1952a:=integrate(acoth((1-z)/(1+z))*(I*z)^(1/2), z= 0..1,"noPole")
+--S 108 of 224
+in1952a:=integrate(acoth((1-z)/(1+z))*(%i*z)^(1/2), z= 0..1,"noPole")
 --R 
 --R
---R            +-+
---R          2\|I
---R   (134)  -----
---R            9
---R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 136
+--R            +--+
+--R          2\|%i
+--R   (108)  ------
+--R             9
+--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
+--E 108
 
---S 137 of 267
-in1954a:=integrate(acoth((1-z)/(1+z))/(I*z)^(1/2), z= 0..1,"noPole")
+--S 109 of 224
+in1954a:=integrate(acoth((1-z)/(1+z))/(%i*z)^(1/2), z= 0..1,"noPole")
 --R 
 --R
---R            +-+
---R          2\|I
---R   (135)  -----
---R            I
---R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 137
+--R                +--+
+--R   (109)  - 2%i\|%i
+--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
+--E 109
 
---S 138 of 267
+--S 110 of 224
 in202a:=integrate(acsc(z), z= 0..1/2,"noPole")
 --R 
 --R
@@ -3851,16 +4004,16 @@ in202a:=integrate(acsc(z), z= 0..1/2,"noPole")
 --R              +-+     2\|2 \|3             +-+
 --R          - 6\|2 atan(---------) - 3atan(4\|3 ) + 2%pi
 --R                          5
---R   (136)  --------------------------------------------
+--R   (110)  --------------------------------------------
 --R                               12
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 138
+--E 110
 
---S 139 of 267
+--S 111 of 224
 in206a:=integrate(sqrt(1-1/z), z= %pi..2*%pi,"noPole")
 --R 
 --R
---R   (137)
+--R   (111)
 --R               +--------+              +-------+
 --R               |2%pi - 1               |%pi - 1
 --R       - 2log( |--------  + 1) + 2log( |-------  + 1)
@@ -3880,24 +4033,24 @@ in206a:=integrate(sqrt(1-1/z), z= %pi..2*%pi,"noPole")
 --R  /
 --R     4
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 139
+--E 111
 
---S 140 of 267
+--S 112 of 224
 in211:=integrate(acos(sin(2*z))*cos(z), z= 0..4*%pi/3)
 --R 
 --R
 --R                +-+
 --R          13%pi\|3  + 36
---R   (138)  --------------
+--R   (112)  --------------
 --R                12
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 140
+--E 112
 
---S 141 of 267
+--S 113 of 224
 in213a:=integrate(log(abs(1+1/(-z)^(1/3))), z= 0..1,"noPole")
 --R 
 --R
---R   (139)
+--R   (113)
 --R                                      3+---+2    3+---+
 --R         3+---+2    3+---+            \|- 1   + 2\|- 1  + 1    3+---+2    3+---+
 --R   - log(\|- 1   + 2\|- 1  + 1) + log(---------------------) - \|- 1   + 2\|- 1
@@ -3906,149 +4059,100 @@ in213a:=integrate(log(abs(1+1/(-z)^(1/3))), z= 0..1,"noPole")
 --R   -----------------------------------------------------------------------------
 --R                                         2
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 141
+--E 113
 
---S 142 of 267
+--S 114 of 224
 in216a:=integrate(1/(1/z-1)^(1/3), z= 0..1,"noPole")
 --R 
 --R
 --R           2%pi
---R   (140)  -----
+--R   (114)  -----
 --R            +-+
 --R          3\|3
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 142
+--E 114
 
---S 143 of 267
+--S 115 of 224
 in2023a:=integrate((1-z)/(-1+z^(1/2)), z= 1..2,"noPole")
 --R 
 --R
 --R              +-+
 --R          - 4\|2  - 1
---R   (141)  -----------
+--R   (115)  -----------
 --R               3
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 143
+--E 115
 
---S 144 of 267
+--S 116 of 224
 in2024a:=integrate(log(1-1/z)+csc(z-1), z= 0..1,"noPole")
 --R 
 --R
---R   (142)  - infinity
+--R   (116)  - infinity
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 144
+--E 116
 
---S 145 of 267
+--S 117 of 224
 in2032a:=integrate(acoth(z)/z^(1/2), z= 0..1,"noPole")
 --R 
 --R
 --R          - 2log(2) + %pi
---R   (143)  ---------------
+--R   (117)  ---------------
 --R                 2
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 145
+--E 117
 
---S 146 of 267
+--S 118 of 224
 in2040a:=integrate(log(1-1/z^4)+cot(z), z= -1..1,"noPole")
 --R 
 --R
---R   (144)  log(16) + log(4) + %pi
+--R   (118)  log(16) + log(4) + %pi
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 146
+--E 118
 
---S 147 of 267
+--S 119 of 224
 in2050a:=integrate(-csc(z-1)-1/z^(1/3), z= -1..1,"noPole")
 --R 
 --R
---R   (145)   + infinity
+--R   (119)   + infinity
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 147
+--E 119
 
---S 148 of 267
-in2051a:=integrate((z^2+I*z-1)^(1/2)*z, z= -1..1,"noPole")
+--S 120 of 224
+in2051a:=integrate((z^2+%i*z-1)^(1/2)*z, z= -1..1,"noPole")
 --R 
 --R
---R   (146)
---R                    7        5        3          +---+      8       7       6
---R               (108I  - 1776I  - 7104I  + 6912I)\|- I  - 18I  + 228I  + 936I
---R             + 
---R                      5        4        3        2
---R               - 1104I  + 2208I  - 7488I  - 7296I  + 2304I
---R          *
---R              +-+
---R             \|I
---R         + 
---R                      8       7       6        5        4        3        2
---R                 - 18I  - 228I  + 936I  + 1104I  + 2208I  + 7488I  - 7296I
---R               + 
---R                 - 2304I
---R          *
---R              +---+
---R             \|- I
+--R   (120)
+--R                    +----+                  +--+                   +----+
+--R           (12132%i\|- %i  + 8550 + 8460%i)\|%i  + (8550 - 8460%i)\|- %i
 --R         + 
---R             9       7         3
---R           3I  - 744I  + 11904I  - 768I
+--R           - 11925%i
 --R      *
---R                        +---+    2
---R         log((- 4I + 8)\|- I  + I  - 8I + 4)
+--R                       +----+
+--R         log((8 - 4%i)\|- %i  + 3 - 8%i)
 --R     + 
---R                      7        5        3          +---+      8       7       6
---R               (- 108I  + 1776I  + 7104I  - 6912I)\|- I  + 18I  - 228I  - 936I
---R             + 
---R                    5        4        3        2
---R               1104I  - 2208I  + 7488I  + 7296I  - 2304I
---R          *
---R              +-+
---R             \|I
+--R                      +----+                  +--+                     +----+
+--R           (- 12132%i\|- %i  - 8550 - 8460%i)\|%i  + (- 8550 + 8460%i)\|- %i
 --R         + 
---R                 8       7       6        5        4        3        2
---R             (18I  + 228I  - 936I  - 1104I  - 2208I  - 7488I  + 7296I  + 2304I)
---R          *
---R              +---+
---R             \|- I
---R         + 
---R               9       7         3
---R           - 3I  + 744I  - 11904I  + 768I
+--R           11925%i
 --R      *
---R                        +-+    2
---R         log((- 4I - 8)\|I  + I  + 8I + 4)
+--R                         +--+
+--R         log((- 8 - 4%i)\|%i  + 3 + 8%i)
 --R     + 
---R                 6         4        2  +---+      8       7        6        5
---R           (1728I  - 10752I  - 5120I )\|- I  - 12I  - 424I  + 2736I  + 6816I
---R         + 
---R                  4        3        2
---R           - 6208I  + 1152I  - 3840I  - 512I
---R      *
---R          +-+
---R         \|I
---R     + 
---R           8       7        6        5        4        3        2         +---+
---R       (12I  - 424I  - 2736I  + 6816I  + 6208I  + 1152I  + 3840I  - 512I)\|- I
---R     + 
---R           8        6        4        2
---R       144I  - 6848I  + 3840I  + 3072I
+--R               +----+                  +--+                   +----+
+--R       (- 7360\|- %i  - 5116 + 5576%i)\|%i  + (5116 + 5576%i)\|- %i  + 7760
 --R  /
---R                 4         2          +---+       5        4         3         2
---R           (3456I  - 70656I  + 55296)\|- I  - 576I  + 7296I  + 32256I  - 64512I
---R         + 
---R           - 58368I + 18432
---R      *
---R          +-+
---R         \|I
---R     + 
---R              5        4         3         2                   +---+      6
---R       (- 576I  - 7296I  + 32256I  + 64512I  - 58368I - 18432)\|- I  + 96I
+--R               +----+                    +--+                       +----+
+--R       (129408\|- %i  + 90240 - 91200%i)\|%i  + (- 90240 - 91200%i)\|- %i
 --R     + 
---R               4         2
---R       - 24192I  + 96768I  - 6144
---R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 148
+--R       - 127200
+--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
+--E 120
 
---S 149 of 267
+--S 121 of 224
 in2053a:=integrate(atan(2*z-1), z= 0..infinity,"noPole")
 --R 
 --R
---R   (147)
+--R   (121)
 --R                      4            3            2
 --R       - log(4infinity  - 8infinity  + 8infinity  - 4infinity + 1)
 --R     + 
@@ -4059,117 +4163,84 @@ in2053a:=integrate(atan(2*z-1), z= 0..infinity,"noPole")
 --R  /
 --R     8
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 149
+--E 121
 
---S 150 of 267
+--S 122 of 224
 in2054:=integrate(atan(1/z^(1/2))+1, z= -1..1)
+--R 
 --R
---R                      4            3            2
---R       - log(4infinity  - 8infinity  + 8infinity  - 4infinity + 1)
---R     + 
---R                                  2infinity - 1
---R       (- 4infinity + 2)atan(----------------------) - %pi
---R                                      2
---R                             2infinity  - 2infinity
---R  /
---R     8
---R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---R NOTE: 150 USED TO WORK
---E 150
+--R   (122)  potentialPole
+--R                                         Type: Union(pole: potentialPole,...)
+--E 122
 
---S 151 of 267
+--S 123 of 224
 in2056a:=integrate(z^(1/2)-acoth(1-z), z= 0..1,"noPole")
 --R 
 --R
 --R          - 3log(4) + 4
---R   (149)  -------------
+--R   (123)  -------------
 --R                6
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 151
+--E 123
 
---S 152 of 267
-in2058a:=integrate((z^2+I*z-3)^(1/2)+z, z= -1..1,"noPole")
+--S 124 of 224
+in2058a:=integrate((z^2+%i*z-3)^(1/2)+z, z= -1..1,"noPole")
 --R 
 --R
---R   (150)
---R                     4       2        +-------+     5      4      3       2
---R               (- 16I  - 128I  + 768)\|- I - 2  + 4I  - 24I  - 32I  - 320I
---R             + 
---R               - 960I - 384
---R          *
---R              +-----+
---R             \|I - 2
---R         + 
---R              5      4      3       2               +-------+    6      4
---R           (4I  + 24I  - 32I  + 320I  - 960I + 384)\|- I - 2  - I  + 60I
+--R   (124)
+--R                  +--------+               +--------+
+--R           (- 880\|- 2 - %i  + 88 + 924%i)\|- 2 + %i
 --R         + 
---R               2
---R           848I  - 192
+--R                          +--------+
+--R           (- 88 + 924%i)\|- 2 - %i  + 979
 --R      *
---R                        +-------+    2
---R         log((- 4I + 8)\|- I - 2  + I  - 8I - 4)
+--R                       +--------+
+--R         log((8 - 4%i)\|- 2 - %i  - 5 - 8%i)
 --R     + 
---R                   4       2        +-------+     5      4      3       2
---R               (16I  + 128I  - 768)\|- I - 2  - 4I  + 24I  + 32I  + 320I  + 960I
---R             + 
---R               384
---R          *
---R              +-----+
---R             \|I - 2
---R         + 
---R                5      4      3       2               +-------+    6      4
---R           (- 4I  - 24I  + 32I  - 320I  + 960I - 384)\|- I - 2  + I  - 60I
+--R                +--------+               +--------+                +--------+
+--R           (880\|- 2 - %i  - 88 - 924%i)\|- 2 + %i  + (88 - 924%i)\|- 2 - %i
 --R         + 
---R                 2
---R           - 848I  + 192
+--R           - 979
 --R      *
---R                        +-----+    2
---R         log((- 4I - 8)\|I - 2  + I  + 8I - 4)
+--R                         +--------+
+--R         log((- 8 - 4%i)\|- 2 + %i  - 5 + 8%i)
 --R     + 
---R                    3          +-------+     5      4       3        2
---R             (- 256I  + 1024I)\|- I - 2  + 4I  + 72I  - 288I  - 1088I  + 64I
---R           + 
---R             1152
---R      *
---R          +-----+
---R         \|I - 2
---R     + 
---R            5      4       3        2               +-------+      5       3
---R       (- 4I  + 72I  + 288I  - 1088I  - 64I + 1152)\|- I - 2  - 32I  + 768I
+--R                 +--------+                 +--------+
+--R       (- 1280%i\|- 2 - %i  - 2312 - 356%i)\|- 2 + %i
 --R     + 
---R       - 2560I
+--R                        +--------+
+--R       (- 2312 + 356%i)\|- 2 - %i  + 3360%i
 --R  /
---R             2         +-------+      3       2                +-----+
---R       ((256I  - 1024)\|- I - 2  - 64I  + 384I  + 1280I + 512)\|I - 2
+--R             +--------+                 +--------+                  +--------+
+--R       (1280\|- 2 - %i  - 128 - 1344%i)\|- 2 + %i  + (128 - 1344%i)\|- 2 - %i
 --R     + 
---R             3       2                +-------+      4        2
---R       (- 64I  - 384I  + 1280I - 512)\|- I - 2  + 16I  - 1152I  + 256
---R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 152
+--R       - 1424
+--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
+--E 124
 
---S 153 of 267
-in2068a:=integrate(1/(I*z)^(1/2)-csch(z), z= 0..1,"noPole")
+--S 125 of 224
+in2068a:=integrate(1/(%i*z)^(1/2)-csch(z), z= 0..1,"noPole")
 --R 
 --R
---R   (151)  - infinity
---R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 153
+--R   (125)  - infinity
+--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
+--E 125
 
---S 154 of 267
+--S 126 of 224
 in2071a:=integrate(1/(3+z)^3*acoth(z), z= -1..1,"noPole")
 --R 
 --R
 --R          - 3log(16) + 3log(4) - 2
---R   (152)  ------------------------
+--R   (126)  ------------------------
 --R                     128
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 154
+--E 126
 
---S 155 of 267
+--S 127 of 224
 in2090a:=integrate(exp(z^(1/3))*(3+z)^9, z= -1..1,"noPole")
 --R 
 --R
---R   (153)
+--R   (127)
 --R                                         3+---+2
 --R         13467752003249079711273325865856\|- 1
 --R       + 
@@ -4184,577 +4255,153 @@ in2090a:=integrate(exp(z^(1/3))*(3+z)^9, z= -1..1,"noPole")
 --R   + 
 --R     - 9746099248106233432776547720320%e
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 155
+--E 127
 
---S 156 of 267
+--S 128 of 224
 in2094a:=integrate(asinh(z)-acoth(z), z= -1..1,"noPole")
 --R 
 --R
 --R                +-+                +-+
 --R          log(2\|2  + 3) + log(- 2\|2  + 3)
---R   (154)  ---------------------------------
+--R   (128)  ---------------------------------
 --R                          2
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 156
+--E 128
 
---S 157 of 267
+--S 129 of 224
 in2096a:=integrate(log(z)^2, z= %minusInfinity..%plusInfinity,"noPole")
 --R 
 --R
---R   (155)   + infinity
+--R   (129)   + infinity
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 157
+--E 129
 
---S 158 of 267
+--S 130 of 224
 in2098a:=integrate(1/z^(1/3)-z^2/(z-1)^2, z= -1..1,"noPole")
 --R 
 --R
---R   (156)  - infinity
+--R   (130)  - infinity
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 158
+--E 130
 
---S 159 of 267
-in2105a:=integrate(-1/(z^2-I*z+2)^(1/2)/z, z= 0..1,"noPole")
+--S 131 of 224
+in2105a:=integrate(-1/(z^2-%i*z+2)^(1/2)/z, z= 0..1,"noPole")
 --R 
 --R
---R   (157)  - infinity
---R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 159
+--R   (131)  - infinity
+--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
+--E 131
 
---S 160 of 267
+--S 132 of 224
 in2106a:=integrate(acos(z)+acoth(1-z), z= 0..1,"noPole")
 --R 
 --R
 --R          log(4) + 2
---R   (158)  ----------
+--R   (132)  ----------
 --R               2
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 160
-
---S 161 of 267
-in2108a:=integrate((1-I/(1+I/z)^2)^(1/2), z= -1..1,"noPole")
---R 
---R
---R   (159)
---R   [
---R                 +-----------+            +----------+
---R               2 | 2              3    2  | 2
---R             (I \|I  - 3I + 1  - I  + I )\|I  + I + 1
---R           + 
---R                         +-----------+
---R                 3    2  | 2              4    2
---R             (- I  - I )\|I  - 3I + 1  + I  - I
---R        *
---R           log
---R                        3     2           +-------+     4     3     2
---R                    ((4I  - 4I  + 2I - 2)\|- I + 1  - 2I  + 4I  - 6I  + 4I)
---R                 *
---R                     +----------+
---R                     | 2
---R                    \|I  + I + 1
---R                + 
---R                       4     3     2       +-------+     5     4     3     2
---R                  (- 4I  + 2I  - 2I  + 4I)\|- I + 1  + 2I  - 3I  + 5I  - 4I
---R                + 
---R                  2I - 2
---R             /
---R                         +----------+
---R                         | 2              2
---R                (2I + 2)\|I  + I + 1  - 2I  - 3I - 2
---R       + 
---R                                    +-----------+
---R                    +---+ +-------+ | 2               2      +---+ +-------+
---R               (- I\|- I \|- I + 1 \|I  - 3I + 1  + (I  - I)\|- I \|- I + 1 )
---R            *
---R                +----------+
---R                | 2
---R               \|I  + I + 1
---R           + 
---R                                    +-----------+
---R             2      +---+ +-------+ | 2                 3      +---+ +-------+
---R           (I  + I)\|- I \|- I + 1 \|I  - 3I + 1  + (- I  + I)\|- I \|- I + 1
---R        *
---R           log
---R                                                                 +-----------+
---R                      2            +---+     3      2            | 2
---R                  ((4I  - 10I + 4)\|- I  + 2I  - 10I  + 10I - 2)\|I  - 3I + 1
---R                + 
---R                       3      2            +---+     4      3      2
---R                  (- 4I  + 16I  - 16I + 4)\|- I  - 2I  + 13I  - 24I  + 13I - 2
---R             /
---R                                     +-----------+
---R                   3     2           | 2               4     3      2
---R                (2I  - 6I  + 6I - 2)\|I  - 3I + 1  - 2I  + 9I  - 14I  + 9I - 2
---R       + 
---R                                  +-----------+
---R                  +---+ +-------+ | 2                 2      +---+ +-------+
---R               (I\|- I \|- I + 1 \|I  - 3I + 1  + (- I  + I)\|- I \|- I + 1 )
---R            *
---R                +----------+
---R                | 2
---R               \|I  + I + 1
---R           + 
---R                                      +-----------+
---R               2      +---+ +-------+ | 2               3      +---+ +-------+
---R           (- I  - I)\|- I \|- I + 1 \|I  - 3I + 1  + (I  - I)\|- I \|- I + 1
---R        *
---R           log
---R                                                                +----------+
---R                        2           +---+     3     2           | 2
---R                  ((- 4I  - 6I - 4)\|- I  + 2I  + 2I  + 2I + 2)\|I  + I + 1
---R                + 
---R                     3     2           +---+     4     3     2
---R                  (4I  + 8I  + 8I + 4)\|- I  - 2I  - 3I  - 4I  - 3I - 2
---R             /
---R                                     +----------+
---R                   3     2           | 2              4     3      2
---R                (2I  + 6I  + 6I + 2)\|I  + I + 1  - 2I  - 7I  - 10I  - 7I - 2
---R       + 
---R                   +-----------+            +----------+
---R                 2 | 2              3    2  | 2
---R             (- I \|I  - 3I + 1  + I  - I )\|I  + I + 1
---R           + 
---R                       +-----------+
---R               3    2  | 2              4    2
---R             (I  + I )\|I  - 3I + 1  - I  + I
---R        *
---R           log
---R                          3     2           +-------+     4     3      2
---R                    ((- 4I  + 8I  - 6I + 2)\|- I + 1  - 2I  + 8I  - 10I  + 4I)
---R                 *
---R                     +-----------+
---R                     | 2
---R                    \|I  - 3I + 1
---R                + 
---R                     4      3      2       +-------+     5      4      3      2
---R                  (4I  - 14I  + 14I  - 4I)\|- I + 1  + 2I  - 11I  + 21I  - 20I
---R                + 
---R                  10I - 2
---R             /
---R                         +-----------+
---R                         | 2               2
---R                (2I - 2)\|I  - 3I + 1  - 2I  + 5I - 2
---R       + 
---R                        +-----------+                       +----------+
---R              +-------+ | 2                      +-------+  | 2
---R         (- 4\|- I + 1 \|I  - 3I + 1  + (6I - 4)\|- I + 1 )\|I  + I + 1
---R       + 
---R                            +-----------+
---R                  +-------+ | 2                  2           +-------+
---R         (2I + 4)\|- I + 1 \|I  - 3I + 1  + (- 4I  - 4I + 4)\|- I + 1
---R    /
---R                      +-----------+                         +----------+
---R            +-------+ | 2                        +-------+  | 2
---R         (2\|- I + 1 \|I  - 3I + 1  + (- 2I + 2)\|- I + 1 )\|I  + I + 1
---R       + 
---R                              +-----------+
---R                    +-------+ | 2                2      +-------+
---R         (- 2I - 2)\|- I + 1 \|I  - 3I + 1  + (2I  - 2)\|- I + 1
---R     ,
---R
---R                                  +-----------+
---R                    +---+ +-----+ | 2               2      +---+ +-----+
---R               (- I\|- I \|I - 1 \|I  - 3I + 1  + (I  - I)\|- I \|I - 1 )
---R            *
---R                +----------+
---R                | 2
---R               \|I  + I + 1
---R           + 
---R                                    +-----------+
---R               2      +---+ +-----+ | 2                 3      +---+ +-----+
---R             (I  + I)\|- I \|I - 1 \|I  - 3I + 1  + (- I  + I)\|- I \|I - 1
---R        *
---R           log
---R                                                                 +-----------+
---R                      2            +---+     3      2            | 2
---R                  ((4I  - 10I + 4)\|- I  + 2I  - 10I  + 10I - 2)\|I  - 3I + 1
---R                + 
---R                       3      2            +---+     4      3      2
---R                  (- 4I  + 16I  - 16I + 4)\|- I  - 2I  + 13I  - 24I  + 13I - 2
---R             /
---R                                     +-----------+
---R                   3     2           | 2               4     3      2
---R                (2I  - 6I  + 6I - 2)\|I  - 3I + 1  - 2I  + 9I  - 14I  + 9I - 2
---R       + 
---R                                +-----------+
---R                  +---+ +-----+ | 2                 2      +---+ +-----+
---R               (I\|- I \|I - 1 \|I  - 3I + 1  + (- I  + I)\|- I \|I - 1 )
---R            *
---R                +----------+
---R                | 2
---R               \|I  + I + 1
---R           + 
---R                                      +-----------+
---R                 2      +---+ +-----+ | 2               3      +---+ +-----+
---R             (- I  - I)\|- I \|I - 1 \|I  - 3I + 1  + (I  - I)\|- I \|I - 1
---R        *
---R           log
---R                                                                +----------+
---R                        2           +---+     3     2           | 2
---R                  ((- 4I  - 6I - 4)\|- I  + 2I  + 2I  + 2I + 2)\|I  + I + 1
---R                + 
---R                     3     2           +---+     4     3     2
---R                  (4I  + 8I  + 8I + 4)\|- I  - 2I  - 3I  - 4I  - 3I - 2
---R             /
---R                                     +----------+
---R                   3     2           | 2              4     3      2
---R                (2I  + 6I  + 6I + 2)\|I  + I + 1  - 2I  - 7I  - 10I  - 7I - 2
---R       + 
---R                    +-----------+              +----------+
---R                  2 | 2               3     2  | 2
---R             (- 4I \|I  - 3I + 1  + 4I  - 4I )\|I  + I + 1
---R           + 
---R                         +-----------+
---R                3     2  | 2               4     2
---R             (4I  + 4I )\|I  - 3I + 1  - 4I  + 4I
---R        *
---R                         +----------+
---R                 +-----+ | 2              +-----+
---R                \|I - 1 \|I  + I + 1  - I\|I - 1
---R           atan(---------------------------------)
---R                              I - 1
---R       + 
---R                    +-----------+              +----------+
---R                  2 | 2               3     2  | 2
---R             (- 4I \|I  - 3I + 1  + 4I  - 4I )\|I  + I + 1
---R           + 
---R                         +-----------+
---R                3     2  | 2               4     2
---R             (4I  + 4I )\|I  - 3I + 1  - 4I  + 4I
---R        *
---R                         +-----------+
---R                 +-----+ | 2               +-----+
---R                \|I - 1 \|I  - 3I + 1  - I\|I - 1
---R           atan(----------------------------------)
---R                               I - 1
---R       + 
---R                      +-----------+                     +----------+
---R              +-----+ | 2                      +-----+  | 2
---R         (- 4\|I - 1 \|I  - 3I + 1  + (6I - 4)\|I - 1 )\|I  + I + 1
---R       + 
---R                          +-----------+
---R                  +-----+ | 2                  2           +-----+
---R         (2I + 4)\|I - 1 \|I  - 3I + 1  + (- 4I  - 4I + 4)\|I - 1
---R    /
---R                    +-----------+                       +----------+
---R            +-----+ | 2                        +-----+  | 2
---R         (2\|I - 1 \|I  - 3I + 1  + (- 2I + 2)\|I - 1 )\|I  + I + 1
---R       + 
---R                            +-----------+
---R                    +-----+ | 2                2      +-----+
---R         (- 2I - 2)\|I - 1 \|I  - 3I + 1  + (2I  - 2)\|I - 1
---R     ,
---R
---R                 +-----------+            +----------+
---R               2 | 2              3    2  | 2
---R             (I \|I  - 3I + 1  - I  + I )\|I  + I + 1
---R           + 
---R                         +-----------+
---R                 3    2  | 2              4    2
---R             (- I  - I )\|I  - 3I + 1  + I  - I
---R        *
---R           log
---R                        3     2           +-------+     4     3     2
---R                    ((4I  - 4I  + 2I - 2)\|- I + 1  - 2I  + 4I  - 6I  + 4I)
---R                 *
---R                     +----------+
---R                     | 2
---R                    \|I  + I + 1
---R                + 
---R                       4     3     2       +-------+     5     4     3     2
---R                  (- 4I  + 2I  - 2I  + 4I)\|- I + 1  + 2I  - 3I  + 5I  - 4I
---R                + 
---R                  2I - 2
---R             /
---R                         +----------+
---R                         | 2              2
---R                (2I + 2)\|I  + I + 1  - 2I  - 3I - 2
---R       + 
---R                   +-----------+            +----------+
---R                 2 | 2              3    2  | 2
---R             (- I \|I  - 3I + 1  + I  - I )\|I  + I + 1
---R           + 
---R                       +-----------+
---R               3    2  | 2              4    2
---R             (I  + I )\|I  - 3I + 1  - I  + I
---R        *
---R           log
---R                          3     2           +-------+     4     3      2
---R                    ((- 4I  + 8I  - 6I + 2)\|- I + 1  - 2I  + 8I  - 10I  + 4I)
---R                 *
---R                     +-----------+
---R                     | 2
---R                    \|I  - 3I + 1
---R                + 
---R                     4      3      2       +-------+     5      4      3      2
---R                  (4I  - 14I  + 14I  - 4I)\|- I + 1  + 2I  - 11I  + 21I  - 20I
---R                + 
---R                  10I - 2
---R             /
---R                         +-----------+
---R                         | 2               2
---R                (2I - 2)\|I  - 3I + 1  - 2I  + 5I - 2
---R       + 
---R                                   +-----------+
---R                     +-------+ +-+ | 2                2       +-------+ +-+
---R               (- 4I\|- I + 1 \|I \|I  - 3I + 1  + (4I  - 4I)\|- I + 1 \|I )
---R            *
---R                +----------+
---R                | 2
---R               \|I  + I + 1
---R           + 
---R                                    +-----------+
---R              2       +-------+ +-+ | 2                  3       +-------+ +-+
---R           (4I  + 4I)\|- I + 1 \|I \|I  - 3I + 1  + (- 4I  + 4I)\|- I + 1 \|I
---R        *
---R                          +-+
---R                         \|I
---R           atan(----------------------)
---R                 +-----------+
---R                 | 2
---R                \|I  - 3I + 1  - I + 1
---R       + 
---R                                   +-----------+
---R                     +-------+ +-+ | 2                2       +-------+ +-+
---R               (- 4I\|- I + 1 \|I \|I  - 3I + 1  + (4I  - 4I)\|- I + 1 \|I )
---R            *
---R                +----------+
---R                | 2
---R               \|I  + I + 1
---R           + 
---R                                    +-----------+
---R              2       +-------+ +-+ | 2                  3       +-------+ +-+
---R           (4I  + 4I)\|- I + 1 \|I \|I  - 3I + 1  + (- 4I  + 4I)\|- I + 1 \|I
---R        *
---R                          +-+
---R                         \|I
---R           atan(---------------------)
---R                 +----------+
---R                 | 2
---R                \|I  + I + 1  - I - 1
---R       + 
---R                        +-----------+                       +----------+
---R              +-------+ | 2                      +-------+  | 2
---R         (- 4\|- I + 1 \|I  - 3I + 1  + (6I - 4)\|- I + 1 )\|I  + I + 1
---R       + 
---R                            +-----------+
---R                  +-------+ | 2                  2           +-------+
---R         (2I + 4)\|- I + 1 \|I  - 3I + 1  + (- 4I  - 4I + 4)\|- I + 1
---R    /
---R                      +-----------+                         +----------+
---R            +-------+ | 2                        +-------+  | 2
---R         (2\|- I + 1 \|I  - 3I + 1  + (- 2I + 2)\|- I + 1 )\|I  + I + 1
---R       + 
---R                              +-----------+
---R                    +-------+ | 2                2      +-------+
---R         (- 2I - 2)\|- I + 1 \|I  - 3I + 1  + (2I  - 2)\|- I + 1
---R     ,
---R
---R                    +-----------+              +----------+
---R                  2 | 2               3     2  | 2
---R             (- 2I \|I  - 3I + 1  + 2I  - 2I )\|I  + I + 1
---R           + 
---R                         +-----------+
---R                3     2  | 2               4     2
---R             (2I  + 2I )\|I  - 3I + 1  - 2I  + 2I
---R        *
---R                         +----------+
---R                 +-----+ | 2              +-----+
---R                \|I - 1 \|I  + I + 1  - I\|I - 1
---R           atan(---------------------------------)
---R                              I - 1
---R       + 
---R                    +-----------+              +----------+
---R                  2 | 2               3     2  | 2
---R             (- 2I \|I  - 3I + 1  + 2I  - 2I )\|I  + I + 1
---R           + 
---R                         +-----------+
---R                3     2  | 2               4     2
---R             (2I  + 2I )\|I  - 3I + 1  - 2I  + 2I
---R        *
---R                         +-----------+
---R                 +-----+ | 2               +-----+
---R                \|I - 1 \|I  - 3I + 1  - I\|I - 1
---R           atan(----------------------------------)
---R                               I - 1
---R       + 
---R                                 +-----------+
---R                     +-----+ +-+ | 2                2       +-----+ +-+
---R               (- 2I\|I - 1 \|I \|I  - 3I + 1  + (2I  - 2I)\|I - 1 \|I )
---R            *
---R                +----------+
---R                | 2
---R               \|I  + I + 1
---R           + 
---R                                    +-----------+
---R                2       +-----+ +-+ | 2                  3       +-----+ +-+
---R             (2I  + 2I)\|I - 1 \|I \|I  - 3I + 1  + (- 2I  + 2I)\|I - 1 \|I
---R        *
---R                          +-+
---R                         \|I
---R           atan(----------------------)
---R                 +-----------+
---R                 | 2
---R                \|I  - 3I + 1  - I + 1
---R       + 
---R                                 +-----------+
---R                     +-----+ +-+ | 2                2       +-----+ +-+
---R               (- 2I\|I - 1 \|I \|I  - 3I + 1  + (2I  - 2I)\|I - 1 \|I )
---R            *
---R                +----------+
---R                | 2
---R               \|I  + I + 1
---R           + 
---R                                    +-----------+
---R                2       +-----+ +-+ | 2                  3       +-----+ +-+
---R             (2I  + 2I)\|I - 1 \|I \|I  - 3I + 1  + (- 2I  + 2I)\|I - 1 \|I
---R        *
---R                          +-+
---R                         \|I
---R           atan(---------------------)
---R                 +----------+
---R                 | 2
---R                \|I  + I + 1  - I - 1
---R       + 
---R                      +-----------+                     +----------+
---R              +-----+ | 2                      +-----+  | 2
---R         (- 2\|I - 1 \|I  - 3I + 1  + (3I - 2)\|I - 1 )\|I  + I + 1
---R       + 
---R                         +-----------+
---R                 +-----+ | 2                  2           +-----+
---R         (I + 2)\|I - 1 \|I  - 3I + 1  + (- 2I  - 2I + 2)\|I - 1
---R    /
---R                   +-----------+                      +----------+
---R           +-----+ | 2                       +-----+  | 2
---R         (\|I - 1 \|I  - 3I + 1  + (- I + 1)\|I - 1 )\|I  + I + 1
---R       + 
---R                           +-----------+
---R                   +-----+ | 2               2      +-----+
---R         (- I - 1)\|I - 1 \|I  - 3I + 1  + (I  - 1)\|I - 1
---R     ]
---R               Type: Union(f2: List OrderedCompletion Expression Integer,...)
---E 161
-
---S 162 of 267
-in2109a:=integrate((1+I*z)^(1/2)+cot(z-1), z= 0..1,"noPole")
---R 
---R
---R   (160)  - infinity
---R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 162
+--E 132
 
---S 163 of 267
+--S 133 of 224
 in2112a:=integrate(-cot(z-1)+log(1-1/z^4), z= -1..1,"noPole")
 --R 
 --R
---R   (161)   + infinity
+--R   (133)   + infinity
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 163
+--E 133
 
---S 164 of 267
+--S 134 of 224
 in2115a:=integrate(-z/(z-1)+log(1-z^(1/3)), z= -1..1,"noPole")
 --R 
 --R
---R   (162)   + infinity
---R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 164
-
---S 165 of 267
-in2120a:=integrate(-z+1/(z^2+I*z-3)^(1/2), z= -1..1,"noPole")
---R 
---R
---R   (163)
---R                      +-------+    2
---R       log((- 4I + 8)\|- I - 2  + I  - 8I - 4)
---R     + 
---R                        +-----+    2
---R       - log((- 4I - 8)\|I - 2  + I  + 8I - 4)
---R  /
---R     2
+--R   (134)   + infinity
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 165
+--E 134
 
---S 166 of 267
-in2124a:=integrate(-1/z-1/(I/(z+I))^(1/2), z= -1..0,"noPole")
+--S 135 of 224
+in2120a:=integrate(-z+1/(z^2+%i*z-3)^(1/2), z= -1..1,"noPole")
 --R 
 --R
---R   (164)   + infinity
---R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 166
+--R   (135)
+--R                 +--------+                              +--------+
+--R   log((8 - 4%i)\|- 2 - %i  - 5 - 8%i) - log((- 8 - 4%i)\|- 2 + %i  - 5 + 8%i)
+--R   ---------------------------------------------------------------------------
+--R                                        2
+--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
+--E 135
 
---S 167 of 267
-in25:=integrate(cos(z), z= I..a)
+--S 136 of 224
+in25:=integrate(cos(z), z= %i..a)
 --R 
 --R
---R   (165)  sin(a) - sin(I)
---R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 167
+--R   (136)  sin(a) - sin(%i)
+--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
+--E 136
 
---S 168 of 267
+--S 137 of 224
 in25a:=integrate(cos(z), z= %i..a)
 --R 
 --R
---R   (166)  sin(a) - sin(%i)
+--R   (137)  sin(a) - sin(%i)
 --R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
---E 168
+--E 137
 
---S 169 of 267
-in25b:=integrate(exp(I*z), z= I..I*infinity)
+--S 138 of 224
+in25b:=integrate(exp(%i*z), z= %i..%i*infinity)
 --R 
 --R
---R             2              2
---R            I infinity     I
---R          %e           - %e
---R   (167)  -------------------
---R                   I
---R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 169
+--R                    - infinity
+--R          - %i %e %e           + %i
+--R   (138)  -------------------------
+--R                      %e
+--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
+--E 138
 
---S 170 of 267
-in25c:=integrate(exp(%i*z), z= %i..I*infinity)
+--S 139 of 224
+in25c:=integrate(exp(%i*z), z= %i..%i*infinity)
 --R 
 --R
---R                    %i I infinity
---R          - %i %e %e              + %i
---R   (168)  ----------------------------
---R                       %e
+--R                    - infinity
+--R          - %i %e %e           + %i
+--R   (139)  -------------------------
+--R                      %e
 --R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
---E 170
+--E 139
 
---S 171 of 267
+--S 140 of 224
 in28a:=integrate(1/z, z=1..z,"noPole")
 --R 
 --R
 --R               2
 --R          log(z )
---R   (169)  -------
+--R   (140)  -------
 --R             2
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 171
+--E 140
 
---S 172 of 267
+--S 141 of 224
 in30:=integrate(sin(3*asin(1/(1+z^2))), z= 0..%plusInfinity)
 --R 
 --R
 --R          3%pi
---R   (170)  ----
+--R   (141)  ----
 --R            4
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 172
+--E 141
 
---S 173 of 267
+--S 142 of 224
 in32:=integrate(exp(-z), z= 0..%plusInfinity)
 --R 
 --R
---R   (171)  1
+--R   (142)  1
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 173
+--E 142
 
---S 174 of 267
+--S 143 of 224
 in34a:=integrate(1/(sin(z)-1/2), z= 0..1,"noPole")
 --R 
 --R
---R   (172)
+--R   (143)
 --R       log
 --R                              2                                   2
 --R                    - 12sin(1)  + (42cos(1) + 48)sin(1) - 36cos(1)  - 84cos(1)
@@ -4776,315 +4423,202 @@ in34a:=integrate(1/(sin(z)-1/2), z= 0..1,"noPole")
 --R      +-+
 --R     \|3
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 174
+--E 143
 
---S 175 of 267
+--S 144 of 224
 in37:=integrate(atan(tan(1/z)), z= 0..1)
 --R 
 --R
---R   (173)   + infinity
+--R   (144)   + infinity
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 175
+--E 144
 
---S 176 of 267
+--S 145 of 224
 in40:=integrate(atan(tan(z)), z= 0..%plusInfinity)
 --R 
 --R
---R   (174)   + infinity
+--R   (145)   + infinity
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 176
+--E 145
 
---S 177 of 267
+--S 146 of 224
 in2157a:=integrate(acoth(z)-1/(1+z^(1/2)), z= 0..1,"noPole")
 --R 
 --R
 --R          log(4) + 10log(2) - 8
---R   (175)  ---------------------
+--R   (146)  ---------------------
 --R                    4
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 177
+--E 146
 
---S 178 of 267
+--S 147 of 224
 in2158a:=integrate(2*acoth(1-(1-z)^(1/2)), z= 0..1,"noPole")
 --R 
 --R
---R   (176)  2log(4) - 2
---R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 178
-
---S 179 of 267
-in2168a:=integrate(-csch(z-1)-(1+I*z)^(1/2), z= 0..1,"noPole")
---R 
---R
---R   (177)   + infinity
+--R   (147)  2log(4) - 2
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 179
+--E 147
 
---S 180 of 267
-in2179a:=integrate((z^3-I*(1-z^4)^(1/2))^4, z= -1..1,"noPole")
+--S 148 of 224
+in2168a:=integrate(-csch(z-1)-(1+%i*z)^(1/2), z= 0..1,"noPole")
 --R 
 --R
---R                4         2
---R          64064I  + 28080I  + 6930
---R   (178)  ------------------------
---R                    45045
---R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 180
+--R   (148)   + infinity
+--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
+--E 148
 
---S 181 of 267
-in2185a:=integrate(csch(z)+(z^2-I*z+1)^(1/2), z= 0..1,"noPole")
+--S 149 of 224
+in2185a:=integrate(csch(z)+(z^2-%i*z+1)^(1/2), z= 0..1,"noPole")
 --R 
 --R
---R   (179)   + infinity
---R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 181
+--R   (149)   + infinity
+--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
+--E 149
 
---S 182 of 267
+--S 150 of 224
 in2195a:=integrate(1-acoth(1-(1-z)^(1/2)), z= -1..1,"noPole")
 --R 
 --R
---R   (180)
+--R   (150)
 --R         +-+            +-+                 +-+          +-+
 --R   2log(\|2 ) - log(- 2\|2  + 3) + 3log(- 4\|2  + 6) + 4\|2  - 4log(4) + 8
 --R   -----------------------------------------------------------------------
 --R                                      4
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 182
+--E 150
 
---S 183 of 267
+--S 151 of 224
 in2201a:=integrate(acoth(z)+%pi-asec(z-1), z= 0..1,"noPole")
 --R 
 --R
 --R                +-+
 --R          - %pi\|2  + log(4) + 2%pi
---R   (181)  -------------------------
+--R   (151)  -------------------------
 --R                      2
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 183
+--E 151
 
---S 184 of 267
+--S 152 of 224
 in221:=integrate(log(z+sqrt(z^2-1)), z)
 --R 
 --R
 --R             +------+           +------+          +------+
 --R             | 2         2      | 2               | 2         2
 --R          (z\|z  - 1  - z )log(\|z  - 1  + z) + z\|z  - 1  - z  + 1
---R   (182)  ---------------------------------------------------------
+--R   (152)  ---------------------------------------------------------
 --R                                 +------+
 --R                                 | 2
 --R                                \|z  - 1  - z
 --R                                          Type: Union(Expression Integer,...)
---E 184
+--E 152
 
---S 185 of 267
+--S 153 of 224
 in227a:=integrate(atan(sin(z))+atan(1/(sin(z))), z= 0..1,"noPole")
 --R 
 --R
 --R            %pi
---R   (183)  - ---
+--R   (153)  - ---
 --R             2
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 185
+--E 153
 
---S 186 of 267
+--S 154 of 224
 in237a:=integrate(sin(z)*(1-cos(z)/sqrt(1-sin(z)^2))^2, z= 0..1,"noPole")
 --R 
 --R
---R   (184)  - 4cos(1) + 4
---R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 186
-
---S 187 of 267
-in2221:=integrate((z-I)*(-1+1/(z-I)), z= 0..%plusInfinity)
---R 
---R
---R   (185)  - infinity
+--R   (154)  - 4cos(1) + 4
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 187
+--E 154
 
---S 188 of 267
-in2243a:=integrate(-1/sinh(z-1)+1/(I*z)^(1/2), z= 0..1,"noPole")
+--S 155 of 224
+in2221:=integrate((z-%i)*(-1+1/(z-%i)), z= 0..%plusInfinity)
 --R 
 --R
---R   (186)   + infinity
---R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 188
+--R   (155)  - infinity
+--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
+--E 155
 
---S 189 of 267
-in2247a:=integrate(1/(z^2-I*z+2)^(1/2)+csc(z), z= 0..1,"noPole")
+--S 156 of 224
+in2243a:=integrate(-1/sinh(z-1)+1/(%i*z)^(1/2), z= 0..1,"noPole")
 --R 
 --R
---R   (187)   + infinity
---R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 189
+--R   (156)   + infinity
+--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
+--E 156
 
---S 190 of 267
+--S 157 of 224
 in2254a:=integrate(cosh(z^(1/2))-acoth(1-z), z= 0..1,"noPole")
 --R 
 --R
 --R          - %e log(4) + 4%e - 4
---R   (188)  ---------------------
+--R   (157)  ---------------------
 --R                   2%e
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 190
+--E 157
 
---S 191 of 267
-in2270a:=integrate(log(z)*log(1/z)*(I*z)^(1/3), z= -1..1,"noPole")
+--S 158 of 224
+in2270a:=integrate(log(z)*log(1/z)*(%i*z)^(1/3), z= -1..1,"noPole")
 --R 
 --R
---R              3+-+     3+---+
---R          - 27\|I  - 27\|- I
---R   (189)  -------------------
---R                   32
---R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 191
+--R              3+--+     3+----+
+--R          - 27\|%i  - 27\|- %i
+--R   (158)  ---------------------
+--R                    32
+--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
+--E 158
 
---S 192 of 267
+--S 159 of 224
 in2274a:=integrate(acoth(1-z)-acosh(1/z), z= -1..1,"noPole")
 --R 
 --R
 --R          3log(9) - 4%pi
---R   (190)  --------------
+--R   (159)  --------------
 --R                 4
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 192
+--E 159
 
---S 193 of 267
-in2275a:=integrate((z^2+I*z-3)^(1/2)*(3+z^2), z= -1..1,"noPole")
+--S 160 of 224
+in2275a:=integrate((z^2+%i*z-3)^(1/2)*(3+z^2), z= -1..1,"noPole")
 --R 
 --R
---R   (191)
---R                         10         8           6           4            2
---R                   - 960I   + 49920I  + 1320960I  + 3563520I  - 40550400I
---R                 + 
---R                   8847360
---R              *
---R                  +-------+
---R                 \|- I - 2
---R             + 
---R                   11        10         9         8          7           6
---R               120I   - 2640I   - 23520I  + 10560I  - 318720I  + 1359360I
---R             + 
---R                       5           4            3           2
---R               3056640I  + 9922560I  + 36034560I  - 2396160I  - 40919040I
---R             + 
---R               15482880
---R          *
---R              +-----+
---R             \|I - 2
+--R   (160)
+--R                       +--------+                          +--------+
+--R           (- 51691200\|- 2 - %i  - 26455440 + 73601880%i)\|- 2 + %i
 --R         + 
---R                   11        10         9         8          7           6
---R               120I   + 2640I   - 23520I  - 10560I  - 318720I  - 1359360I
---R             + 
---R                       5           4            3           2
---R               3056640I  - 9922560I  + 36034560I  + 2396160I  - 40919040I
---R             + 
---R               - 15482880
---R          *
---R              +-------+
---R             \|- I - 2
---R         + 
---R                12         10         8           6            4            2
---R           - 15I   + 12360I   + 67440I  - 3283200I  - 21131520I  + 73451520I
---R         + 
---R           - 27095040
+--R                                   +--------+
+--R           (26455440 + 73601880%i)\|- 2 - %i  + 118339815
 --R      *
---R                        +-------+    2
---R         log((- 4I + 8)\|- I - 2  + I  - 8I - 4)
+--R                       +--------+
+--R         log((8 - 4%i)\|- 2 - %i  - 5 - 8%i)
 --R     + 
---R                         10         8           6           4            2
---R                     960I   - 49920I  - 1320960I  - 3563520I  + 40550400I
---R                   + 
---R                     - 8847360
---R              *
---R                  +-------+
---R                 \|- I - 2
---R             + 
---R                     11        10         9         8          7           6
---R               - 120I   + 2640I   + 23520I  - 10560I  + 318720I  - 1359360I
---R             + 
---R                         5           4            3           2
---R               - 3056640I  - 9922560I  - 36034560I  + 2396160I  + 40919040I
---R             + 
---R               - 15482880
---R          *
---R              +-----+
---R             \|I - 2
---R         + 
---R                     11        10         9         8          7           6
---R               - 120I   - 2640I   + 23520I  + 10560I  + 318720I  + 1359360I
---R             + 
---R                         5           4            3           2
---R               - 3056640I  + 9922560I  - 36034560I  - 2396160I  + 40919040I
---R             + 
---R               15482880
---R          *
---R              +-------+
---R             \|- I - 2
---R         + 
---R              12         10         8           6            4            2
---R           15I   - 12360I   - 67440I  + 3283200I  + 21131520I  - 73451520I
+--R                     +--------+                          +--------+
+--R           (51691200\|- 2 - %i  + 26455440 - 73601880%i)\|- 2 + %i
 --R         + 
---R           27095040
+--R                                     +--------+
+--R           (- 26455440 - 73601880%i)\|- 2 - %i  - 118339815
 --R      *
---R                        +-----+    2
---R         log((- 4I - 8)\|I - 2  + I  + 8I - 4)
+--R                         +--------+
+--R         log((- 8 - 4%i)\|- 2 + %i  - 5 + 8%i)
 --R     + 
---R                    9            5            3              +-------+      11
---R           (- 20480I  + 17170432I  - 48234496I  + 57671680I)\|- I - 2  + 60I
---R         + 
---R                10         9          8          7           6            5
---R           3800I   - 39408I  - 172896I  - 790144I  - 6873344I  + 13455872I
---R         + 
---R                    4            3            2
---R           53588992I  - 16978944I  - 85084160I  + 9687040I + 21897216
---R      *
---R          +-----+
---R         \|I - 2
+--R                      +--------+                           +--------+
+--R       (- 123056128%i\|- 2 - %i  - 167267016 - 40872532%i)\|- 2 + %i
 --R     + 
---R                11        10         9          8          7           6
---R           - 60I   + 3800I   + 39408I  - 172896I  + 790144I  - 6873344I
---R         + 
---R                      5            4            3            2
---R           - 13455872I  + 53588992I  + 16978944I  - 85084160I  - 9687040I
---R         + 
---R           21897216
---R      *
---R          +-------+
---R         \|- I - 2
---R     + 
---R             11          9           7            5             3
---R       - 960I   + 133888I  + 3352576I  - 44081152I  + 129318912I  - 59834368I
+--R                                  +--------+
+--R       (- 167267016 + 40872532%i)\|- 2 - %i  + 236452160%i
 --R  /
---R                  6           4            2            +-------+        7
---R           (49152I  - 3735552I  + 14942208I  - 3145728)\|- I - 2  - 6144I
---R         + 
---R                  6           5           4            3           2
---R           135168I  + 1351680I  - 3784704I  - 15237120I  + 1769472I  + 14548992I
---R         + 
---R           - 5505024
---R      *
---R          +-----+
---R         \|I - 2
+--R                 +--------+                          +--------+
+--R       (21872640\|- 2 - %i  + 11194368 - 31143936%i)\|- 2 + %i
 --R     + 
---R                  7          6           5           4            3           2
---R           - 6144I  - 135168I  + 1351680I  + 3784704I  - 15237120I  - 1769472I
---R         + 
---R           14548992I + 5505024
---R      *
---R          +-------+
---R         \|- I - 2
---R     + 
---R           8          6            4            2
---R       768I  - 651264I  + 12066816I  - 27721728I  + 9633792
---R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 193
+--R                                 +--------+
+--R       (- 11194368 - 31143936%i)\|- 2 - %i  - 50074368
+--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
+--E 160
 
---S 194 of 267
+--S 161 of 224
 in2276a:=integrate((1-tanh(log(1+z^(1/3))))^5, z= -1..1,"noPole")
 --R 
 --R
---R   (192)
+--R   (161)
 --R                3+---+2          3+---+                3+---+
 --R       (- 918750\|- 1   + 1200000\|- 1  + 2100000)atan(\|- 1  + 1)
 --R     + 
@@ -5096,23 +4630,23 @@ in2276a:=integrate((1-tanh(log(1+z^(1/3))))^5, z= -1..1,"noPole")
 --R          3+---+2        3+---+
 --R     30625\|- 1   - 40000\|- 1  - 70000
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 194
+--E 161
 
---S 195 of 267
+--S 162 of 224
 in2278a:=integrate(acoth(1-z)+log(abs(z-1)/z), z= 0..1,"noPole")
 --R 
 --R
 --R          log(4)
---R   (193)  ------
+--R   (162)  ------
 --R             2
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 195
+--E 162
 
---S 196 of 267
+--S 163 of 224
 in2279a:=integrate(acoth(1/(z^2-z+1)^(1/2)), z= -1..1,"noPole")
 --R 
 --R
---R   (194)
+--R   (163)
 --R                                                                     +-+
 --R               +-+               +-+               +-+            - \|3  - 2
 --R       2log(12\|3  + 21) + log(6\|3  + 12) - log(2\|3  + 4) + log(----------)
@@ -5123,184 +4657,148 @@ in2279a:=integrate(acoth(1/(z^2-z+1)^(1/2)), z= -1..1,"noPole")
 --R  /
 --R     4
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 196
+--E 163
 
---S 197 of 267
-in2307a:=integrate(tan(z)-1/(z^2+I*z-3)^(1/2), z= -1..1,"noPole")
+--S 164 of 224
+in2311a:=integrate(-1/sinh(z-1)+1/(%i*z)^(1/2), z= 0..%pi,"noPole")
 --R 
 --R
---R   (195)
---R                        +-------+    2
---R       - log((- 4I + 8)\|- I - 2  + I  - 8I - 4)
+--R   (164)
+--R              %pi - 1 2      %pi - 1               %pi - 1 2      %pi - 1
+--R       log((%e       )  + 2%e        + 1) - log((%e       )  - 2%e        + 1)
 --R     + 
---R                      +-----+    2
---R       log((- 4I - 8)\|I - 2  + I  + 8I - 4)
+--R                              2                    2
+--R             +------+       %e  + 2%e + 1        %e  - 2%e + 1
+--R       - 4%i\|%i %pi  - log(-------------) + log(-------------)
+--R                                   2                    2
+--R                                 %e                   %e
 --R  /
 --R     2
---R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 197
-
---S 198 of 267
-in2311a:=integrate(-1/sinh(z-1)+1/(I*z)^(1/2), z= 0..%pi,"noPole")
---R 
---R
---R   (196)
---R                %pi - 1 2      %pi - 1
---R       I log((%e       )  + 2%e        + 1)
---R     + 
---R                                                                    2
---R                  %pi - 1 2      %pi - 1          +-----+         %e  + 2%e + 1
---R       - I log((%e       )  - 2%e        + 1) + 4\|I %pi  - I log(-------------)
---R                                                                         2
---R                                                                       %e
---R     + 
---R               2
---R             %e  - 2%e + 1
---R       I log(-------------)
---R                    2
---R                  %e
---R  /
---R     2I
---R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 198
+--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
+--E 164
 
---S 199 of 267
-in2312:=integrate(sin(z)-1/(z^2+I*z-1)^(1/2), z= -1..1)
+--S 165 of 224
+in2312:=integrate(sin(z)-1/(z^2+%i*z-1)^(1/2), z= -1..1)
 --R 
 --R
---R   (197)  potentialPole
+--R   (165)  potentialPole
 --R                                         Type: Union(pole: potentialPole,...)
---E 199
+--E 165
 
---S 200 of 267
-in2312a:=integrate(sin(z)-1/(z^2+I*z-1)^(1/2), z= -1..1,"noPole")
+--S 166 of 224
+in2312a:=integrate(sin(z)-1/(z^2+%i*z-1)^(1/2), z= -1..1,"noPole")
 --R 
 --R
---R   (198)
---R                    +---+    2                            +-+    2
---R   - log((- 4I + 8)\|- I  + I  - 8I + 4) + log((- 4I - 8)\|I  + I  + 8I + 4)
---R   -------------------------------------------------------------------------
---R                                       2
---R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 200
+--R                          +----+                              +--+
+--R          - log((8 - 4%i)\|- %i  + 3 - 8%i) + log((- 8 - 4%i)\|%i  + 3 + 8%i)
+--R   (166)  -------------------------------------------------------------------
+--R                                           2
+--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
+--E 166
 
---S 201 of 267
+--S 167 of 224
 in2324a:=integrate(cosh(z^(1/2)-1)+acoth(1-z), z= 0..1,"noPole")
 --R 
 --R
 --R                         2
 --R          %e log(4) + 2%e  - 4%e + 2
---R   (199)  --------------------------
+--R   (167)  --------------------------
 --R                      2%e
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 201
+--E 167
 
---S 202 of 267
-in2330a:=integrate(exp(-z)+1/(z^2+I*z-1)^(1/2), z= -1..1,"noPole")
+--S 168 of 224
+in2330a:=integrate(exp(-z)+1/(z^2+%i*z-1)^(1/2), z= -1..1,"noPole")
 --R 
 --R
---R   (200)
---R                         +---+    2
---R       %e log((- 4I + 8)\|- I  + I  - 8I + 4)
+--R   (168)
+--R                        +----+                                 +--+
+--R       %e log((8 - 4%i)\|- %i  + 3 - 8%i) - %e log((- 8 - 4%i)\|%i  + 3 + 8%i)
 --R     + 
---R                           +-+    2                2
---R       - %e log((- 4I - 8)\|I  + I  + 8I + 4) + 2%e  - 2
+--R          2
+--R       2%e  - 2
 --R  /
 --R     2%e
---R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 202
+--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
+--E 168
 
---S 203 of 267
+--S 169 of 224
 in2332a:=integrate(acoth(z^(1/2))*(1-z^(1/2)), z= 0..1,"noPole")
 --R 
 --R
 --R          log(16) - log(4) - 10log(2) + 8
---R   (201)  -------------------------------
+--R   (169)  -------------------------------
 --R                         12
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 203
+--E 169
 
---S 204 of 267
+--S 170 of 224
 in2333a:=integrate(acoth(z)+1/(z^2+z+2)^(1/2), z= 0..1,"noPole")
 --R 
 --R
 --R                  +-+
 --R          log(- 4\|2  + 9) + log(4)
---R   (202)  -------------------------
+--R   (170)  -------------------------
 --R                      2
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 204
-
---S 205 of 267
-in2340a:=integrate(exp(I*(I*z)^(1/2))+cot(z-1), z= -1..1,"noPole")
---R 
---R
---R   (203)  - infinity
---R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 205
+--E 170
 
---S 206 of 267
-in2360a:=integrate(1/(1-I*z^2)^(1/2)-csch(z-1), z= -1..1,"noPole")
+--S 171 of 224
+in2360a:=integrate(1/(1-%i*z^2)^(1/2)-csch(z-1), z= -1..1,"noPole")
 --R 
 --R
---R   (204)  [ + infinity, + infinity]
---R               Type: Union(f2: List OrderedCompletion Expression Integer,...)
---E 206
+--R   (171)  [ + infinity, + infinity]
+--R       Type: Union(f2: List OrderedCompletion Expression Complex Integer,...)
+--E 171
 
---S 207 of 267
-in2367a:=integrate(log(1-z^2)-1/(I/(z-I))^(1/2), z= -1..1,"noPole")
+--S 172 of 224
+in2367a:=integrate(log(1-z^2)-1/(%i/(z-%i))^(1/2), z= -1..1,"noPole")
 --R 
 --R
---R   (205)
---R                         4                   4                   1
---R               3log(-----------) + 3log(-----------) - 3log(-----------)
---R                     2                   2                   2
---R                    I  - 2I + 1         I  + 2I + 1         I  - 2I + 1
---R             + 
---R                           1
---R               - 3log(-----------) + 6log(4) - 24
---R                       2
---R                      I  + 2I + 1
+--R   (172)
+--R                                         %i           %i
+--R             (6log(4) + 3log(2%i) - 3log(--) - 3log(- --) + 3log(- 2%i) - 24)
+--R                                          2            2
 --R          *
---R              +-------+
---R              |    I
---R              |- -----
---R             \|  I - 1
+--R              +--------+
+--R              |    %i
+--R              |- ------
+--R             \|  1 + %i
 --R         + 
---R           4I - 4
+--R           - 4 - 4%i
 --R      *
---R          +-------+
---R          |    I
---R          |- -----
---R         \|  I + 1
---R     + 
---R                  +-------+
---R                  |    I
---R       (- 4I - 4) |- -----
---R                 \|  I - 1
+--R          +------+
+--R          |   1
+--R          |------
+--R         \|1 + %i
+--R     + 
+--R                 +--------+
+--R                 |    %i
+--R       (4 + 4%i) |- ------
+--R                \|  1 + %i
 --R  /
---R        +-------+ +-------+
---R        |    I    |    I
---R     6  |- -----  |- -----
---R       \|  I - 1 \|  I + 1
---R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 207
+--R        +--------+ +------+
+--R        |    %i    |   1
+--R     6  |- ------  |------
+--R       \|  1 + %i \|1 + %i
+--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
+--E 172
 
---S 208 of 267
+--S 173 of 224
 in2375a:=integrate(acoth(1-z^(1/2))+1/z^(1/3), z= 0..1,"noPole")
 --R 
 --R
 --R          2log(4) + 1
---R   (206)  -----------
+--R   (173)  -----------
 --R               2
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 208
+--E 173
 
---S 209 of 267
+--S 174 of 224
 in2376a:=integrate(log(1-z^(1/3)-z^(2/3)), z= 0..infinity,"noPole")
 --R 
 --R
---R   (207)
+--R   (174)
 --R           +-+
 --R         3\|5
 --R      *
@@ -5326,341 +4824,230 @@ in2376a:=integrate(log(1-z^(1/3)-z^(2/3)), z= 0..infinity,"noPole")
 --R  /
 --R     6
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 209
+--E 174
 
---S 210 of 267
-in2378a:=integrate((z^2+I*z-3)^(1/2)-tanh(z-1), z= -1..1,"noPole")
+--S 175 of 224
+in2378a:=integrate((z^2+%i*z-3)^(1/2)-tanh(z-1), z= -1..1,"noPole")
 --R 
 --R
---R   (208)
---R                     4       2        +-------+     5      4      3       2
---R               (- 16I  - 128I  + 768)\|- I - 2  + 4I  - 24I  - 32I  - 320I
---R             + 
---R               - 960I - 384
---R          *
---R              +-----+
---R             \|I - 2
---R         + 
---R              5      4      3       2               +-------+    6      4
---R           (4I  + 24I  - 32I  + 320I  - 960I + 384)\|- I - 2  - I  + 60I
+--R   (175)
+--R                  +--------+               +--------+
+--R           (- 880\|- 2 - %i  + 88 + 924%i)\|- 2 + %i
 --R         + 
---R               2
---R           848I  - 192
+--R                          +--------+
+--R           (- 88 + 924%i)\|- 2 - %i  + 979
 --R      *
---R                        +-------+    2
---R         log((- 4I + 8)\|- I - 2  + I  - 8I - 4)
+--R                       +--------+
+--R         log((8 - 4%i)\|- 2 - %i  - 5 - 8%i)
 --R     + 
---R                   4       2        +-------+     5      4      3       2
---R               (16I  + 128I  - 768)\|- I - 2  - 4I  + 24I  + 32I  + 320I  + 960I
---R             + 
---R               384
---R          *
---R              +-----+
---R             \|I - 2
---R         + 
---R                5      4      3       2               +-------+    6      4
---R           (- 4I  - 24I  + 32I  - 320I  + 960I - 384)\|- I - 2  + I  - 60I
+--R                +--------+               +--------+                +--------+
+--R           (640\|- 2 - %i  - 64 - 672%i)\|- 2 + %i  + (64 - 672%i)\|- 2 - %i
 --R         + 
---R                 2
---R           - 848I  + 192
+--R           - 712
 --R      *
---R                        +-----+    2
---R         log((- 4I - 8)\|I - 2  + I  + 8I - 4)
---R     + 
---R                                   2 4       2 2
---R                    2           (%e )  + 2(%e )  + 1           2
---R               (128I  - 512)log(--------------------) + (- 128I  + 512)log(4)
---R                                          2 4
---R                                       (%e )
---R             + 
---R                     3       2
---R               - 256I  + 512I  + 1024I - 2048
---R          *
---R              +-------+
---R             \|- I - 2
+--R                2 4       2 2
+--R             (%e )  + 2(%e )  + 1
+--R         log(--------------------)
+--R                       2 4
+--R                    (%e )
+--R     + 
+--R                +--------+               +--------+                +--------+
+--R           (880\|- 2 - %i  - 88 - 924%i)\|- 2 + %i  + (88 - 924%i)\|- 2 - %i
 --R         + 
---R                                               2 4       2 2
---R                 3       2                  (%e )  + 2(%e )  + 1
---R           (- 32I  + 192I  + 640I + 256)log(--------------------)
---R                                                      2 4
---R                                                   (%e )
---R         + 
---R               3       2                         5      4       3       2
---R           (32I  - 192I  - 640I - 256)log(4) + 4I  + 72I  - 416I  - 320I
---R         + 
---R           2624I + 2176
+--R           - 979
 --R      *
---R          +-----+
---R         \|I - 2
---R     + 
---R                                               2 4       2 2
---R                 3       2                  (%e )  + 2(%e )  + 1
---R           (- 32I  - 192I  + 640I - 256)log(--------------------)
---R                                                      2 4
---R                                                   (%e )
---R         + 
---R               3       2                         5      4       3        2
---R           (32I  + 192I  - 640I + 256)log(4) - 4I  + 72I  + 160I  - 1856I
+--R                         +--------+
+--R         log((- 8 - 4%i)\|- 2 + %i  - 5 + 8%i)
+--R     + 
+--R                                         +--------+
+--R           (- 640log(4) + 2560 - 1280%i)\|- 2 - %i  + (64 + 672%i)log(4) - 2568
 --R         + 
---R           2496I + 128
+--R           - 3044%i
 --R      *
---R          +-------+
---R         \|- I - 2
+--R          +--------+
+--R         \|- 2 + %i
 --R     + 
---R                                 2 4       2 2
---R          4       2           (%e )  + 2(%e )  + 1
---R       (8I  - 576I  + 128)log(--------------------)
---R                                        2 4
---R                                     (%e )
+--R                                              +--------+
+--R       ((- 64 + 672%i)log(4) - 2056 - 2332%i)\|- 2 - %i  + 712log(4) - 2848
 --R     + 
---R            4       2                   5      4       3        2
---R       (- 8I  + 576I  - 128)log(4) - 32I  + 32I  + 768I  - 2304I  - 2560I + 512
+--R       3360%i
 --R  /
---R             2         +-------+      3       2                +-----+
---R       ((256I  - 1024)\|- I - 2  - 64I  + 384I  + 1280I + 512)\|I - 2
+--R             +--------+                 +--------+                  +--------+
+--R       (1280\|- 2 - %i  - 128 - 1344%i)\|- 2 + %i  + (128 - 1344%i)\|- 2 - %i
 --R     + 
---R             3       2                +-------+      4        2
---R       (- 64I  - 384I  + 1280I - 512)\|- I - 2  + 16I  - 1152I  + 256
---R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 210
+--R       - 1424
+--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
+--E 175
 
---S 211 of 267
+--S 176 of 224
 in2386a:=integrate(acoth(1-z)-(z^2-z+2)^(1/2), z= 0..1,"noPole")
 --R 
 --R
 --R                   +-+                 +-+          +-+
 --R          - 7log(4\|2  + 9) + 7log(- 4\|2  + 9) - 8\|2  + 8log(4)
---R   (209)  -------------------------------------------------------
+--R   (176)  -------------------------------------------------------
 --R                                     16
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 211
+--E 176
 
---S 212 of 267
-in2390a:=integrate((z^2-I*z-2)^(1/2)+1/sec(z-1), z= -1..1,"noPole")
+--S 177 of 224
+in2390a:=integrate((z^2-%i*z-2)^(1/2)+1/sec(z-1), z= -1..1,"noPole")
 --R 
 --R
---R   (210)
---R                     8        6         4          2  +-------+     9       8
---R               (- 64I  + 3840I  + 18432I  - 131072I )\|- I - 1  - 8I  + 176I
---R             + 
---R                    7        6        5         4          3         2
---R               1472I  - 3456I  - 1536I  - 33792I  - 102400I  + 40960I  + 65536I
---R          *
---R              +-----+
---R             \|I - 1
+--R   (177)
+--R                   2%i +--------+                  2%i  +--------+
+--R           (- 560%e   \|- 1 - %i  + (168 - 476%i)%e   )\|- 1 + %i
 --R         + 
---R                   9       8        7        6        5         4          3
---R               - 8I  - 176I  + 1472I  + 3456I  - 1536I  + 33792I  - 102400I
---R             + 
---R                       2
---R               - 40960I  + 65536I
---R          *
---R              +-------+
---R             \|- I - 1
---R         + 
---R              10       8        6         4          2
---R           - I   + 792I  - 6016I  - 84992I  + 110592I  - 32768
+--R                            2%i +--------+        2%i
+--R           (- 168 - 476%i)%e   \|- 1 - %i  + 455%e
 --R      *
---R                      +-----+    2
---R         log((4I + 8)\|I - 1  + I  + 8I)
+--R                       +--------+
+--R         log((8 + 4%i)\|- 1 + %i  - 1 + 8%i)
 --R     + 
---R                   8        6         4          2  +-------+     9       8
---R               (64I  - 3840I  - 18432I  + 131072I )\|- I - 1  + 8I  - 176I
---R             + 
---R                    7        6        5         4          3         2
---R             - 1472I  + 3456I  + 1536I  + 33792I  + 102400I  - 40960I  - 65536I
---R          *
---R              +-----+
---R             \|I - 1
---R         + 
---R                 9       8        7        6        5         4          3
---R               8I  + 176I  - 1472I  - 3456I  + 1536I  - 33792I  + 102400I
---R             + 
---R                     2
---R               40960I  - 65536I
---R          *
---R              +-------+
---R             \|- I - 1
---R         + 
---R            10       8        6         4          2
---R           I   - 792I  + 6016I  + 84992I  - 110592I  + 32768
---R      *
---R                      +-------+    2
---R         log((4I - 8)\|- I - 1  + I  - 8I)
---R     + 
---R                     6         4          2               7         5          3
---R               (1024I  - 69632I  + 262144I )sin(2) + 1536I  - 63488I  + 262144I
---R             + 
---R               - 131072I
---R          *
---R              +-------+
---R             \|- I - 1
---R         + 
---R                  7        6         5         4          3         2
---R             (128I  - 2816I  - 24576I  + 77824I  + 221184I  - 81920I  - 131072I)
---R          *
---R             sin(2)
+--R                 2%i +--------+                    2%i  +--------+
+--R           (560%e   \|- 1 - %i  + (- 168 + 476%i)%e   )\|- 1 + %i
 --R         + 
---R             9       8        7         6         5          4          3
---R           4I  + 264I  - 3456I  - 24320I  + 67072I  + 199680I  - 122880I
---R         + 
---R                    2
---R           - 245760I  + 16384I + 32768
+--R                          2%i +--------+        2%i
+--R           (168 + 476%i)%e   \|- 1 - %i  - 455%e
 --R      *
---R          +-----+
---R         \|I - 1
+--R                         +--------+
+--R         log((- 8 + 4%i)\|- 1 - %i  - 1 - 8%i)
 --R     + 
---R                  7        6         5         4          3         2
---R             (128I  + 2816I  - 24576I  - 77824I  + 221184I  + 81920I  - 131072I)
---R          *
---R             sin(2)
+--R                       2%i 2            2%i          +--------+
+--R           (- 640%i (%e   )  + 1280%i %e    + 640%i)\|- 1 - %i
 --R         + 
---R               9       8        7         6         5          4          3
---R           - 4I  + 264I  + 3456I  - 24320I  - 67072I  + 199680I  + 122880I
---R         + 
---R                    2
---R           - 245760I  - 16384I + 32768
+--R                           2%i 2                     2%i
+--R           (544 + 192%i)(%e   )  + (- 1480 - 580%i)%e    - 544 - 192%i
 --R      *
---R          +-------+
---R         \|- I - 1
+--R          +--------+
+--R         \|- 1 + %i
 --R     + 
---R           8         6          4          2                     9         7
---R       (16I  - 12800I  + 198656I  - 229376I  + 65536)sin(2) + 64I  - 13824I
+--R                        2%i 2                     2%i                +--------+
+--R       ((544 - 192%i)(%e   )  + (- 1480 + 580%i)%e    - 544 + 192%i)\|- 1 - %i
 --R     + 
---R              5          3
---R       174080I  - 327680I  + 131072I
+--R                2%i 2            2%i
+--R       520%i (%e   )  - 1824%i %e    - 520%i
 --R  /
---R                 6         4          2  +-------+       7        6         5
---R           (1024I  - 69632I  + 262144I )\|- I - 1  + 128I  - 2816I  - 24576I
---R         + 
---R                 4          3         2
---R           77824I  + 221184I  - 81920I  - 131072I
---R      *
---R          +-----+
---R         \|I - 1
+--R              2%i +--------+                     2%i  +--------+
+--R       (1280%e   \|- 1 - %i  + (- 384 + 1088%i)%e   )\|- 1 + %i
 --R     + 
---R              7        6         5         4          3         2
---R         (128I  + 2816I  - 24576I  - 77824I  + 221184I  + 81920I  - 131072I)
---R      *
---R          +-------+
---R         \|- I - 1
---R     + 
---R          8         6          4          2
---R       16I  - 12800I  + 198656I  - 229376I  + 65536
---R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 212
+--R                       2%i +--------+         2%i
+--R       (384 + 1088%i)%e   \|- 1 - %i  - 1040%e
+--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
+--E 177
 
---S 213 of 267
+--S 178 of 224
 in2392a:=integrate(1/sec(z-1)+acoth(1-z^(1/2)), z= 0..1,"noPole")
 --R 
 --R
---R   (211)  sin(1) + log(4) - 1
+--R   (178)  sin(1) + log(4) - 1
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 213
+--E 178
 
---S 214 of 267
-in2404a:=integrate(1/(1+I*z^2)^(1/2)+acoth(z), z= -1..1,"noPole")
+--S 179 of 224
+in2404a:=integrate(1/(1+%i*z^2)^(1/2)+acoth(z), z= -1..1,"noPole")
 --R 
 --R
---R   (212)
+--R   (179)
 --R   [
---R         -
---R            log
---R                       2       +-+     2       +-----+        2       +-+     3
---R                   ((2I  + 4I)\|I  + 4I  + 2I)\|I + 1  + (- 4I  - 4I)\|I  - 2I
---R                 + 
---R                       2
---R                   - 5I  - 2I
---R              /
---R                   +-----+
---R                 2\|I + 1  - I - 2
+--R            +-----+
+--R           \|- 4%i
+--R        *
+--R           log
+--R                             +-----+             +------+               +-----+
+--R                  ((4 - 8%i)\|- 4%i  + 8 + 16%i)\|1 + %i  + (- 8 + 8%i)\|- 4%i
+--R                + 
+--R                  - 20%i
+--R             /
+--R                  +------+
+--R                2\|1 + %i  - 2 - %i
 --R       + 
---R         log
---R                      2       +-+     2       +-----+      2       +-+     3
---R                ((- 2I  - 4I)\|I  + 4I  + 2I)\|I + 1  + (4I  + 4I)\|I  - 2I
---R              + 
---R                    2
---R                - 5I  - 2I
---R           /
---R                +-----+
---R              2\|I + 1  - I - 2
+--R         -
+--R               +-----+
+--R              \|- 4%i
+--R           *
+--R              log
+--R                                  +-----+             +------+
+--R                     ((- 4 + 8%i)\|- 4%i  + 8 + 16%i)\|1 + %i
+--R                   + 
+--R                               +-----+
+--R                     (8 - 8%i)\|- 4%i  - 20%i
+--R                /
+--R                     +------+
+--R                   2\|1 + %i  - 2 - %i
 --R    /
---R         +-+
---R       2\|I
+--R       4
 --R     ,
---R           +---+ +-----+    +---+
---R          \|- I \|I + 1  - \|- I
---R    4atan(-----------------------)
---R                     I
---R    ------------------------------]
---R                 +---+
---R                \|- I
---R               Type: Union(f2: List OrderedCompletion Expression Integer,...)
---E 214
+--R                      +------+
+--R        +---+     2%i\|1 + %i  - 2%i
+--R    - 2\|4%i atan(------------------)]
+--R                         +---+
+--R                        \|4%i
+--R       Type: Union(f2: List OrderedCompletion Expression Complex Integer,...)
+--E 179
 
---S 215 of 267
-in2409a:=integrate(tan(z)+1/(I/(z+I))^(1/2), z= 0..1/2*%pi,"noPole")
+--S 180 of 224
+in2409a:=integrate(tan(z)+1/(%i/(z+%i))^(1/2), z= 0..1/2*%pi,"noPole")
 --R 
 --R
---R   (213)   + infinity
---R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 215
+--R   (180)   + infinity
+--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
+--E 180
 
---S 216 of 267
-in248a:=integrate(log(z^I)^2, z= 0..1,"noPole")
+--S 181 of 224
+in248a:=integrate(log(z^%i)^2, z= 0..1,"noPole")
 --R 
 --R
---R            2
---R   (214)  2I
---R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 216
+--R   (181)  - 2
+--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
+--E 181
 
---S 217 of 267
+--S 182 of 224
 in248b:=integrate(log(z^%i)^2, z= 0..1,"noPole")
 --R 
 --R
---R   (215)  - 2
+--R   (182)  - 2
 --R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
---E 217
+--E 182
 
---S 218 of 267
+--S 183 of 224
 in249a:=integrate((sin(z)/(cos(z)-1))^(1/3), z= 0..%pi,"noPole")
 --R 
 --R
 --R                 3+-+           3+-+         +-+
 --R          3log(32\|2 ) - 12log(2\|2 ) - 4%pi\|3
---R   (216)  --------------------------------------
+--R   (183)  --------------------------------------
 --R                            24
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 218
+--E 183
 
---S 219 of 267
+--S 184 of 224
 in251a:=integrate((-1)^z*exp(-z)*sin(z), z= 0..%plusInfinity,"noPole")
 --R 
 --R
 --R               2
 --R          - %pi  + 2
---R   (217)  ----------
+--R   (184)  ----------
 --R              4
 --R           %pi  + 4
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 219
+--E 184
 
---S 220 of 267
+--S 185 of 224
 in2434a:=integrate(acoth(z^(1/2))+log(abs(z-1)), z= 0..1,"noPole")
 --R 
 --R
 --R          log(16) + log(4) - 6log(2)
---R   (218)  --------------------------
+--R   (185)  --------------------------
 --R                       4
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 220
+--E 185
 
---S 221 of 267
+--S 186 of 224
 in2443a:=integrate(sech(z)+log(abs(1-1/z^(1/3))), z= -1..1,"noPole")
 --R 
 --R
---R   (219)
+--R   (186)
 --R                                        3+---+2    3+---+
 --R           3+---+2    3+---+            \|- 1   - 2\|- 1  + 1
 --R       log(\|- 1   - 2\|- 1  + 1) + log(---------------------) + 4atan(%e)
@@ -5673,75 +5060,70 @@ in2443a:=integrate(sech(z)+log(abs(1-1/z^(1/3))), z= -1..1,"noPole")
 --R  /
 --R     2
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 221
+--E 186
 
---S 222 of 267
+--S 187 of 224
 in2462a:=integrate(log((1+(1-z)^(1/2))/z)+csch(z), z= -1..0,"noPole")
 --R 
 --R
---R   (220)  - infinity
+--R   (187)  - infinity
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 222
+--E 187
 
---S 223 of 267
-in2469a:=integrate(1/(2+z)^2+1/(z^2-I*z-2)^(1/2), z= -1..1,"noPole")
+--S 188 of 224
+in2469a:=integrate(1/(2+z)^2+1/(z^2-%i*z-2)^(1/2), z= -1..1,"noPole")
 --R 
 --R
---R   (221)
---R                 +-----+    2                       +-------+    2
---R   3log((4I + 8)\|I - 1  + I  + 8I) - 3log((4I - 8)\|- I - 1  + I  - 8I) + 4
---R   -------------------------------------------------------------------------
---R                                       6
---R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 223
+--R   (188)
+--R                      +--------+
+--R       3log((8 + 4%i)\|- 1 + %i  - 1 + 8%i)
+--R     + 
+--R                          +--------+
+--R       - 3log((- 8 + 4%i)\|- 1 - %i  - 1 - 8%i) + 4
+--R  /
+--R     6
+--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
+--E 188
 
---S 224 of 267
+--S 189 of 224
 in2484a:=integrate(log(1-z^2)+sinh(z^(1/2)), z= 0..%plusInfinity,"noPole")
 --R 
 --R
---R   (222)   + infinity
+--R   (189)   + infinity
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 224
+--E 189
 
---S 225 of 267
+--S 190 of 224
 in2485a:=integrate(log(1-z^(1/2))-acoth(z^(1/2)), z= 0..1,"noPole")
 --R 
 --R
 --R          - log(16) + log(4) + 2log(2) - 10
---R   (223)  ---------------------------------
+--R   (190)  ---------------------------------
 --R                          4
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 225
+--E 190
 
---S 226 of 267
+--S 191 of 224
 in2521a:=integrate(acoth(z^(1/2))+cos(z^(1/2)-1), z= 0..1,"noPole")
 --R 
 --R
---R   (224)  - 2cos(1) + 3
+--R   (191)  - 2cos(1) + 3
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 226
+--E 191
 
---S 227 of 267
+--S 192 of 224
 in2524a:=integrate(log(abs(1+1/z^(1/3)))+log(1+1/z), z= -1..0,"noPole")
 --R 
 --R
---R   (225)  - infinity
+--R   (192)  - infinity
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 227
-
---S 228 of 267
-in2527a:=integrate(1/(1+I*z^(1/3))+cosh(z), z= %minusInfinity..0,"noPole")
---R 
---R
---R   (226)   + infinity
---R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 228
+--E 192
 
---S 229 of 267
+--S 193 of 224
 in2533a:=integrate(log(abs(1-1/z^(1/3)))-log(1-1/z), z= -1..0,"noPole")
 --R 
 --R
---R   (227)
+--R   (193)
 --R                                          3+---+2    3+---+
 --R              3+---+2   3+---+            \|- 1   - 2\|- 1  + 1    3+---+2
 --R       - log(3\|- 1   + \|- 1  - 1) + log(---------------------) + \|- 1
@@ -5753,104 +5135,52 @@ in2533a:=integrate(log(abs(1-1/z^(1/3)))-log(1-1/z), z= -1..0,"noPole")
 --R  /
 --R     2
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 229
+--E 193
 
---S 230 of 267
+--S 194 of 224
 in2566a:=integrate(log(1+(1-z)^(1/2))+acoth(1-z), z= -1..1,"noPole")
 --R 
 --R
 --R                +-+          +-+
 --R          4log(\|2  + 1) + 4\|2  + 3log(9) - 4
---R   (228)  ------------------------------------
+--R   (194)  ------------------------------------
 --R                            4
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 230
-
---S 231 of 267
-in2567a:=integrate(1/(I*z)^(1/3)*log(abs(z-1)), z= 0..1/2*%pi,"noPole")
---R 
---R
---R   (229)
---R                      3+---+3+-----+2     3+-+3+---+2 3+-----+   2 3+-+2
---R          3+-+2    - I\|- I \|I %pi   - 2I\|2 \|- I   \|I %pi + I  \|2
---R       6I \|2  log(----------------------------------------------------)
---R                                           3+-+2
---R                                           \|2
---R     + 
---R       -
---R               3+-+2
---R            3I \|2
---R         *
---R            log
---R                       3+---+3+-----+2               3+-+3+---+2 3+-----+
---R                   - 6I\|- I \|I %pi   + (I %pi + 4I)\|2 \|- I   \|I %pi
---R                 + 
---R                      2        2 3+-+2
---R                   (2I %pi + 2I )\|2
---R              /
---R                  3+-+2
---R                 2\|2
---R     + 
---R                          3+---+2 3+-----+   3+-+
---R           3+-+2 +-+     2\|- I   \|I %pi + I\|2
---R       12I \|2  \|3 atan(------------------------)
---R                                  3+-+ +-+
---R                                 I\|2 \|3
---R     + 
---R                2
---R             %pi  - 4%pi + 4       3+---+3+-----+2      3+-+2     2
---R       (6log(---------------) - 18)\|- I \|I %pi   - 3I \|2  log(I )
---R                    4
---R     + 
---R                3+-+2 +-+
---R       - 2I %pi \|2  \|3
---R  /
---R        3+-+2 3+---+
---R     8I \|2   \|- I
---R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 231
+--E 194
 
---S 232 of 267
+--S 195 of 224
 in2586a:=integrate(acoth(z^(1/2))+atan(z^(1/2)), z= 0..1,"noPole")
 --R 
 --R
 --R          log(16) - log(4) - 2log(2) + 2%pi
---R   (230)  ---------------------------------
+--R   (195)  ---------------------------------
 --R                          4
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 232
+--E 195
 
---S 233 of 267
+--S 196 of 224
 in2591a:=integrate(log(z)/(1-z^(1/2))^3-log(z)*log(-z), z= 0..1,"noPole")
 --R 
 --R
---R   (231)  - infinity
+--R   (196)  - infinity
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 233
-
---S 234 of 267
-in2597a:=integrate((1+I/z)^(1/2)-log(1-1/z^2), z= 0..%plusInfinity,"noPole")
---R 
---R
---R   (232)   + infinity
---R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 234
+--E 196
 
---S 235 of 267
+--S 197 of 224
 in2598a:=integrate(exp(-z^(1/2))+acoth(1-z^(1/2)), z= 0..1,"noPole")
 --R 
 --R
 --R          %e log(4) + %e - 4
---R   (233)  ------------------
+--R   (197)  ------------------
 --R                  %e
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 235
+--E 197
 
---S 236 of 267
+--S 198 of 224
 in2604a:=integrate(acoth(1-z^(1/2))+log(1+z^(1/3)), z= 1..2,"noPole")
 --R 
 --R
---R   (234)
+--R   (198)
 --R             6+-+2                6+-+3                6+-+3         6+-+4
 --R       18log(\|2   + 1) + 3log(- 2\|2   + 3) - 6log(- 4\|2   + 6) + 3\|2
 --R     + 
@@ -5859,55 +5189,54 @@ in2604a:=integrate(acoth(1-z^(1/2))+log(1+z^(1/3)), z= 1..2,"noPole")
 --R  /
 --R     6
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 236
+--E 198
 
---S 237 of 267
+--S 199 of 224
 in271a:=integrate(1/sqrt((z^2-1)*(z^2-1)), z= 2..%plusInfinity,"noPole")
 --R 
 --R
 --R          log(9)
---R   (235)  ------
+--R   (199)  ------
 --R             4
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 237
+--E 199
 
---S 238 of 267
-in275c:=integrate(sqrt(z), z= -I..I,"noPole")
+--S 200 of 224
+in275c:=integrate(sqrt(z), z= -%i..%i,"noPole")
 --R 
 --R
---R             +-+      +---+
---R          2I\|I  + 2I\|- I
---R   (236)  -----------------
---R                  3
---R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 238
+--R              +--+       +----+
+--R          2%i\|%i  + 2%i\|- %i
+--R   (200)  ---------------------
+--R                    3
+--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
+--E 200
 
---S 239 of 267
-in275a:=integrate(1/(1+z), z= -I..I,"noPole")
+--S 201 of 224
+in275a:=integrate(1/(1+z), z= -%i..%i,"noPole")
 --R 
 --R
---R               2                  2
---R          log(I  + 2I + 1) - log(I  - 2I + 1)
---R   (237)  -----------------------------------
---R                           2
---R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 239
+--R          log(2%i) - log(- 2%i)
+--R   (201)  ---------------------
+--R                    2
+--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
+--E 201
 
---S 240 of 267
+--S 202 of 224
 in275b:=integrate(1/(1+z), z= -%i..%i,"noPole")
 --R 
 --R
 --R          log(2%i) - log(- 2%i)
---R   (238)  ---------------------
+--R   (202)  ---------------------
 --R                    2
 --R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
---E 240
+--E 202
 
---S 241 of 267
+--S 203 of 224
 in276a:=integrate(log(1-z^(1/3)-z^(2/3)), z= 0..sqrt(5)-2,"noPole")
 --R 
 --R
---R   (239)
+--R   (203)
 --R           +-+
 --R         3\|5
 --R      *
@@ -5932,258 +5261,155 @@ in276a:=integrate(log(1-z^(1/3)-z^(2/3)), z= 0..sqrt(5)-2,"noPole")
 --R  /
 --R     6
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 241
+--E 203
 
---S 242 of 267
-in2634a:=integrate(1/(z^2+I*z-1)^(1/2)+log(abs(z-1)), z= -1..1,"noPole")
+--S 204 of 224
+in2634a:=integrate(1/(z^2+%i*z-1)^(1/2)+log(abs(z-1)), z= -1..1,"noPole")
 --R 
 --R
---R   (240)
---R                      +---+    2                            +-+    2
---R       log((- 4I + 8)\|- I  + I  - 8I + 4) - log((- 4I - 8)\|I  + I  + 8I + 4)
+--R   (204)
+--R                     +----+                              +--+
+--R       log((8 - 4%i)\|- %i  + 3 - 8%i) - log((- 8 - 4%i)\|%i  + 3 + 8%i)
 --R     + 
 --R       2log(4) - 4
 --R  /
 --R     2
---R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 242
+--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
+--E 204
 
---S 243 of 267
+--S 205 of 224
 in2656a:=integrate(acoth(1-(1-z)^(1/2))-log(1-1/z), z= -1..1,"noPole")
 --R 
 --R
---R   (241)
+--R   (205)
 --R            +-+            +-+                 +-+          +-+
 --R   - 10log(\|2 ) + log(- 2\|2  + 3) - 3log(- 4\|2  + 6) - 4\|2  + 2log(4)
 --R   ----------------------------------------------------------------------
 --R                                      4
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 243
+--E 205
 
---S 244 of 267
+--S 206 of 224
 in2676a:=integrate(acoth(1-(1-z)^(1/2))-log(1-1/z), z= -1..1,"noPole")
 --R 
 --R
---R   (242)
+--R   (206)
 --R            +-+            +-+                 +-+          +-+
 --R   - 10log(\|2 ) + log(- 2\|2  + 3) - 3log(- 4\|2  + 6) - 4\|2  + 2log(4)
 --R   ----------------------------------------------------------------------
 --R                                      4
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 244
+--E 206
 
---S 245 of 267
+--S 207 of 224
 in2664aa:=integrate(atanh(1/z)+(1+z^2)^(1/2), z= 0..%plusInfinity,"noPole")
 --R 
 --R
---R   (243)   + infinity
+--R   (207)   + infinity
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 245
+--E 207
 
---S 246 of 267
-in2681a:=integrate((z^2-I*z-3)^(1/2)+%pi-acot(z-1), z= -1..1,"noPole")
+--S 208 of 224
+in2681a:=integrate((z^2-%i*z-3)^(1/2)+%pi-acot(z-1), z= -1..1,"noPole")
 --R 
 --R
---R   (244)
---R                     4       2        +-------+     5      4      3       2
---R               (- 16I  - 128I  + 768)\|- I - 2  - 4I  + 24I  + 32I  + 320I
---R             + 
---R               960I + 384
---R          *
---R              +-----+
---R             \|I - 2
---R         + 
---R                5      4      3       2               +-------+    6      4
---R           (- 4I  - 24I  + 32I  - 320I  + 960I - 384)\|- I - 2  - I  + 60I
+--R   (208)
+--R                  +--------+               +--------+                +--------+
+--R           (- 880\|- 2 - %i  - 88 - 924%i)\|- 2 + %i  + (88 - 924%i)\|- 2 - %i
 --R         + 
---R               2
---R           848I  - 192
+--R           979
 --R      *
---R                      +-----+    2
---R         log((4I + 8)\|I - 2  + I  + 8I - 4)
+--R                       +--------+
+--R         log((8 + 4%i)\|- 2 + %i  - 5 + 8%i)
 --R     + 
---R                   4       2        +-------+     5      4      3       2
---R               (16I  + 128I  - 768)\|- I - 2  + 4I  - 24I  - 32I  - 320I  - 960I
---R             + 
---R               - 384
---R          *
---R              +-----+
---R             \|I - 2
+--R                +--------+               +--------+                  +--------+
+--R           (880\|- 2 - %i  + 88 + 924%i)\|- 2 + %i  + (- 88 + 924%i)\|- 2 - %i
 --R         + 
---R              5      4      3       2               +-------+    6      4
---R           (4I  + 24I  - 32I  + 320I  - 960I + 384)\|- I - 2  + I  - 60I
---R         + 
---R                 2
---R           - 848I  + 192
+--R           - 979
 --R      *
---R                      +-------+    2
---R         log((4I - 8)\|- I - 2  + I  - 8I - 4)
+--R                         +--------+
+--R         log((- 8 + 4%i)\|- 2 - %i  - 5 - 8%i)
 --R     + 
---R                   2                      2             4         2
---R               (64I  - 256)log(25) + (256I  - 1024)atan(-) + (512I  - 2048)%pi
---R                                                        3
---R             + 
---R                   3
---R               256I  - 1024I
---R          *
---R              +-------+
---R             \|- I - 2
---R         + 
---R               3      2
---R           (16I  - 96I  - 320I - 128)log(25)
+--R                                   - 4 + 3%i                      +--------+
+--R           (320log(25) - 640%i log(---------) + 2560%pi + 1280%i)\|- 2 - %i
+--R                                    4 + 3%i
 --R         + 
---R               3       2                    4
---R           (64I  - 384I  - 1280I - 512)atan(-)
---R                                            3
+--R                                                 - 4 + 3%i
+--R           (32 + 336%i)log(25) + (672 - 64%i)log(---------) + (256 + 2688%i)%pi
+--R                                                  4 + 3%i
 --R         + 
---R                3       2                        5      4       3        2
---R           (128I  - 768I  - 2560I - 1024)%pi + 4I  + 72I  - 288I  - 1088I  + 64I
---R         + 
---R           1152
+--R           - 2312 - 356%i
 --R      *
---R          +-----+
---R         \|I - 2
+--R          +--------+
+--R         \|- 2 + %i
 --R     + 
---R               3      2
---R           (16I  + 96I  - 320I + 128)log(25)
---R         + 
---R               3       2                    4
---R           (64I  + 384I  - 1280I + 512)atan(-)
---R                                            3
---R         + 
---R                3       2                        5      4       3        2
---R           (128I  + 768I  - 2560I + 1024)%pi - 4I  + 72I  + 288I  - 1088I  - 64I
+--R                                                   - 4 + 3%i
+--R           (- 32 + 336%i)log(25) + (672 + 64%i)log(---------)
+--R                                                    4 + 3%i
 --R         + 
---R           1152
+--R           (- 256 + 2688%i)%pi - 2312 + 356%i
 --R      *
---R          +-------+
---R         \|- I - 2
+--R          +--------+
+--R         \|- 2 - %i
 --R     + 
---R          4       2                    4        2            4
---R       (4I  - 288I  + 64)log(25) + (16I  - 1152I  + 256)atan(-)
---R                                                             3
---R     + 
---R           4        2                5       3
---R       (32I  - 2304I  + 512)%pi + 32I  - 768I  + 2560I
+--R                                - 4 + 3%i
+--R       - 356log(25) + 712%i log(---------) - 2848%pi - 3360%i
+--R                                 4 + 3%i
 --R  /
---R             2         +-------+      3       2                +-----+
---R       ((256I  - 1024)\|- I - 2  + 64I  - 384I  - 1280I - 512)\|I - 2
---R     + 
---R           3       2                +-------+      4        2
---R       (64I  + 384I  - 1280I + 512)\|- I - 2  + 16I  - 1152I  + 256
---R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 246
-
---S 247 of 267
-in2691a:=integrate(1/(z^2+I*z-1)^(1/2)+(1-I*z)^(1/2), z= -1..1,"noPole")
---R 
---R
---R   (245)
---R                         +---+    2
---R       3I log((- 4I + 8)\|- I  + I  - 8I + 4)
---R     + 
---R                           +-+    2                      +-----+
---R       - 3I log((- 4I - 8)\|I  + I  + 8I + 4) + (4I + 4)\|I + 1
+--R             +--------+                 +--------+                    +--------+
+--R       (1280\|- 2 - %i  + 128 + 1344%i)\|- 2 + %i  + (- 128 + 1344%i)\|- 2 - %i
 --R     + 
---R                +-------+
---R       (4I - 4)\|- I + 1
---R  /
---R     6I
---R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 247
+--R       - 1424
+--R            Type: Union(f1: OrderedCompletion Expression Complex Integer,...)
+--E 208
 
+--S 209 of 224
 in2720a:=integrate(acoth(1-(1-z)^(1/2))+atan(z-1), z= 0..1,"noPole")
 --R 
 --R
 --R          5log(4) - %pi - 4
---R   (246)  -----------------
+--R   (209)  -----------------
 --R                  4
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 248
+--E 209
 
---S 249 of 267
+--S 210 of 224
 in2724a:=integrate(log(1-1/z^3)-(1+1/z^2)^(1/2), z= 0..%plusInfinity,"noPole")
 --R 
 --R
---R   (247)  - infinity
+--R   (210)  - infinity
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 249
+--E 210
 
---S 250 of 267
+--S 211 of 224
 in2732:=integrate(atan(1/3*3^(1/2)*(2*z-1)), z= 0..%plusInfinity)
 --R 
 --R
---R   (248)  - infinity
+--R   (211)  - infinity
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 250
+--E 211
 
---S 251 of 267
+--S 212 of 224
 in2783a:=integrate(1/z^(1/3)+atanh(1/z^(1/2)), z= 0..%plusInfinity,"noPole")
 --R 
 --R
---R   (249)   + infinity
+--R   (212)   + infinity
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 251
-
---S 252 of 267
-in2815a:=integrate((I*z)^(1/2)-(1+1/(I*z)^(1/2))^(1/2), z= -1..1,"noPole")
---R 
---R
---R   (250)
---R               +----------+              +--------+
---R               | +---+                   | +-+
---R               |\|- I  + 1               |\|I  + 1
---R       - 6log( |----------  + 1) + 6log( |--------  + 1)
---R               |   +---+                 |   +-+
---R              \|  \|- I                 \|  \|I
---R     + 
---R                      +--------+
---R                      | +-+
---R                  +-+ |\|I  + 1      +-+
---R              - 2\|I  |--------  + 2\|I  + 1
---R                      |   +-+
---R                     \|  \|I
---R       - 3log(------------------------------)
---R                            +-+
---R                           \|I
---R     + 
---R                      +----------+
---R                      | +---+
---R                +---+ |\|- I  + 1      +---+
---R            - 2\|- I  |----------  + 2\|- I  + 1
---R                      |   +---+
---R                     \|  \|- I
---R       3log(------------------------------------)
---R                            +---+
---R                           \|- I
---R     + 
---R                        +----------+                    +--------+
---R                        | +---+                         | +-+
---R           +---+        |\|- I  + 1          +-+        |\|I  + 1        +-+
---R       (12\|- I  - 24I) |----------  + (- 12\|I  - 24I) |--------  + 16I\|I
---R                        |   +---+                       |   +-+
---R                       \|  \|- I                       \|  \|I
---R     + 
---R           +---+
---R       16I\|- I
---R  /
---R     24I
---R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 252
+--E 212
 
---S 253 of 267
+--S 213 of 224
 in285:=integrate(sqrt(1+sqrt(z-1)), z)
 --R 
 --R
 --R                                 +------------+
 --R             +-----+             | +-----+
 --R          (4\|z - 1  + 12z - 20)\|\|z - 1  + 1
---R   (251)  -------------------------------------
+--R   (213)  -------------------------------------
 --R                            15
 --R                                          Type: Union(Expression Integer,...)
---E 253
+--E 213
 
---S 254 of 267
+--S 214 of 224
 in295a:=integrate(z*sqrt(1+sqrt(z^2-1)), z)
 --R 
 --R
@@ -6191,285 +5417,71 @@ in295a:=integrate(z*sqrt(1+sqrt(z^2-1)), z)
 --R             +------+             | +------+
 --R             | 2          2       | | 2
 --R          (2\|z  - 1  + 6z  - 10)\|\|z  - 1  + 1
---R   (252)  ---------------------------------------
+--R   (214)  ---------------------------------------
 --R                             15
 --R                                          Type: Union(Expression Integer,...)
---E 254
+--E 214
 
---S 255 of 267
+--S 215 of 224
 in295ba:=integrate(z*sqrt(1+sqrt(z^2-1)), z= 1..sqrt(2),"noPole")
 --R 
 --R
 --R            +-+
 --R          4\|2  + 4
---R   (253)  ---------
+--R   (215)  ---------
 --R              15
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 255
+--E 215
 
---S 256 of 267
+--S 216 of 224
 integrate(1/sqrt(20+x^2+y^2), x = -5..5,"noPole")
 --R 
 --R
 --R                 +-------+                       +-------+
 --R                 | 2          2                  | 2          2
 --R          log(10\|y  + 45  + y  + 70) - log(- 10\|y  + 45  + y  + 70)
---R   (254)  -----------------------------------------------------------
+--R   (216)  -----------------------------------------------------------
 --R                                       2
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 256
+--E 216
 
---S 257 of 267
+--S 217 of 224
 in291:=integrate(cos(2*atan(z-sqrt(2)))-sin(2*atan(z-sqrt(2))), z = 0..%plusInfinity)
 --R 
 --R
---R   (255)  - infinity
---R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 257
-
---S 258 of 267
-in2924a:=integrate(1/(I*z)^(1/2)+(1+1/(I*z)^(1/2))^(1/2), z= -1..1,"noPole")
---R 
---R
---R   (256)
---R                       +----------+                        +--------+
---R                       | +---+                             | +-+
---R         +---+ +-+     |\|- I  + 1           +---+ +-+     |\|I  + 1
---R       2\|- I \|I log( |----------  + 1) - 2\|- I \|I log( |--------  + 1)
---R                       |   +---+                           |   +-+
---R                      \|  \|- I                           \|  \|I
---R     + 
---R                             +--------+
---R                             | +-+
---R                         +-+ |\|I  + 1      +-+
---R                     - 2\|I  |--------  + 2\|I  + 1
---R                             |   +-+
---R        +---+ +-+           \|  \|I
---R       \|- I \|I log(------------------------------)
---R                                   +-+
---R                                  \|I
---R     + 
---R                                 +----------+
---R                                 | +---+
---R                           +---+ |\|- I  + 1      +---+
---R                       - 2\|- I  |----------  + 2\|- I  + 1
---R                                 |   +---+
---R          +---+ +-+             \|  \|- I
---R       - \|- I \|I log(------------------------------------)
---R                                       +---+
---R                                      \|- I
---R     + 
---R                           +----------+                             +--------+
---R                           | +---+                                  | +-+
---R           +---+       +-+ |\|- I  + 1        +---+ +-+      +---+  |\|I  + 1
---R       (8I\|- I  + 4I)\|I  |----------  + (8I\|- I \|I  + 4I\|- I ) |--------
---R                           |   +---+                                |   +-+
---R                          \|  \|- I                                \|  \|I
---R     + 
---R           +-+       +---+
---R       16I\|I  + 16I\|- I
---R  /
---R        +---+ +-+
---R     8I\|- I \|I
+--R   (217)  - infinity
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 258
-
---S 259 of 267
-in2963a:=integrate(cosh(-1+(1-z)^(1/2))+(z^2+I*z-3)^(1/2), z= -1..1,"noPole")
---R 
---R
---R   (257)
---R                                           +-+
---R                     4       2            \|2  - 1 +-------+
---R               (- 16I  - 128I  + 768)%e %e        \|- I - 2
---R             + 
---R                                                             +-+
---R                  5      4      3       2                   \|2  - 1
---R               (4I  - 24I  - 32I  - 320I  - 960I - 384)%e %e
---R          *
---R              +-----+
---R             \|I - 2
---R         + 
---R                                                         +-+
---R              5      4      3       2                   \|2  - 1 +-------+
---R           (4I  + 24I  - 32I  + 320I  - 960I + 384)%e %e        \|- I - 2
---R         + 
---R                                            +-+
---R               6      4       2            \|2  - 1
---R           (- I  + 60I  + 848I  - 192)%e %e
---R      *
---R                        +-------+    2
---R         log((- 4I + 8)\|- I - 2  + I  - 8I - 4)
---R     + 
---R                                         +-+
---R                   4       2            \|2  - 1 +-------+
---R               (16I  + 128I  - 768)%e %e        \|- I - 2
---R             + 
---R                                                               +-+
---R                    5      4      3       2                   \|2  - 1
---R               (- 4I  + 24I  + 32I  + 320I  + 960I + 384)%e %e
---R          *
---R              +-----+
---R             \|I - 2
---R         + 
---R                                                           +-+
---R                5      4      3       2                   \|2  - 1 +-------+
---R           (- 4I  - 24I  + 32I  - 320I  + 960I - 384)%e %e        \|- I - 2
---R         + 
---R                                          +-+
---R             6      4       2            \|2  - 1
---R           (I  - 60I  - 848I  + 192)%e %e
---R      *
---R                        +-----+    2
---R         log((- 4I - 8)\|I - 2  + I  + 8I - 4)
---R     + 
---R                                                              +-+     2
---R                     2           +-+          2              \|2  - 1
---R               ((256I  - 1024)%e\|2  + (- 256I  + 1024)%e)(%e        )
---R             + 
---R                       2          2          3                  2
---R                 ((256I  - 1024)%e  + (- 256I  + 1024I)%e + 256I  - 1024)
---R              *
---R                    +-+
---R                   \|2  - 1
---R                 %e
---R             + 
---R                      2           +-+          2
---R               (- 256I  + 1024)%e\|2  + (- 256I  + 1024)%e
---R          *
---R              +-------+
---R             \|- I - 2
---R         + 
---R                     3       2                  +-+
---R               (- 64I  + 384I  + 1280I + 512)%e\|2
---R             + 
---R                   3       2
---R               (64I  - 384I  - 1280I - 512)%e
---R          *
---R                 +-+     2
---R                \|2  - 1
---R             (%e        )
---R         + 
---R                     3       2                 2
---R               (- 64I  + 384I  + 1280I + 512)%e
---R             + 
---R                  5      4       3        2                      3       2
---R               (4I  + 72I  - 288I  - 1088I  + 64I + 1152)%e - 64I  + 384I
---R             + 
---R               1280I + 512
---R          *
---R                +-+
---R               \|2  - 1
---R             %e
---R         + 
---R               3       2                  +-+       3       2
---R           (64I  - 384I  - 1280I - 512)%e\|2  + (64I  - 384I  - 1280I - 512)%e
---R      *
---R          +-----+
---R         \|I - 2
---R     + 
---R                     3       2                  +-+
---R               (- 64I  - 384I  + 1280I - 512)%e\|2
---R             + 
---R                   3       2
---R               (64I  + 384I  - 1280I + 512)%e
---R          *
---R                 +-+     2
---R                \|2  - 1
---R             (%e        )
---R         + 
---R                     3       2                 2
---R               (- 64I  - 384I  + 1280I - 512)%e
---R             + 
---R                    5      4       3        2                      3       2
---R               (- 4I  + 72I  + 288I  - 1088I  - 64I + 1152)%e - 64I  - 384I
---R             + 
---R               1280I - 512
---R          *
---R                +-+
---R               \|2  - 1
---R             %e
---R         + 
---R               3       2                  +-+       3       2
---R           (64I  + 384I  - 1280I + 512)%e\|2  + (64I  + 384I  - 1280I + 512)%e
---R      *
---R          +-------+
---R         \|- I - 2
---R     + 
---R                                                                    +-+     2
---R            4        2          +-+         4        2             \|2  - 1
---R       ((16I  - 1152I  + 256)%e\|2  + (- 16I  + 1152I  - 256)%e)(%e        )
---R     + 
---R               4        2         2         5       3                 4        2
---R           (16I  - 1152I  + 256)%e  + (- 32I  + 768I  - 2560I)%e + 16I  - 1152I
---R         + 
---R           256
---R      *
---R            +-+
---R           \|2  - 1
---R         %e
---R     + 
---R             4        2          +-+         4        2
---R       (- 16I  + 1152I  - 256)%e\|2  + (- 16I  + 1152I  - 256)%e
---R  /
---R                               +-+
---R                2             \|2  - 1 +-------+
---R           (256I  - 1024)%e %e        \|- I - 2
---R         + 
---R                                               +-+
---R                 3       2                    \|2  - 1
---R           (- 64I  + 384I  + 1280I + 512)%e %e
---R      *
---R          +-----+
---R         \|I - 2
---R     + 
---R                                           +-+
---R             3       2                    \|2  - 1 +-------+
---R       (- 64I  - 384I  + 1280I - 512)%e %e        \|- I - 2
---R     + 
---R                                  +-+
---R           4        2            \|2  - 1
---R       (16I  - 1152I  + 256)%e %e
---R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 259
+--E 217
 
---S 260 of 267
+--S 218 of 224
 in2992a:=integrate(acoth(1-z^(1/2))+log(1+z^(1/3)), z= 1..%plusInfinity,"noPole")
 --R 
 --R
---R   (258)   + infinity
+--R   (218)   + infinity
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 260
+--E 218
 
---S 261 of 267
+--S 219 of 224
 in2997a:=integrate(log(1+1/z^3)-log(abs(1+z)), z= %minusInfinity..%plusInfinity,"noPole")
 --R 
 --R
---R   (259)  - infinity
+--R   (219)  - infinity
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 261
-
---S 262 of 267
-in3001a:=integrate(((I*z)^(1/2)-1)/(-2+(I*z)^(1/2)), z= 0..%plusInfinity,"noPole")
---R 
---R
---R   (260)   + infinity
---R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 262
+--E 219
 
---S 263 of 267
+--S 220 of 224
 in3008a:=integrate(exp(-z^(1/3))+atanh(1/z^(1/2)), z= 0..%plusInfinity,"noPole")
 --R 
 --R
---R   (261)   + infinity
+--R   (220)   + infinity
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 263
+--E 220
 
---S 264 of 267
+--S 221 of 224
 in303a:=integrate(1/(1+cosh(n*z)^2), z= 0..1,"noPole")
 --R 
 --R
---R   (262)
+--R   (221)
 --R       log
 --R                     +-+           - n 8          +-+          - n 6
 --R              (- 816\|2  + 1154)(%e   )  + (- 560\|2  + 792)(%e   )
@@ -6486,13 +5498,13 @@ in303a:=integrate(1/(1+cosh(n*z)^2), z= 0..1,"noPole")
 --R        +-+
 --R     4n\|2
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 264
+--E 221
 
---S 265 of 267
+--S 222 of 224
 in314a:=integrate(1/(sin(z)-1/2), z= 0..1,"noPole")
 --R 
 --R
---R   (263)
+--R   (222)
 --R       log
 --R                              2                                   2
 --R                    - 12sin(1)  + (42cos(1) + 48)sin(1) - 36cos(1)  - 84cos(1)
@@ -6514,25 +5526,25 @@ in314a:=integrate(1/(sin(z)-1/2), z= 0..1,"noPole")
 --R      +-+
 --R     \|3
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 265
+--E 222
 
---S 266 of 267
+--S 223 of 224
 in317:=integrate((cos(z)^a)^(1/a), z= 0..%pi)
 --R 
 --R
---R   (264)  0
+--R   (223)  0
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 266
+--E 223
 
---S 267 of 267
+--S 224 of 224
 in319a:=integrate(exp(-z)*atan(sin(z)/(1+cos(z))), z=0..%plusInfinity,"noPole")
 --R 
 --R
 --R          1
---R   (265)  -
+--R   (224)  -
 --R          2
 --R                    Type: Union(f1: OrderedCompletion Expression Integer,...)
---E 267
+--E 224
 )spool 
 )lisp (bye)
  



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========================================================================
diff --git a/changelog b/changelog
index a244a50..4916b6a 100644
--- a/changelog
+++ b/changelog
@@ -1,3 +1,9 @@
+20080409 tpd src/input/Makefile add integration regression testing	
+20080409 tpd src/input/schaum24.input integrals of inverse trig functions
+20080409 tpd src/input/schaum23.input integrals of csc(ax)
+20080409 tpd src/input/schaum22.input integrals of sec(ax)
+20080409 tpd src/input/schaum21.input integrals of cot(ax)
+20080409 tpd src/input/schaum20.input integrals of tan(ax)
 20080408 tpd src/input/mapleok.input fix I->%i, reorganize
 20080406 tpd src/input/Makefile add integration regression testing
 20080406 tpd src/input/schaum19.input integrals of sin(ax) and cos(ax)
diff --git a/src/input/Makefile.pamphlet b/src/input/Makefile.pamphlet
index 8170a48..c184fbe 100644
--- a/src/input/Makefile.pamphlet
+++ b/src/input/Makefile.pamphlet
@@ -359,7 +359,8 @@ REGRES= algaggr.regress algbrbf.regress  algfacob.regress alist.regress  \
     schaum5.regress   schaum6.regress  schaum7.regress  schaum8.regress \
     schaum9.regress   schaum10.regress schaum11.regress schaum12.regress \
     schaum13.regress  schaum14.regress schaum15.regress schaum16.regress \
-    schaum17.regress  schaum18.regress schaum19.regress \
+    schaum17.regress  schaum18.regress schaum19.regress schaum20.regress \
+    schaum21.regress  schaum22.regress schaum23.regress schaum24.regress \
     scherk.regress    scope.regress    seccsc.regress \
     segbind.regress   seg.regress \
     series2.regress   series.regress   sersolve.regress set.regress \
@@ -638,6 +639,8 @@ FILES= ${OUT}/algaggr.input  ${OUT}/algbrbf.input    ${OUT}/algfacob.input \
        ${OUT}/schaum11.input ${OUT}/schaum12.input   ${OUT}/schaum13.input \
        ${OUT}/schaum14.input ${OUT}/schaum15.input   ${OUT}/schaum16.input \
        ${OUT}/schaum17.input ${OUT}/schaum18.input   ${OUT}/schaum19.input \
+       ${OUT}/schaum20.input ${OUT}/schaum21.input   ${OUT}/schaum22.input \
+       ${OUT}/schaum23.input ${OUT}/schaum24.input \
        ${OUT}/saddle.input \
        ${OUT}/scherk.input   ${OUT}/scope.input      ${OUT}/seccsc.input \
        ${OUT}/segbind.input  ${OUT}/seg.input        ${OUT}/series2.input \
@@ -945,7 +948,9 @@ DOCFILES= \
   ${DOC}/schaum13.input.dvi    ${DOC}/schaum14.input.dvi \
   ${DOC}/schaum15.input.dvi    ${DOC}/schaum16.input.dvi \
   ${DOC}/schaum17.input.dvi    ${DOC}/schaum18.input.dvi \
-  ${DOC}/schaum19.input.dvi \
+  ${DOC}/schaum19.input.dvi    ${DOC}/schaum20.input.dvi \
+  ${DOC}/schaum21.input.dvi    ${DOC}/schaum22.input.dvi \
+  ${DOC}/schaum23.input.dvi    ${DOC}/schaum24.input.dvi \
   ${DOC}/s01eaf.input.dvi      ${DOC}/s13aaf.input.dvi     \
   ${DOC}/s13acf.input.dvi      ${DOC}/s13adf.input.dvi     \
   ${DOC}/s14aaf.input.dvi      ${DOC}/s14abf.input.dvi     \
diff --git a/src/input/schaum20.input.pamphlet b/src/input/schaum20.input.pamphlet
new file mode 100644
index 0000000..a25209e
--- /dev/null
+++ b/src/input/schaum20.input.pamphlet
@@ -0,0 +1,249 @@
+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/input schaum20.input}
+\author{Timothy Daly}
+\maketitle
+\eject
+\tableofcontents
+\eject
+\section{\cite{1}:14.429~~~~~$\displaystyle
+\int{\tan{ax}}~dx$}
+$$\int{\tan{ax}}=
+-\frac{1}{a}\ln~\cos{ax}=
+\frac{1}{a}\ln~\sec{ax}
+$$
+<<*>>=
+)spool schaum20.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1 of 11
+aa:=integrate(tan(a*x),x)
+--R 
+--R
+--R                    2
+--R        log(tan(a x)  + 1)
+--R   (1)  ------------------
+--R                2a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.430~~~~~$\displaystyle
+\int{\tan^2{ax}}~dx$}
+$$\int{\tan^2{ax}}=
+\frac{\tan{ax}}{x}-x
+$$
+<<*>>=
+)clear all
+
+--S 2 of 11
+aa:=integrate(tan(a*x)^2,x)
+--R 
+--R
+--R        tan(a x) - a x
+--R   (1)  --------------
+--R               a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.431~~~~~$\displaystyle
+\int{\tan^3{ax}}~dx$}
+$$\int{\tan^3{ax}}=
+\frac{\tan^2{ax}}{2a}+\frac{1}{a}\ln~\cos{ax}
+$$
+<<*>>=
+)clear all
+
+--S 3 of 11
+aa:=integrate(tan(a*x)^3,x)
+--R 
+--R
+--R                      2                2
+--R        - log(tan(a x)  + 1) + tan(a x)
+--R   (1)  --------------------------------
+--R                       2a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.432~~~~~$\displaystyle
+\int{\tan^n{ax}\sec^2{ax}}~dx$}
+$$\int{\tan^n{ax}\sec^2{ax}}=
+\frac{\tan^{n+1}{ax}}{(n+1)a}
+$$
+<<*>>=
+)clear all
+
+--S 4 of 11
+aa:=integrate(tan(a*x)^n*sec(a*x)^2,x)
+--R 
+--R
+--R                        sin(a x)
+--R                  n log(--------)
+--R                        cos(a x)
+--R        sin(a x)%e
+--R   (1)  -------------------------
+--R            (a n + a)cos(a x)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.433~~~~~$\displaystyle
+\int{\frac{\sec^2{ax}}{\tan{ax}}}~dx$}
+$$\int{\frac{\sec^2{ax}}{\tan{ax}}}=
+\frac{1}{a}\ln~\tan{ax}
+$$
+<<*>>=
+)clear all
+
+--S 5 of 11
+aa:=integrate(sec(a*x)^2/tan(a*x),x)
+--R 
+--R
+--R              sin(a x)              2cos(a x)
+--R        log(------------) - log(- ------------)
+--R            cos(a x) + 1          cos(a x) + 1
+--R   (1)  ---------------------------------------
+--R                           a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.434~~~~~$\displaystyle
+\int{\frac{dx}{\tan{ax}}}~dx$}
+$$\int{\frac{1}{\tan{ax}}}=
+\frac{1}{a}\ln~\sin{ax}
+$$
+<<*>>=
+)clear all
+
+--S 6 of 11
+aa:=integrate(1/tan(a*x),x)
+--R 
+--R
+--R                      2
+--R        - log(tan(a x)  + 1) + 2log(tan(a x))
+--R   (1)  -------------------------------------
+--R                          2a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.435~~~~~$\displaystyle
+\int{x\tan{ax}}~dx$}
+$$\int{x\tan{ax}}=
+\frac{1}{a^2}\left\{\frac{(ax)^3}{3}+\frac{(ax)^5}{15}+\frac{2(ax)^7}{105}
++\cdots+\frac{2^{2n}(2^{2n}-1)B_n(ax)^{2n+1}}{(2n+1)!}+\cdots\right\}
+$$
+<<*>>=
+)clear all
+
+--S 7 of 11
+aa:=integrate(x*tan(a*x),x)
+--R 
+--R
+--R           x
+--R         ++
+--I   (1)   |   %I tan(%I a)d%I
+--R        ++
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.436~~~~~$\displaystyle
+\int{\frac{\tan{ax}}{x}}~dx$}
+$$\int{\frac{\tan{ax}}{x}}=
+ax+\frac{(ax)^3}{9}+\frac{2(ax)^5}{75}+\cdots
++\frac{2^{2n}(2^{2n}-1)B_n(ax)^{2n-1}}{(2n-1)(2n)!}+\cdots
+$$
+<<*>>=
+)clear all
+
+--S 8 of 11
+aa:=integrate(tan(a*x)/x,x)
+--R 
+--R
+--R           x
+--I         ++  tan(%I a)
+--I   (1)   |   --------- d%I
+--I        ++       %I
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.437~~~~~$\displaystyle
+\int{x\tan^2{ax}}~dx$}
+$$\int{x\tan^2{ax}}=
+\frac{x\tan{ax}}{a}+\frac{1}{a^2}\ln~\cos{ax}-\frac{x^2}{2}
+$$
+<<*>>=
+)clear all
+
+--S 9 of 11
+aa:=integrate(x*tan(a*x)^2,x)
+--R 
+--R
+--R                      2                         2 2
+--R        - log(tan(a x)  + 1) + 2a x tan(a x) - a x
+--R   (1)  -------------------------------------------
+--R                              2
+--R                            2a
+--R                                          Type: Union(Expression Integer,...)
+--E
+@
+
+\section{\cite{1}:14.438~~~~~$\displaystyle
+\int{\frac{dx}{p+q\tan{ax}}}~dx$}
+$$\int{\frac{1}{p+q\tan{ax}}}=
+\frac{px}{p^2+q^2}+\frac{q}{a(p^2+q^2)}\ln(q\sin{ax}+p\cos{ax})
+$$
+<<*>>=
+)clear all
+
+--S 10 of 11
+aa:=integrate(1/(p+q*tan(a*x)),x)
+--R 
+--R
+--R                        2
+--R        - q log(tan(a x)  + 1) + 2q log(q tan(a x) + p) + 2a p x
+--R   (1)  --------------------------------------------------------
+--R                                  2       2
+--R                              2a q  + 2a p
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.439~~~~~$\displaystyle
+\int{\tan^n{ax}}~dx$}
+$$\int{\tan^n{ax}}=
+\frac{\tan^{n-1}{ax}}{(n-1)a}-\int{\tan^{n-2}{ax}}
+$$
+<<*>>=
+)clear all
+
+--S 11 of 11
+aa:=integrate(tan(a*x)^n,x)
+--R 
+--R
+--R           x
+--R         ++           n
+--I   (1)   |   tan(%I a) d%I
+--R        ++
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+)spool
+)lisp (bye)
+@
+
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} Spiegel, Murray R.
+{\sl Mathematical Handbook of Formulas and Tables}\\
+Schaum's Outline Series McGraw-Hill 1968 p80
+\end{thebibliography}
+\end{document}
diff --git a/src/input/schaum21.input.pamphlet b/src/input/schaum21.input.pamphlet
new file mode 100644
index 0000000..6e02ffe
--- /dev/null
+++ b/src/input/schaum21.input.pamphlet
@@ -0,0 +1,262 @@
+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/input schaum21.input}
+\author{Timothy Daly}
+\maketitle
+\eject
+\tableofcontents
+\eject
+\section{\cite{1}:14.440~~~~~$\displaystyle
+\int{\cot{ax}}~dx$}
+$$\int{\cot{ax}}=
+\frac{1}{a}\ln\sin{ax}
+$$
+<<*>>=
+)spool schaum21.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1 of 11
+aa:=integrate(cot(a*x),x)
+--R 
+--R
+--R               sin(2a x)                2
+--R        2log(-------------) - log(-------------)
+--R             cos(2a x) + 1        cos(2a x) + 1
+--R   (1)  ----------------------------------------
+--R                           2a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.441~~~~~$\displaystyle
+\int{\cot^2{ax}}~dx$}
+$$\int{\cot^2{ax}}=
+-\frac{\cot{ax}}{a}-x
+$$
+<<*>>=
+)clear all
+
+--S 2 of 11
+aa:=integrate(cot(a*x)^2,x)
+--R 
+--R
+--R        - a x sin(2a x) - cos(2a x) - 1
+--R   (1)  -------------------------------
+--R                  a sin(2a x)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.442~~~~~$\displaystyle
+\int{\cot^3{ax}}~dx$}
+$$\int{\cot^3{ax}}=
+-\frac{\cot^2{ax}}{2a}-\frac{1}{a}\ln\sin{ax}
+$$
+<<*>>=
+)clear all
+
+--S 3 of 11
+aa:=integrate(cot(a*x)^3,x)
+--R 
+--R
+--R   (1)
+--R                               sin(2a x)                               2
+--R       (- 2cos(2a x) + 2)log(-------------) + (cos(2a x) - 1)log(-------------)
+--R                             cos(2a x) + 1                       cos(2a x) + 1
+--R     + 
+--R       cos(2a x) + 1
+--R  /
+--R     2a cos(2a x) - 2a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.443~~~~~$\displaystyle
+\int{\cot^n{ax}\csc^2{ax}}~dx$}
+$$\int{\cot^n{ax}\csc^2{ax}}=
+-\frac{\cot^{n+1}{ax}}{(n+1)a}
+$$
+<<*>>=
+)clear all
+
+--S 4 of 11
+aa:=integrate(cot(a*x)^n*csc(a*x)^2,x)
+--R 
+--R
+--R                          cos(a x)
+--R                    n log(--------)
+--R                          sin(a x)
+--R          cos(a x)%e
+--R   (1)  - -------------------------
+--R              (a n + a)sin(a x)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.444~~~~~$\displaystyle
+\int{\frac{\csc^2{ax}}{\cot{ax}}}~dx$}
+$$\int{\frac{\csc^2{ax}}{\cot{ax}}}=
+-\frac{1}{a}\ln\cot{ax}
+$$
+<<*>>=
+)clear all
+
+--S 5 of 11
+aa:=integrate(csc(a*x)^2/cot(a*x),x)
+--R 
+--R
+--R              sin(a x)              2cos(a x)
+--R        log(------------) - log(- ------------)
+--R            cos(a x) + 1          cos(a x) + 1
+--R   (1)  ---------------------------------------
+--R                           a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.445~~~~~$\displaystyle
+\int{\frac{dx}{\cot{ax}}}~dx$}
+$$\int{\frac{1}{\cot{ax}}}=
+-\frac{1}{a}\ln\cos{ax}
+$$
+<<*>>=
+)clear all
+
+--S 6 of 11
+aa:=integrate(1/cot(a*x),x)
+--R 
+--R
+--R                  2
+--R        log(-------------)
+--R            cos(2a x) + 1
+--R   (1)  ------------------
+--R                2a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.446~~~~~$\displaystyle
+\int{x\cot{ax}}~dx$}
+$$\int{x\cot{ax}}=
+\frac{1}{a^2}\left\{ax
+-\frac{(ax)^3}{9}-\frac{(ax)^5}{225}
+-\cdots-\frac{2^{2n}B_n(ax)^{2n+1}}{(2n+1)!}-\cdots\right\}
+$$
+<<*>>=
+)clear all
+
+--S 7 of 11
+aa:=integrate(x*cot(a*x),x)
+--R 
+--R
+--R           x
+--R         ++
+--I   (1)   |   %I cot(%I a)d%I
+--R        ++
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.447~~~~~$\displaystyle
+\int{\frac{\cot{ax}}{x}}~dx$}
+$$\int{\frac{\cot{ax}}{x}}=
+-\frac{1}{ax}-\frac{ax}{3}-\frac{(ax)^3}{135}-\cdots
+-\frac{2^{2n}B_n(ax)^{2n-1}}{(2n-1)(2n)!}-\cdots
+$$
+<<*>>=
+)clear all
+
+--S 8 of 11
+aa:=integrate(cot(a*x)/x,x)
+--R 
+--R
+--R           x
+--I         ++  cot(%I a)
+--I   (1)   |   --------- d%I
+--I        ++       %I
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.448~~~~~$\displaystyle
+\int{x\cot^2{ax}}~dx$}
+$$\int{x\cot^2{ax}}=
+-\frac{x\cot{ax}}{a}+\frac{1}{a^2}\ln\sin{ax}-\frac{x^2}{2}
+$$
+<<*>>=
+)clear all
+
+--S 9 of 11
+aa:=integrate(x*cot(a*x)^2,x)
+--R 
+--R
+--R   (1)
+--R                       sin(2a x)                         2
+--R       2sin(2a x)log(-------------) - sin(2a x)log(-------------)
+--R                     cos(2a x) + 1                 cos(2a x) + 1
+--R     + 
+--R          2 2
+--R       - a x sin(2a x) - 2a x cos(2a x) - 2a x
+--R  /
+--R       2
+--R     2a sin(2a x)
+--R                                          Type: Union(Expression Integer,...)
+--E
+@
+
+\section{\cite{1}:14.449~~~~~$\displaystyle
+\int{\frac{dx}{p+q\cot{ax}}}~dx$}
+$$\int{\frac{1}{p+q\cot{ax}}}=
+\frac{px}{p^2+q^2}-\frac{q}{a(p^2+q^2)}\ln(p\sin{ax}+q\cos{ax})
+$$
+<<*>>=
+)clear all
+
+--S 10 of 11
+aa:=integrate(1/(p+q*cot(a*x)),x)
+--R 
+--R
+--R   (1)
+--R            p sin(2a x) + q cos(2a x) + q                2
+--R   - 2q log(-----------------------------) + q log(-------------) + 2a p x
+--R                    cos(2a x) + 1                  cos(2a x) + 1
+--R   -----------------------------------------------------------------------
+--R                                    2       2
+--R                                2a q  + 2a p
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.450~~~~~$\displaystyle
+\int{\cot^n{ax}}~dx$}
+$$\int{\cot^n{ax}}=
+-\frac{\cot^{n-1}{ax}}{(n-1)a}-\int{\cos^{n-2}{ax}}
+$$
+<<*>>=
+)clear all
+
+--S 11 of 11
+aa:=integrate(cot(a*x)^n,x)
+--R 
+--R
+--R           x
+--R         ++           n
+--I   (1)   |   cot(%I a) d%I
+--R        ++
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+)spool
+)lisp (bye)
+@
+
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} Spiegel, Murray R.
+{\sl Mathematical Handbook of Formulas and Tables}\\
+Schaum's Outline Series McGraw-Hill 1968 p81
+\end{thebibliography}
+\end{document}
diff --git a/src/input/schaum22.input.pamphlet b/src/input/schaum22.input.pamphlet
new file mode 100644
index 0000000..66befb9
--- /dev/null
+++ b/src/input/schaum22.input.pamphlet
@@ -0,0 +1,254 @@
+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/input schaum22.input}
+\author{Timothy Daly}
+\maketitle
+\eject
+\tableofcontents
+\eject
+\section{\cite{1}:14.451~~~~~$\displaystyle
+\int{\sec{ax}}~dx$}
+$$\int{\sec{ax}}=
+\frac{1}{a}\ln(\sec{ax}+\tan{ax})=
+\frac{1}{a}\ln\tan\left(\frac{ax}{2}+\frac{\pi}{4}\right)
+$$
+<<*>>=
+)spool schaum22.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1 of 10
+aa:=integrate(sec(a*x),x)
+--R 
+--R
+--R            sin(a x) + cos(a x) + 1        sin(a x) - cos(a x) - 1
+--R        log(-----------------------) - log(-----------------------)
+--R                  cos(a x) + 1                   cos(a x) + 1
+--R   (1)  -----------------------------------------------------------
+--R                                     a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.452~~~~~$\displaystyle
+\int{\sec^2{ax}}~dx$}
+$$\int{\sec^2{ax}}=
+\frac{\tan{ax}}{a}
+$$
+<<*>>=
+)clear all
+
+--S 2 of 10
+aa:=integrate(sec(a*x)^2,x)
+--R 
+--R
+--R         sin(a x)
+--R   (1)  ----------
+--R        a cos(a x)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.453~~~~~$\displaystyle
+\int{\sec^3{ax}}~dx$}
+$$\int{\sec^3{ax}}=
+\frac{\sec{ax}\tan{ax}}{2a}+\frac{1}{2a}\ln(\sec{ax}+\tan{ax})
+$$
+<<*>>=
+)clear all
+
+--S 3 of 10
+aa:=integrate(sec(a*x)^3,x)
+--R 
+--R
+--R   (1)
+--R               2    sin(a x) + cos(a x) + 1
+--R       cos(a x) log(-----------------------)
+--R                          cos(a x) + 1
+--R     + 
+--R                 2    sin(a x) - cos(a x) - 1
+--R       - cos(a x) log(-----------------------) + sin(a x)
+--R                            cos(a x) + 1
+--R  /
+--R                2
+--R     2a cos(a x)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.454~~~~~$\displaystyle
+\int{\sec^n{ax}\tan{ax}}~dx$}
+$$\int{\sec^n{ax}\tan{ax}}=
+\frac{\sec^n{ax}}{na}
+$$
+<<*>>=
+)clear all
+
+--S 4 of 10
+aa:=integrate(sec(a*x)^n*tan(a*x),x)
+--R
+--R                    1
+--R          n log(---------)
+--R                        2
+--R                cos(a x)
+--R          ----------------
+--R                  2
+--R        %e
+--R   (1)  ------------------
+--R                a n
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.455~~~~~$\displaystyle
+\int{\frac{dx}{\sec{ax}}}~dx$}
+$$\int{\frac{1}{\sec{ax}}}=
+\frac{\sin{ax}}{a}
+$$
+<<*>>=
+)clear all
+
+--S 5 of 10
+aa:=integrate(1/sec(a*x),x)
+--R 
+--R
+--R        sin(a x)
+--R   (1)  --------
+--R            a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.456~~~~~$\displaystyle
+\int{x\sec{ax}}~dx$}
+$$\int{x\sec{ax}}=
+\frac{1}{a^2}\left\{\frac{(ax)^2}{2}+\frac{(ax)^4}{8}+\frac{5(ax)^6}{144}
++\cdots+\frac{E_n(ax)^{2n+2}}{(2n+2)(2n)!}+\cdots\right\}
+$$
+<<*>>=
+)clear all
+
+--S 6 of 10
+aa:=integrate(x*sec(a*x),x)
+--R 
+--R
+--R           x
+--R         ++
+--I   (1)   |   %N sec(%N a)d%N
+--R        ++
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.457~~~~~$\displaystyle
+\int{\frac{\sec{ax}}{x}}~dx$}
+$$\int{\frac{\sec{ax}}{x}}=
+\ln{x}+\frac{(ax)^2}{4}+\frac{5(ax)^4}{96}+\frac{61(ax)^6}{4320}
++\cdots+\frac{E_n(ax)^{2n}}{(2n)(2n)!}+\cdots
+$$
+<<*>>=
+)clear all
+
+--S 7 of 10
+aa:=integrate(sec(a*x)/x,x)
+--R 
+--R
+--R           x
+--I         ++  sec(%N a)
+--I   (1)   |   --------- d%N
+--I        ++       %N
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.458~~~~~$\displaystyle
+\int{x\sec^2{ax}}~dx$}
+$$\int{x\sec^2{ax}}=
+\frac{x}{a}\tan{ax}+\frac{1}{a^2}\ln\cos{ax}
+$$
+<<*>>=
+)clear all
+
+--S 8 of 10
+aa:=integrate(x*sec(a*x)^2,x)
+--R 
+--R
+--R   (1)
+--R                       2                         2cos(a x)
+--R   - cos(a x)log(------------) + cos(a x)log(- ------------) + a x sin(a x)
+--R                 cos(a x) + 1                  cos(a x) + 1
+--R   ------------------------------------------------------------------------
+--R                                   2
+--R                                  a cos(a x)
+--R                                          Type: Union(Expression Integer,...)
+--E
+@
+
+\section{\cite{1}:14.459~~~~~$\displaystyle
+\int{\frac{dx}{q+p\sec{ax}}}~dx$}
+$$\int{\frac{1}{q+p\sec{ax}}}=
+\frac{x}{q}-\frac{p}{q}\int{\frac{dx}{p+q\cos{ax}}}
+$$
+<<*>>=
+)clear all
+
+--S 9 of 10
+aa:=integrate(1/(q+p*sec(a*x)),x)
+--R 
+--R
+--R   (1)
+--R                             +-------+
+--R                             | 2    2      2    2                 +-------+
+--R          (- p cos(a x) - q)\|q  - p   + (q  - p )sin(a x)        | 2    2
+--R    p log(------------------------------------------------) + a x\|q  - p
+--R                           q cos(a x) + p
+--R   [-----------------------------------------------------------------------,
+--R                                     +-------+
+--R                                     | 2    2
+--R                                 a q\|q  - p
+--R                         +---------+
+--R                         |   2    2          +---------+
+--R                sin(a x)\|- q  + p           |   2    2
+--R    - 2p atan(-----------------------) + a x\|- q  + p
+--R              (q + p)cos(a x) + q + p
+--R    ----------------------------------------------------]
+--R                           +---------+
+--R                           |   2    2
+--R                       a q\|- q  + p
+--R                                     Type: Union(List Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.460~~~~~$\displaystyle
+\int{\sec^n{ax}}~dx$}
+$$\int{\sec^n{ax}}=
+\frac{\sec^{n-2}{ax}\tan{ax}}{a(n-1)}
++\frac{n-2}{n-1}\int{\sec^{n-2}{ax}}
+$$
+<<*>>=
+)clear all
+
+--S 10 of 10
+aa:=integrate(sec(a*x)^n,x)
+--R 
+--R
+--R           x
+--R         ++           n
+--I   (1)   |   sec(%N a) d%N
+--R        ++
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+)spool
+)lisp (bye)
+@
+
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} Spiegel, Murray R.
+{\sl Mathematical Handbook of Formulas and Tables}\\
+Schaum's Outline Series McGraw-Hill 1968 pp81-82
+\end{thebibliography}
+\end{document}
diff --git a/src/input/schaum23.input.pamphlet b/src/input/schaum23.input.pamphlet
new file mode 100644
index 0000000..679e775
--- /dev/null
+++ b/src/input/schaum23.input.pamphlet
@@ -0,0 +1,262 @@
+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/input schaum23.input}
+\author{Timothy Daly}
+\maketitle
+\eject
+\tableofcontents
+\eject
+\section{\cite{1}:14.461~~~~~$\displaystyle
+\int{\csc{ax}}~dx$}
+$$\int{\csc{ax}}=
+\frac{1}{a}\ln(\csc{ax}-\cot{ax})=
+\frac{1}{a}\ln\tan{\frac{ax}{2}}
+$$
+<<*>>=
+)spool schaum23.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1 of 10
+aa:=integrate(csc(a*x),x)
+--R 
+--R
+--R              sin(a x)
+--R        log(------------)
+--R            cos(a x) + 1
+--R   (1)  -----------------
+--R                a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.462~~~~~$\displaystyle
+\int{\csc^2{ax}}~dx$}
+$$\int{\csc^2{ax}}=
+-\frac{\cot{ax}}{a}
+$$
+<<*>>=
+)clear all
+
+--S 2 of 10
+aa:=integrate(csc(a*x)^2,x)
+--R 
+--R
+--R           cos(a x)
+--R   (1)  - ----------
+--R          a sin(a x)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.463~~~~~$\displaystyle
+\int{\csc^3{ax}}~dx$}
+$$\int{\csc^3{ax}}=
+-\frac{\csc{ax}\cot{ax}}{2a}+\frac{1}{2a}\ln\tan{\frac{ax}{2}}
+$$
+<<*>>=
+)clear all
+
+--S 3 of 10
+aa:=integrate(csc(a*x)^3,x)
+--R 
+--R
+--R                 2           sin(a x)
+--R        (cos(a x)  - 1)log(------------) + cos(a x)
+--R                           cos(a x) + 1
+--R   (1)  -------------------------------------------
+--R                                2
+--R                     2a cos(a x)  - 2a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.464~~~~~$\displaystyle
+\int{\csc^n{ax}\cot{ax}}~dx$}
+$$\int{\csc^n{ax}\cot{ax}}=
+-\frac{csc^n{ax}}{na}
+$$
+<<*>>=
+)clear all
+
+--S 4 of 10
+aa:=integrate(csc(a*x)^n*cot(a*x),x)
+--R 
+--R
+--R                          1
+--R            n log(- -------------)
+--R                            2
+--R                    cos(a x)  - 1
+--R            ----------------------
+--R                       2
+--R          %e
+--R   (1)  - ------------------------
+--R                     a n
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.465~~~~~$\displaystyle
+\int{\frac{dx}{\csc{ax}}}~dx$}
+$$\int{\frac{1}{\csc{ax}}}=
+-\frac{\cos{ax}}{a}
+$$
+<<*>>=
+)clear all
+
+--S 5 of 10
+aa:=integrate(1/csc(a*x),x)
+--R 
+--R
+--R          cos(a x)
+--R   (1)  - --------
+--R              a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.466~~~~~$\displaystyle
+\int{x\csc{ax}}~dx$}
+$$\int{x\csc{ax}}=
+\frac{1}{a^2}\left\{ax+\frac{(ax)^3}{18}+\frac{7(ax)^5}{1800}
++\cdots+\frac{2(2^{2n-1}-1)B_n(ax)^{2n+1}}{(2n+1)!}+\cdots\right\}
+$$
+<<*>>=
+)clear all
+
+--S 6 of 10
+aa:=integrate(x*csc(a*x),x)
+--R 
+--R
+--R           x
+--R         ++
+--I   (1)   |   %H csc(%H a)d%H
+--R        ++
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.467~~~~~$\displaystyle
+\int{\frac{\csc{ax}}{x}}~dx$}
+$$\int{\frac{\csc{ax}}{x}}=
+-\frac{1}{ax}+\frac{(ax)}{6}+\frac{7(ax)^3}{1800}
++\cdots+\frac{2(2^{2n-1}-1)B_n(ax)^{2n-1}}{(2n-1)(2n)!}+\cdots
+$$
+<<*>>=
+)clear all
+
+--S 7 of 10
+aa:=integrate(csc(a*x)/x,x)
+--R 
+--R
+--R           x
+--I         ++  csc(%H a)
+--I   (1)   |   --------- d%H
+--I        ++       %H
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.468~~~~~$\displaystyle
+\int{x\csc^2{ax}}~dx$}
+$$\int{x\csc^2{ax}}=
+-\frac{x\cot{ax}}{a}+\frac{1}{a^2}\ln\sin{ax}
+$$
+<<*>>=
+)clear all
+
+--S 8 of 10
+aa:=integrate(x*csc(a*x)^2,x)
+--R 
+--R
+--R                      sin(a x)                        2
+--R        sin(a x)log(------------) - sin(a x)log(------------) - a x cos(a x)
+--R                    cos(a x) + 1                cos(a x) + 1
+--R   (1)  --------------------------------------------------------------------
+--R                                      2
+--R                                     a sin(a x)
+--R                                          Type: Union(Expression Integer,...)
+--E
+@
+
+\section{\cite{1}:14.469~~~~~$\displaystyle
+\int{\frac{dx}{q+p\csc{ax}}}~dx$}
+$$\int{\frac{1}{q+p\csc{ax}}}=
+\frac{x}{q}-\frac{p}{q}\int{\frac{1}{p+q\sin{ax}}}
+$$
+<<*>>=
+)clear all
+
+--S 9 of 10
+aa:=integrate(1/(q+p*csc(a*x)),x)
+--R 
+--R
+--R   (1)
+--R   [
+--R           p
+--R        *
+--R           log
+--R                                                          +-------+
+--R                                    2    2             2  | 2    2
+--R                  (p q sin(a x) + (q  - p )cos(a x) + q )\|q  - p
+--R                + 
+--R                      2    3              3    2              3    2
+--R                  (p q  - p )sin(a x) + (q  - p q)cos(a x) + q  - p q
+--R             /
+--R                q sin(a x) + p
+--R       + 
+--R             +-------+
+--R             | 2    2
+--R         a x\|q  - p
+--R    /
+--R           +-------+
+--R           | 2    2
+--R       a q\|q  - p
+--R     ,
+--R                                          +---------+
+--R                                          |   2    2         +---------+
+--R            (p sin(a x) + q cos(a x) + q)\|- q  + p          |   2    2
+--R    2p atan(-----------------------------------------) + a x\|- q  + p
+--R                     2    2             2    2
+--R                   (q  - p )cos(a x) + q  - p
+--R    --------------------------------------------------------------------]
+--R                                   +---------+
+--R                                   |   2    2
+--R                               a q\|- q  + p
+--R                                     Type: Union(List Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.470~~~~~$\displaystyle
+\int{\csc^n{ax}}~dx$}
+$$\int{\csc^n{ax}}=
+-\frac{\csc^{n-2}{ax}\cot{ax}}{a(n-1)}
++\frac{n-2}{n-1}\int{\csc^{n-2}{ax}}
+$$
+<<*>>=
+)clear all
+
+--S 10 of 10
+aa:=integrate(csc(a*x)^n,x)
+--R 
+--R
+--R           x
+--R         ++           n
+--I   (1)   |   csc(%H a) d%H
+--R        ++
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+)spool
+)lisp (bye)
+@
+
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} Spiegel, Murray R.
+{\sl Mathematical Handbook of Formulas and Tables}\\
+Schaum's Outline Series McGraw-Hill 1968 p82
+\end{thebibliography}
+\end{document}
diff --git a/src/input/schaum24.input.pamphlet b/src/input/schaum24.input.pamphlet
new file mode 100644
index 0000000..1a6b60a
--- /dev/null
+++ b/src/input/schaum24.input.pamphlet
@@ -0,0 +1,1036 @@
+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/input schaum24.input}
+\author{Timothy Daly}
+\maketitle
+\eject
+\tableofcontents
+\eject
+\section{\cite{1}:14.471~~~~~$\displaystyle
+\int{\sin^{-1}{\frac{x}{a}}}~dx$}
+$$\int{\sin^{-1}{\frac{x}{a}}}=
+x\sin^{-1}{\frac{x}{a}}+\sqrt{a^2-x^2}
+$$
+<<*>>=
+)spool schaum24.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1 of 38
+aa:=integrate(asin(x/a),x)
+--R 
+--R
+--R                    +---------+
+--R                    |   2    2       +---------+
+--R                 2x\|- x  + a        |   2    2
+--R        - x atan(--------------) + 2\|- x  + a
+--R                      2    2
+--R                    2x  - a
+--R   (1)  ----------------------------------------
+--R                            2
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.472~~~~~$\displaystyle
+\int{x\sin^{-1}{\frac{x}{a}}}~dx$}
+$$\int{x\sin^{-1}{\frac{x}{a}}}=
+\left(\frac{x^2}{2}-\frac{a^2}{4}\right)\sin^{-1}{\frac{x}{a}}
++\frac{x\sqrt{a^2-x^2}}{4}
+$$
+<<*>>=
+)clear all
+
+--S 2 of 38
+aa:=integrate(x*asin(x/a),x)
+--R 
+--R
+--R                            +---------+
+--R                            |   2    2        +---------+
+--R             2    2      2x\|- x  + a         |   2    2
+--R        (- 2x  + a )atan(--------------) + 2x\|- x  + a
+--R                              2    2
+--R                            2x  - a
+--R   (1)  -------------------------------------------------
+--R                                8
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.473~~~~~$\displaystyle
+\int{x^2\sin^{-1}\frac{x}{a}}~dx$}
+$$\int{x^2\sin^{-1}\frac{x}{a}}=
+\frac{x^3}{3}\sin^{-1}\frac{x}{a}+\frac{(x^2+2a^2)\sqrt{a^2-x^2}}{9}
+$$
+<<*>>=
+)clear all
+
+--S 3 of 38
+aa:=integrate(x^2*asin(x/a),x)
+--R 
+--R
+--R                     +---------+
+--R                     |   2    2                 +---------+
+--R            3     2x\|- x  + a         2     2  |   2    2
+--R        - 3x atan(--------------) + (2x  + 4a )\|- x  + a
+--R                       2    2
+--R                     2x  - a
+--R   (1)  ---------------------------------------------------
+--R                                 18
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.474~~~~~$\displaystyle
+\int{\frac{\sin^{-1}(x/a)}{x}}~dx$}
+$$\int{\frac{\sin^{-1}(x/a)}{x}}=
+\frac{x}{a}+\frac{(x/a)^3}{2\cdot 3\cdot 3}
++\frac{1\cdot 3(x/a)^5}{2\cdot 4\cdot 5\cdot 5}
++\frac{1\cdot 3\cdot 5(x/a)^7}{2\cdot 4\cdot 6\cdot 7\cdot 7}+\cdots
+$$
+<<*>>=
+)clear all
+
+--S 4 of 38
+aa:=integrate(asin(x/a)/x,x)
+--R 
+--R
+--I                  %H
+--R           x asin(--)
+--R         ++        a
+--I   (1)   |   -------- d%H
+--I        ++      %H
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.475~~~~~$\displaystyle
+\int{\frac{\sin^{-1}{(x/a)}}{x^2}}~dx$}
+$$\int{\frac{\sin^{-1}{(x/a)}}{x^2}}=
+-\frac{\sin^{-1}(x/a)}{x}
+-\frac{1}{a}\ln\left(\frac{a+\sqrt{a^2-x^2}}{x}\right)
+$$
+<<*>>=
+)clear all
+
+--S 5 of 38
+aa:=integrate(asin(x/a)/x^2,x)
+--R 
+--R
+--R   (1)
+--R                                                                   +---------+
+--R            +---------+               +---------+                  |   2    2
+--R            |   2    2                |   2    2                2x\|- x  + a
+--R   - x log(\|- x  + a   + a) + x log(\|- x  + a   - a) + a atan(--------------)
+--R                                                                     2    2
+--R                                                                   2x  - a
+--R   ----------------------------------------------------------------------------
+--R                                       2a x
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.476~~~~~$\displaystyle
+\int{\left(sin^{-1}\frac{x}{a}\right)^2}~dx$}
+$$\int{\left(sin^{-1}\frac{x}{a}\right)^2}=
+x\left(\sin^{-1}\frac{x}{a}\right)^2-2x+2\sqrt{a^2-x^2}\sin^{-1}\frac{x}{a}
+$$
+<<*>>=
+)clear all
+
+--S 6 of 38
+aa:=integrate(asin(x/a)^2,x)
+--R 
+--R
+--R                  +---------+ 2                        +---------+
+--R                  |   2    2        +---------+        |   2    2
+--R               2x\|- x  + a         |   2    2      2x\|- x  + a
+--R        x atan(--------------)  - 4\|- x  + a  atan(--------------) - 8x
+--R                    2    2                               2    2
+--R                  2x  - a                              2x  - a
+--R   (1)  ----------------------------------------------------------------
+--R                                        4
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.477~~~~~$\displaystyle
+\int{\cos^{-1}\frac{x}{a}}~dx$}
+$$\int{\cos^{-1}\frac{x}{a}}=
+x\cos^{-1}\frac{x}{a}-\sqrt{a^2-x^2}
+$$
+<<*>>=
+)clear all
+
+--S 7 of 38
+aa:=integrate(acos(x/a),x)
+--R 
+--R
+--R                  +---------+
+--R                  |   2    2       +---------+
+--R               2x\|- x  + a        |   2    2
+--R        x atan(--------------) - 2\|- x  + a
+--R                    2    2
+--R                  2x  - a
+--R   (1)  --------------------------------------
+--R                           2
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.478~~~~~$\displaystyle
+\int{x\cos^{-1}\frac{x}{a}}~dx$}
+$$\int{x\cos^{-1}\frac{x}{a}}=
+\left(\frac{x^2}{2}-\frac{a^2}{4}\right)\cos^{-1}\frac{x}{a}
+-\frac{x\sqrt{a^2-x^2}}{4}
+$$
+<<*>>=
+)clear all
+
+--S 8 of 38
+aa:=integrate(x*acos(x/a),x)
+--R 
+--R
+--R                          +---------+
+--R                          |   2    2        +---------+
+--R           2    2      2x\|- x  + a         |   2    2
+--R        (2x  - a )atan(--------------) - 2x\|- x  + a
+--R                            2    2
+--R                          2x  - a
+--R   (1)  -----------------------------------------------
+--R                               8
+--R                                          Type: Union(Expression Integer,...)
+--E
+@
+
+\section{\cite{1}:14.479~~~~~$\displaystyle
+\int{x^2\cos^{-1}\frac{x}{a}}~dx$}
+$$\int{x^2\cos^{-1}\frac{x}{a}}=
+\frac{x^3}{3}\cos^{-1}\frac{x}{a}-\frac{(x^2+2a^2)\sqrt{a^2-x^2}}{9}
+$$
+<<*>>=
+)clear all
+
+--S 9 of 38
+aa:=integrate(x^2*acos(x/a),x)
+--R 
+--R
+--R                   +---------+
+--R                   |   2    2                   +---------+
+--R          3     2x\|- x  + a           2     2  |   2    2
+--R        3x atan(--------------) + (- 2x  - 4a )\|- x  + a
+--R                     2    2
+--R                   2x  - a
+--R   (1)  ---------------------------------------------------
+--R                                 18
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.480~~~~~$\displaystyle
+\int{\frac{\cos^{-1}(x/a)}{x}}~dx$}
+$$\int{\frac{\cos^{-1}(x/a)}{x}}=
+\frac{x}{2}\ln{x}-\int{\frac{\sin^{-1}(x/a)}{x}}
+$$
+<<*>>=
+)clear all
+
+--S 10 of 38
+aa:=integrate(acos(x/a)/x,x)
+--R 
+--R
+--I                  %H
+--R           x acos(--)
+--R         ++        a
+--I   (1)   |   -------- d%H
+--I        ++      %H
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.481~~~~~$\displaystyle
+\int{\frac{\cos^{-1}(x/a)}{x^2}}~dx$}
+$$\int{\frac{\cos^{-1}(x/a)}{x^2}}=
+-\frac{\cos^{-1}(x/a)}{x}+\frac{1}{a}\ln\left(\frac{a+\sqrt{a^2-x^2}}{x}\right)
+$$
+<<*>>=
+)clear all
+
+--S 11 of 38
+aa:=integrate(acos(x/a)/x^2,x)
+--R 
+--R
+--R   (1)
+--R                                                                 +---------+
+--R          +---------+               +---------+                  |   2    2
+--R          |   2    2                |   2    2                2x\|- x  + a
+--R   x log(\|- x  + a   + a) - x log(\|- x  + a   - a) - a atan(--------------)
+--R                                                                   2    2
+--R                                                                 2x  - a
+--R   --------------------------------------------------------------------------
+--R                                      2a x
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.482~~~~~$\displaystyle
+\int{\left(\cos^{-1}\frac{x}{a}\right)^2}~dx$}
+$$\int{\left(\cos^{-1}\frac{x}{a}\right)^2}=
+x\left(\cos^{-1}\frac{x}{a}\right)^2-2x-2\sqrt{a^2-x^2}\cos^{-1}\frac{x}{a}
+$$
+<<*>>=
+)clear all
+
+--S 12 of 38
+aa:=integrate(acos(x/a)^2,x)
+--R 
+--R
+--R                  +---------+ 2                        +---------+
+--R                  |   2    2        +---------+        |   2    2
+--R               2x\|- x  + a         |   2    2      2x\|- x  + a
+--R        x atan(--------------)  - 4\|- x  + a  atan(--------------) - 8x
+--R                    2    2                               2    2
+--R                  2x  - a                              2x  - a
+--R   (1)  ----------------------------------------------------------------
+--R                                        4
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.483~~~~~$\displaystyle
+\int{\tan^{-1}\frac{x}{a}}~dx$}
+$$\int{\tan^{-1}\frac{x}{a}}=
+x\tan^{-1}\frac{x}{a}-\frac{a}{2}\ln(x^2+a^2)
+$$
+<<*>>=
+)clear all
+
+--S 13 of 38
+aa:=integrate(atan(x/a),x)
+--R 
+--R
+--R                 2    2             2a x
+--R        - a log(x  + a ) - x atan(-------)
+--R                                   2    2
+--R                                  x  - a
+--R   (1)  ----------------------------------
+--R                         2
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.484~~~~~$\displaystyle
+\int{x\tan^{-1}\frac{x}{a}}~dx$}
+$$\int{x\tan^{-1}\frac{x}{a}}=
+\frac{1}{2}(x^2+a^2)\tan^{-1}\frac{x}{a}-\frac{ax}{2}
+$$
+<<*>>=
+)clear all
+
+--S 14 of 38
+aa:=integrate(x*tan(x/a),x)
+--R 
+--R
+--R           x
+--I         ++         %H
+--I   (1)   |   %H tan(--)d%H
+--R        ++           a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.485~~~~~$\displaystyle
+\int{x^2\tan^{-1}\frac{x}{a}}~dx$}
+$$\int{x^2\tan^{-1}\frac{x}{a}}=
+\frac{x^3}{3}\tan^{-1}\frac{x}{a}-\frac{ax^2}{6}+\frac{a^3}{6}\ln(x^2+a^2)
+$$
+<<*>>=
+)clear all
+
+--S 15 of 38
+aa:=integrate(x^2*atan(x/a),x)
+--R 
+--R
+--R         3     2    2     3       2a x        2
+--R        a log(x  + a ) - x atan(-------) - a x
+--R                                 2    2
+--R                                x  - a
+--R   (1)  ---------------------------------------
+--R                           6
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.486~~~~~$\displaystyle
+\int{\frac{\tan^{-1}(x/a)}{x}}~dx$}
+$$\int{\frac{\tan^{-1}(x/a)}{x}}=
+\frac{x}{a}-\frac{(x/a)^3}{3^2}+\frac{(x/a)^5}{5^2}-\frac{(x/a)^7}{7^2}+\cdots
+$$
+<<*>>=
+)clear all
+
+--S 16 of 38
+aa:=integrate(atan(x/a)/x,x)
+--R 
+--R
+--I                  %H
+--R           x atan(--)
+--R         ++        a
+--I   (1)   |   -------- d%H
+--I        ++      %H
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.487~~~~~$\displaystyle
+\int{\frac{\tan^{-1}(x/a)}{x^2}}~dx$}
+$$\int{\frac{\tan^{-1}(x/a)}{x^2}}=
+-\frac{1}{x}\tan^{-1}\frac{x}{a}
+-\frac{1}{2a}\ln\left(\frac{x^2+a^2}{x^2}\right)
+$$
+<<*>>=
+)clear all
+
+--S 17 of 38
+aa:=integrate(atan(x/a)/x^2,x)
+--R 
+--R
+--R                 2    2                         2a x
+--R        - x log(x  + a ) + 2x log(x) + a atan(-------)
+--R                                               2    2
+--R                                              x  - a
+--R   (1)  ----------------------------------------------
+--R                             2a x
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.488~~~~~$\displaystyle
+\int{\cot^{-1}\frac{x}{a}}~dx$}
+$$\int{\cot^{-1}\frac{x}{a}}=
+x\cot^{-1}\frac{x}{a}+\frac{a}{2}\ln(x^2+a^2)
+$$
+<<*>>=
+)clear all
+
+--S 18 of 38
+aa:=integrate(acot(x/a),x)
+--R 
+--R
+--R               2    2             2a x
+--R        a log(x  + a ) + x atan(-------)
+--R                                 2    2
+--R                                x  - a
+--R   (1)  --------------------------------
+--R                        2
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.489~~~~~$\displaystyle
+\int{x\cot^{-1}\frac{x}{a}}~dx$}
+$$\int{x\cot^{-1}\frac{x}{a}}=
+\frac{1}{2}(x^2+a^2)\cot^{-1}\frac{x}{a}+\frac{ax}{2}
+$$
+<<*>>=
+)clear all
+
+--S 19 of 38
+aa:=integrate(x*acot(x/a),x)
+--R 
+--R
+--R          2    2        2a x
+--R        (x  + a )atan(-------) + 2a x
+--R                       2    2
+--R                      x  - a
+--R   (1)  -----------------------------
+--R                      4
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.490~~~~~$\displaystyle
+\int{x^2\cot^{-1}\frac{x}{a}}~dx$}
+$$\int{x^2\cot^{-1}\frac{x}{a}}=
+\frac{x^3}{3}\cot^{-1}\frac{x}{a}+\frac{ax^2}{6}-\frac{a^3}{6}\ln(x^2+a^2)
+$$
+<<*>>=
+)clear all
+
+--S 20 of 38
+aa:=integrate(x^2*acot(x/a),x)
+--R 
+--R
+--R           3     2    2     3       2a x        2
+--R        - a log(x  + a ) + x atan(-------) + a x
+--R                                   2    2
+--R                                  x  - a
+--R   (1)  -----------------------------------------
+--R                            6
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.491~~~~~$\displaystyle
+\int{\frac{\cot^{-1}(x/a)}{x}}~dx$}
+$$\int{\frac{\cot^{-1}(x/a)}{x}}=
+\frac{\pi}{2}\ln{x}-\int{\frac{\tan^{-1}(x/a)}{x}}
+$$
+<<*>>=
+)clear all
+
+--S 21 of 38
+aa:=integrate(acot(x/a)/x,x)
+--R 
+--R
+--I                  %H
+--R           x acot(--)
+--R         ++        a
+--I   (1)   |   -------- d%H
+--I        ++      %H
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.492~~~~~$\displaystyle
+\int{\frac{\cot^{-1}(x/a)}{x^2}}~dx$}
+$$\int{\frac{\cot^{-1}(x/a)}{x^2}}=
+-\frac{cot^{-1}(x/a)}{x}+\frac{1}{2a}\ln\left(\frac{x^2+a^2}{x^2}\right)
+$$
+<<*>>=
+)clear all
+
+--S 22 of 38
+aa:=integrate(acot(x/a)/x^2,x)
+--R 
+--R
+--R               2    2                         2a x
+--R        x log(x  + a ) - 2x log(x) - a atan(-------)
+--R                                             2    2
+--R                                            x  - a
+--R   (1)  --------------------------------------------
+--R                            2a x
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.493~~~~~$\displaystyle
+\int{\sec^{-1}\frac{x}{a}}~dx$}
+$$\int{\sec^{-1}\frac{x}{a}}=
+\left\{
+\begin{array}{l}
+\displaystyle
+x\sec^{-1}\frac{x}{a}-a\ln(x+\sqrt{x^2-a^2}) 
+{\rm \ if\ }0 < \sec^{-1}\frac{x}{a} < \frac{\pi}{2}\\
+\\
+\displaystyle
+x\sec^{-1}\frac{x}{a}+a\ln(x+\sqrt{x^2-a^2})
+{\rm \ if\ }\frac{\pi}{2} < \sec^{-1}\frac{x}{a} < \pi
+\end{array}
+\right.
+$$
+<<*>>=
+)clear all
+
+--S 23 of 38
+aa:=integrate(asec(x/a),x)
+--R 
+--R
+--R   (1)
+--R                          +---------+              +---------+
+--R                      +-+ |   2    2               |   2    2
+--R           +-+     2x\|2 \|- x  + a             2a\|- x  + a
+--R       - a\|2 atan(------------------) + x atan(--------------)
+--R                          2     2                      2
+--R                        3x  - 2a                      x
+--R     + 
+--R                       x
+--R       - 2a atan(------------)
+--R                  +---------+
+--R                  |   2    2
+--R                 \|- x  + a
+--R  /
+--R     2
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.494~~~~~$\displaystyle
+\int{x\sec^{-1}\frac{x}{a}}~dx$}
+$$\int{x\sec^{-1}\frac{x}{a}}=
+\left\{
+\begin{array}{l}
+\displaystyle
+\frac{x^2}{2}\sec^{-1}\frac{x}{a}-\frac{a\sqrt{x^2-a^2}}{2}
+{\rm \ if\ }0 < \sec^{-1}\frac{x}{a} < \frac{\pi}{2}\\
+\\
+\displaystyle
+\frac{x^2}{2}\sec^{-1}\frac{x}{a}+\frac{a\sqrt{x^2-a^2}}{2}
+{\rm \ if\ }\frac{\pi}{2} < \sec^{-1}\frac{x}{a} < \pi
+\end{array}
+\right.
+$$
+<<*>>=
+)clear all
+
+--S 24 of 38
+aa:=integrate(x*asec(x/a),x)
+--R 
+--R
+--R                          +---------+
+--R                          |   2    2        +---------+
+--R          2     2      2a\|- x  + a         |   2    2
+--R        (x  - 2a )atan(--------------) + 2a\|- x  + a
+--R                              2
+--R                             x
+--R   (1)  -----------------------------------------------
+--R                               4
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.495~~~~~$\displaystyle
+\int{x^2\sec^{-1}\frac{x}{a}}~dx$}
+$$\int{x^2\sec^{-1}\frac{x}{a}}=
+\left\{
+\begin{array}{l}
+\displaystyle
+\frac{x^3}{3}\sec^{-1}\frac{x}{a}-\frac{ax\sqrt{x^2-a^2}}{6}
+-\frac{a^3}{6}\ln(x+\sqrt{x^2-a^2})\\
+\\
+\displaystyle
+\hbox{\hskip 3cm}{\rm \ if\ }0 < \sec^{-1}\frac{x}{a} < \frac{\pi}{2}\\
+\\
+\displaystyle
+\frac{x^3}{3}\sec^{-1}\frac{x}{a}+\frac{ax\sqrt{x^2-a^2}}{6}
++\frac{a^3}{6}\ln(x+\sqrt{x^2-a^2})\\
+\\
+\displaystyle
+\hbox{\hskip 3cm}
+{\rm \ if\ }\frac{\pi}{2} < \sec^{-1}\frac{x}{a} < \pi\\
+\end{array}
+\right.
+$$
+<<*>>=
+)clear all
+
+--S 25 of 38
+aa:=integrate(x^2*asec(x/a),x)
+--R 
+--R
+--R   (1)
+--R                            +---------+              +---------+
+--R                        +-+ |   2    2               |   2    2
+--R           3 +-+     2x\|2 \|- x  + a       3     2a\|- x  + a
+--R       - 2a \|2 atan(------------------) + x atan(--------------)
+--R                            2     2                      2
+--R                          3x  - 2a                      x
+--R     + 
+--R                                     +---------+
+--R           3           x             |   2    2
+--R       - 5a atan(------------) + a x\|- x  + a
+--R                  +---------+
+--R                  |   2    2
+--R                 \|- x  + a
+--R  /
+--R     6
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.496~~~~~$\displaystyle
+\int{\frac{\sec^{-1}(x/a)}{x}}~dx$}
+$$\int{\frac{\sec^{-1}(x/a)}{x}}=
+\frac{\pi}{2}\ln{x}+\frac{a}{x}+\frac{(a/x)^3}{2\cdot 3\cdot 3}
++\frac{1\cdot 3(a/x)^5}{2\cdot 4\cdot 5\cdot 5}
++\frac{1\cdot 3\cdot 5(a/x)^7}{2\cdot 4\cdot 6\cdot 7\cdot 7}+\cdots
+$$
+<<*>>=
+)clear all
+
+--S 26 of 38
+aa:=integrate(asec(x/a)/x,x)
+--R 
+--R
+--I                  %H
+--R           x asec(--)
+--R         ++        a
+--I   (1)   |   -------- d%H
+--I        ++      %H
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.497~~~~~$\displaystyle
+\int{\frac{\sec^{-1}(x/a)}{x^2}}~dx$}
+$$\int{\frac{\sec^{-1}(x/a)}{x^2}}=
+\left\{
+\begin{array}{l}
+\displaystyle
+-\frac{\sec^{-1}(x/a)}{x}+\frac{\sqrt{x^2-a^2}}{ax}
+{\rm \ if\ }0 < \sec^{-1}\frac{x}{a} < \frac{\pi}{2}\\
+\\
+\displaystyle
+-\frac{\sec^{-1}(x/a)}{x}-\frac{\sqrt{x^2-a^2}}{ax}
+{\rm \ if\ }\frac{\pi}{2} < \sec^{-1}\frac{x}{a} < \pi\\
+\end{array}
+\right.
+$$
+<<*>>=
+)clear all
+
+--S 27 of 38
+aa:=integrate(asec(x/a)/x^2,x)
+--R 
+--R
+--R                      +---------+                 +---------+
+--R                  +-+ |   2    2                  |   2    2
+--R               2x\|2 \|- x  + a        +-+     2a\|- x  + a
+--R        x atan(------------------) - a\|2 atan(--------------)
+--R                      2     2                         2
+--R                    3x  - 2a                         x
+--R   (1)  ------------------------------------------------------
+--R                                    +-+
+--R                               2a x\|2
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.498~~~~~$\displaystyle
+\int{\csc^{-1}\frac{x}{a}}~dx$}
+$$\int{\csc^{-1}\frac{x}{a}}=
+\left\{
+\begin{array}{l}
+\displaystyle
+x\csc^{-1}\frac{x}{a}+a\ln(x+\sqrt{x^2-a^2})
+{\rm \ if\ }0 < \csc^{-1}\frac{x}{a} < \frac{\pi}{2}\\
+\\
+\displaystyle
+x\csc^{-1}\frac{x}{a}-a\ln(x+\sqrt{x^2-a^2})
+{\rm \ if\ }-\frac{\pi}{2} < \csc^{-1}\frac{x}{a} < 0\\
+\end{array}
+\right.
+$$
+<<*>>=
+)clear all
+
+--S 28 of 38
+aa:=integrate(acsc(x/a),x)
+--R 
+--R
+--R   (1)
+--R                        +---------+              +---------+
+--R                    +-+ |   2    2               |   2    2
+--R         +-+     2x\|2 \|- x  + a             2a\|- x  + a
+--R       a\|2 atan(------------------) - x atan(--------------)
+--R                        2     2                      2
+--R                      3x  - 2a                      x
+--R     + 
+--R                     x
+--R       2a atan(------------)
+--R                +---------+
+--R                |   2    2
+--R               \|- x  + a
+--R  /
+--R     2
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.499~~~~~$\displaystyle
+\int{x\csc^{-1}\frac{x}{a}}~dx$}
+$$\int{x\csc^{-1}\frac{x}{a}}=
+\left\{
+\begin{array}{l}
+\displaystyle
+\frac{x^2}{2}\csc^{-1}\frac{x}{a}+\frac{a\sqrt{x^2-a^2}}{2}
+{\rm \ if\ }0 < \csc^{-1}\frac{x}{a} < \frac{\pi}{2}\\
+\\
+\displaystyle
+\frac{x^2}{2}\csc^{-1}\frac{x}{a}-\frac{a\sqrt{x^2-a^2}}{2}
+{\rm \ if\ }-\frac{\pi}{2} < \csc^{-1}\frac{x}{a} < 0\\
+\end{array}
+\right.
+$$
+<<*>>=
+)clear all
+
+--S 29 of 38
+aa:=integrate(x*acsc(x/a),x)
+--R 
+--R
+--R                            +---------+
+--R                            |   2    2        +---------+
+--R            2     2      2a\|- x  + a         |   2    2
+--R        (- x  + 2a )atan(--------------) - 2a\|- x  + a
+--R                                2
+--R                               x
+--R   (1)  -------------------------------------------------
+--R                                4
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.500~~~~~$\displaystyle
+\int{x^2\csc^{-1}\frac{x}{a}}~dx$}
+$$\int{x^2\csc^{-1}\frac{x}{a}}=
+\left\{
+\begin{array}{l}
+\displaystyle
+\frac{x^3}{3}\csc^{-1}\frac{x}{a}+\frac{ax\sqrt{x^2-a^2}}{6}
++\frac{a^3}{6}\ln(x+\sqrt{x^2-a^2})\\
+\\
+\displaystyle
+\hbox{\hskip 3cm}{\rm \ if\ }0 < \csc^{-1}\frac{x}{a} < \frac{\pi}{2}\\
+\\
+\displaystyle
+\frac{x^3}{3}\sec^{-1}\frac{x}{a}-\frac{ax\sqrt{x^2-a^2}}{6}
+-\frac{a^3}{6}\ln(x+\sqrt{x^2-a^2})\\
+\\
+\displaystyle
+\hbox{\hskip 3cm}
+{\rm \ if\ }-\frac{\pi}{2} < \csc^{-1}\frac{x}{a} < 0\\
+\end{array}
+\right.
+$$
+<<*>>=
+)clear all
+
+--S 30 of 38
+aa:=integrate(x^2*acsc(x/a),x)
+--R 
+--R
+--R   (1)
+--R                          +---------+              +---------+
+--R                      +-+ |   2    2               |   2    2
+--R         3 +-+     2x\|2 \|- x  + a       3     2a\|- x  + a
+--R       2a \|2 atan(------------------) - x atan(--------------)
+--R                          2     2                      2
+--R                        3x  - 2a                      x
+--R     + 
+--R                                   +---------+
+--R         3           x             |   2    2
+--R       5a atan(------------) - a x\|- x  + a
+--R                +---------+
+--R                |   2    2
+--R               \|- x  + a
+--R  /
+--R     6
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.501~~~~~$\displaystyle
+\int{\frac{\csc^{-1}(x/a)}{x}}~dx$}
+$$\int{\frac{\csc^{-1}(x/a)}{x}}=
+-\left(\frac{a}{x}+\frac{(a/x)^3}{2\cdot 3\cdot 3}
++\frac{1\cdot 3(a/x)^5}{2\cdot 4\cdot 5\cdot 5}
++\frac{1\cdot 3\cdot 5(a/x)^7}{2\cdot 4\cdot 6\cdot 7\cdot 7}+\cdots\right)
+$$
+<<*>>=
+)clear all
+
+--S 31 of 38
+aa:=integrate(acsc(x/a)/x,x)
+--R 
+--R
+--I                  %H
+--R           x acsc(--)
+--R         ++        a
+--I   (1)   |   -------- d%H
+--I        ++      %H
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.502~~~~~$\displaystyle
+\int{\frac{\csc^{-1}(x/a)}{x^2}}~dx$}
+$$\int{\frac{\csc^{-1}(x/a)}{x^2}}=
+\left\{
+\begin{array}{l}
+\displaystyle
+-\frac{csc^{-1}(x/a)}{x}-\frac{\sqrt{x^2-a^2}}{ax}
+{\rm \ if\ }0 < \csc^{-1}\frac{x}{a} < \frac{\pi}{2}\\
+\\
+\displaystyle
+-\frac{csc^{-1}(x/a)}{x}+\frac{\sqrt{x^2-a^2}}{ax}
+{\rm \ if\ }-\frac{\pi}{2} < \csc^{-1}\frac{x}{a} < 0\\
+\end{array}
+\right.
+$$
+<<*>>=
+)clear all
+
+--S 32 of 38
+aa:=integrate(acsc(x/a)/x^2,x)
+--R 
+--R
+--R                        +---------+                 +---------+
+--R                    +-+ |   2    2                  |   2    2
+--R                 2x\|2 \|- x  + a        +-+     2a\|- x  + a
+--R        - x atan(------------------) + a\|2 atan(--------------)
+--R                        2     2                         2
+--R                      3x  - 2a                         x
+--R   (1)  --------------------------------------------------------
+--R                                     +-+
+--R                                2a x\|2
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.503~~~~~$\displaystyle
+\int{x^m\sin^{-1}\frac{x}{a}}~dx$}
+$$\int{x^m\sin^{-1}\frac{x}{a}}=
+\frac{x^{m+1}}{m+1}\sin^{-1}\frac{x}{a}-\frac{1}{m+1}\int{\frac{x^{m+1}}{\sqrt{a^2-x^2}}}
+$$
+<<*>>=
+)clear all
+
+--S 33 of 38
+aa:=integrate(x^m*asin(x/a),x)
+--R 
+--R
+--R           x
+--I         ++       %H   m
+--I   (1)   |   asin(--)%H d%H
+--R        ++         a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.504~~~~~$\displaystyle
+\int{x^m\cos^{-1}\frac{x}{a}}~dx$}
+$$\int{x^m\cos^{-1}\frac{x}{a}}=
+\frac{x^{m+1}}{m+1}\cos^{-1}\frac{x}{a}+\frac{1}{m+1}\int{\frac{x^{m+1}}{\sqrt{a^2-x^2}}}
+$$
+<<*>>=
+)clear all
+
+--S 34 of 38
+aa:=integrate(x^m*acos(x/a),x)
+--R 
+--R
+--R           x
+--I         ++       %H   m
+--I   (1)   |   acos(--)%H d%H
+--R        ++         a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.505~~~~~$\displaystyle
+\int{x^m\tan^{-1}\frac{x}{a}}~dx$}
+$$\int{x^m\tan^{-1}\frac{x}{a}}=
+\frac{x^{m_1}}{m+1}\tan^{-1}\frac{x}{a}
+-\frac{a}{m+1}\int{\frac{x^{m+1}}{x^2+a^2}}
+$$
+<<*>>=
+)clear all
+
+--S 35 of 38
+aa:=integrate(x*m*atan(x/a),x)
+--R 
+--R
+--R              2    2         2a x
+--R        (- m x  - a m)atan(-------) - 2a m x
+--R                            2    2
+--R                           x  - a
+--R   (1)  ------------------------------------
+--R                          4
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.506~~~~~$\displaystyle
+\int{x^m\cot^{-1}\frac{x}{a}}~dx$}
+$$\int{x^m\cot^{-1}\frac{x}{a}}=
+\frac{x^{m+1}}{m+1}\cot^{-1}\frac{x}{a}
++\frac{a}{m+1}\int{\frac{x^{m+1}}{x^2+a^2}}
+$$
+<<*>>=
+)clear all
+
+--S 36 of 38
+aa:=integrate(x^m*acot(x/a),x)
+--R 
+--R
+--R           x
+--I         ++       %H   m
+--I   (1)   |   acot(--)%H d%H
+--R        ++         a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.507~~~~~$\displaystyle
+\int{x^m\sec^{-1}\frac{x}{a}}~dx$}
+$$\int{x^m\sec^{-1}\frac{x}{a}}=
+\left\{
+\begin{array}{l}
+\displaystyle
+\frac{x^{m+1}\sec^{-1}(x/a)}{m+1}-\frac{a}{m+1}\int{\frac{x^m}{\sqrt{x^2-a^2}}}
+{\rm \ if\ }0 < \sec^{-1}\frac{x}{a} < \frac{\pi}{2}\\
+\\
+\displaystyle
+\frac{x^{m+1}\sec^{-1}(x/a)}{m+1}+\frac{a}{m+1}\int{\frac{x^m}{\sqrt{x^2-a^2}}}
+{\rm \ if\ }\frac{\pi}{2} < \sec^{-1}\frac{x}{a} < \pi\\
+\end{array}
+\right.
+$$
+<<*>>=
+)clear all
+
+--S 37 of 38
+aa:=integrate(x^m*asec(x/a),x)
+--R 
+--R
+--R           x
+--I         ++       %H   m
+--I   (1)   |   asec(--)%H d%H
+--R        ++         a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.508~~~~~$\displaystyle
+\int{x^m\csc^{-1}\frac{x}{a}}~dx$}
+$$\int{x^m\csc^{-1}\frac{x}{a}}=
+\left\{
+\begin{array}{l}
+\displaystyle
+\frac{x^{m+1}\csc^{-1}(x/a)}{m+1}+\frac{a}{m+1}\int{\frac{x^m}{\sqrt{x^2-a^2}}}
+{\rm \ if\ }0 < \csc^{-1}\frac{x}{a} < \frac{\pi}{2}\\
+\\
+\displaystyle
+\frac{x^{m+1}\csc^{-1}(x/a)}{m+1}-\frac{a}{m+1}\int{\frac{x^m}{\sqrt{x^2-a^2}}}
+{\rm \ if\ }-\frac{\pi}{2} < \csc^{-1}\frac{x}{a} < 0\\
+\end{array}
+\right.
+$$
+<<*>>=
+)clear all
+
+--S 38 of 38
+aa:=integrate(x^m*acsc(x/a),x)
+--R 
+--R
+--R           x
+--I         ++       %H   m
+--I   (1)   |   acsc(--)%H d%H
+--R        ++         a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+)spool
+)lisp (bye)
+@
+
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} Spiegel, Murray R.
+{\sl Mathematical Handbook of Formulas and Tables}\\
+Schaum's Outline Series McGraw-Hill 1968 pp82-84
+\end{thebibliography}
+\end{document}



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Cc: 
Subject: [Axiom-developer] 20080409.02.tpd.patch (add src/doc/toe.gif,
	Max Tegmark)
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The src/doc/toe.gif file will later be used as part of the Axiom
documentation. Max Tegmark <tegmark@mit.edu> has given me permission
to include it in the distribution.

Tim
========================================================================
diff --git a/changelog b/changelog
index 4916b6a..08caf13 100644
--- a/changelog
+++ b/changelog
@@ -1,3 +1,6 @@
+20080409 tpd readme add Max Tegmark
+20080409 tpd src/interp/setq.lisp add Max Tegmark
+20080409 tpd src/doc/toe.gif added, by Max Tegmark <tegmark@mit.edu>
 20080409 tpd src/input/Makefile add integration regression testing	
 20080409 tpd src/input/schaum24.input integrals of inverse trig functions
 20080409 tpd src/input/schaum23.input integrals of csc(ax)
diff --git a/readme b/readme
index 578fc37..27bb2cf 100644
--- a/readme
+++ b/readme
@@ -231,8 +231,9 @@ at the axiom command prompt will prettyprint the list.
 "William Sit            Elena Smirnova         Jonathan Steinbach"
 "Christine Sundaresan   Robert Sutor           Moss E. Sweedler"
 "Eugene Surowitz"
-"James Thatcher         Balbir Thomas          Mike Thomas"
-"Dylan Thurston         Barry Trager           Themos T. Tsikas"
+"Max Tegmark            James Thatcher         Balbir Thomas"
+"Mike Thomas            Dylan Thurston         Barry Trager"
+"Themos T. Tsikas"
 "Gregory Vanuxem"
 "Bernhard Wall          Stephen Watt           Jaap Weel"
 "Juergen Weiss          M. Weller              Mark Wegman"
diff --git a/src/doc/toe.gif b/src/doc/toe.gif
new file mode 100644
index 0000000..2e80aa6
Binary files /dev/null and b/src/doc/toe.gif differ
diff --git a/src/interp/setq.lisp.pamphlet b/src/interp/setq.lisp.pamphlet
index c0aa0a8..6d35e34 100644
--- a/src/interp/setq.lisp.pamphlet
+++ b/src/interp/setq.lisp.pamphlet
@@ -651,8 +651,9 @@
 "William Sit            Elena Smirnova         Jonathan Steinbach"
 "Christine Sundaresan   Robert Sutor           Moss E. Sweedler"
 "Eugene Surowitz"
-"James Thatcher         Balbir Thomas          Mike Thomas"
-"Dylan Thurston         Barry Trager           Themos T. Tsikas"
+"Max Tegmark            James Thatcher         Balbir Thomas"
+"Mike Thomas            Dylan Thurston         Barry Trager"
+"Themos T. Tsikas"
 "Gregory Vanuxem"
 "Bernhard Wall          Stephen Watt           Jaap Weel"
 "Juergen Weiss          M. Weller              Mark Wegman"



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Subject: [Axiom-developer] 20080409.03.tpd.patch (CATS integration
	regression testing)
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More integrals
========================================================================
diff --git a/changelog b/changelog
index 08caf13..bb20757 100644
--- a/changelog
+++ b/changelog
@@ -1,3 +1,5 @@
+20080409 tpd src/input/Makefile add integration regression testing	
+20080409 tpd src/input/schaum25.input integrals of e^(a*x)
 20080409 tpd readme add Max Tegmark
 20080409 tpd src/interp/setq.lisp add Max Tegmark
 20080409 tpd src/doc/toe.gif added, by Max Tegmark <tegmark@mit.edu>
diff --git a/src/input/Makefile.pamphlet b/src/input/Makefile.pamphlet
index c184fbe..9134ab7 100644
--- a/src/input/Makefile.pamphlet
+++ b/src/input/Makefile.pamphlet
@@ -361,6 +361,7 @@ REGRES= algaggr.regress algbrbf.regress  algfacob.regress alist.regress  \
     schaum13.regress  schaum14.regress schaum15.regress schaum16.regress \
     schaum17.regress  schaum18.regress schaum19.regress schaum20.regress \
     schaum21.regress  schaum22.regress schaum23.regress schaum24.regress \
+    schaum25.regress \
     scherk.regress    scope.regress    seccsc.regress \
     segbind.regress   seg.regress \
     series2.regress   series.regress   sersolve.regress set.regress \
@@ -640,7 +641,7 @@ FILES= ${OUT}/algaggr.input  ${OUT}/algbrbf.input    ${OUT}/algfacob.input \
        ${OUT}/schaum14.input ${OUT}/schaum15.input   ${OUT}/schaum16.input \
        ${OUT}/schaum17.input ${OUT}/schaum18.input   ${OUT}/schaum19.input \
        ${OUT}/schaum20.input ${OUT}/schaum21.input   ${OUT}/schaum22.input \
-       ${OUT}/schaum23.input ${OUT}/schaum24.input \
+       ${OUT}/schaum23.input ${OUT}/schaum24.input   ${OUT}/schaum25.input \
        ${OUT}/saddle.input \
        ${OUT}/scherk.input   ${OUT}/scope.input      ${OUT}/seccsc.input \
        ${OUT}/segbind.input  ${OUT}/seg.input        ${OUT}/series2.input \
@@ -951,6 +952,7 @@ DOCFILES= \
   ${DOC}/schaum19.input.dvi    ${DOC}/schaum20.input.dvi \
   ${DOC}/schaum21.input.dvi    ${DOC}/schaum22.input.dvi \
   ${DOC}/schaum23.input.dvi    ${DOC}/schaum24.input.dvi \
+  ${DOC}/schaum25.input.dvi \
   ${DOC}/s01eaf.input.dvi      ${DOC}/s13aaf.input.dvi     \
   ${DOC}/s13acf.input.dvi      ${DOC}/s13adf.input.dvi     \
   ${DOC}/s14aaf.input.dvi      ${DOC}/s14abf.input.dvi     \
diff --git a/src/input/schaum25.input.pamphlet b/src/input/schaum25.input.pamphlet
new file mode 100644
index 0000000..250e7c3
--- /dev/null
+++ b/src/input/schaum25.input.pamphlet
@@ -0,0 +1,383 @@
+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/input schaum25.input}
+\author{Timothy Daly}
+\maketitle
+\eject
+\tableofcontents
+\eject
+\section{\cite{1}:14.509~~~~~$\displaystyle
+\int{e^{ax}}~dx$}
+$$\int{e^{ax}}=
+\frac{e^{ax}}{a}
+$$
+<<*>>=
+)spool schaum25.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1 of 16
+aa:=integrate(e^(a*x),x)
+--R 
+--R
+--R          a x log(e)
+--R        %e
+--R   (1)  ------------
+--R          a log(e)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.510~~~~~$\displaystyle
+\int{xe^{ax}}~dx$}
+$$\int{xe^{ax}}=
+\frac{e^{ax}}{x}\left(x-\frac{1}{a}\right)
+$$
+<<*>>=
+)clear all
+
+--S 2 of 16
+aa:=integrate(x*e^(a*x),x)
+--R 
+--R
+--R                          a x log(e)
+--R        (a x log(e) - 1)%e
+--R   (1)  ----------------------------
+--R                   2      2
+--R                  a log(e)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.511~~~~~$\displaystyle
+\int{x^2e^{ax}}~dx$}
+$$\int{x^2e^{ax}}=
+\frac{e^{ax}}{x}\left(x^2-\frac{2x}{a}+\frac{2}{a^2}\right)
+$$
+<<*>>=
+)clear all
+
+--S 3 of 16
+aa:=integrate(x^2*e^(a*x),x)
+--R 
+--R
+--R          2 2      2                     a x log(e)
+--R        (a x log(e)  - 2a x log(e) + 2)%e
+--R   (1)  -------------------------------------------
+--R                          3      3
+--R                         a log(e)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.512~~~~~$\displaystyle
+\int{x^ne^{ax}}~dx$}
+$$\begin{array}{rl}
+\displaystyle\int{x^ne^{ax}}=&
+\displaystyle
+\frac{x^ne^{ax}}{a}-\frac{n}{a}\int{x^{n-1}e^{ax}}\\
+\\
+&\displaystyle
+=\frac{e^{ax}}{x}\left(x^n-\frac{nx^{n-1}}{a}+\frac{n(n-1)x^{n-2}}{a^2}
+-\cdots \frac{(-1)^nn!}{a^n}\right)
+\\
+&\hbox{\hskip 5cm}{\rm\ if\ }n={\rm positive integer}
+\end{array}
+$$
+<<*>>=
+)clear all
+
+--S 4 of 16
+aa:=integrate(x^n*e^(a*x),x)
+--R 
+--R
+--R           x
+--I         ++    n %I a
+--I   (1)   |   %I e    d%I
+--R        ++
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.513~~~~~$\displaystyle
+\int{\frac{e^{ax}}{x}}~dx$}
+$$\int{\frac{e^{ax}}{x}}=
+\ln{x}+\frac{ax}{1\cdot 1!}+\frac{(ax)^2}{2\cdot 2!}
++\frac{(ax)^3}{3\cdot 3!}+\cdots
+$$
+<<*>>=
+)clear all
+
+--S 5 of 16
+aa:=integrate(e^(a*x)/x,x)
+--R 
+--R
+--R   (1)  Ei(a x log(e))
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.514~~~~~$\displaystyle
+\int{\frac{e^{ax}}{x^n}}~dx$}
+$$\int{\frac{e^{ax}}{x^n}}=
+\frac{-e^{ax}}{(n-1)x^{n-1}}+\frac{a}{n-1}\int{\frac{e^{ax}}{x^{n-1}}}
+$$
+<<*>>=
+)clear all
+
+--S 6 of 16
+aa:=integrate(e^(a*x)/x^n,x)
+--R 
+--R
+--I           x  %I a
+--R         ++  e
+--I   (1)   |   ----- d%I
+--R        ++      n
+--I              %I
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.515~~~~~$\displaystyle
+\int{\frac{dx}{p+qe^{ax}}}~dx$}
+$$\int{\frac{1}{p+qe^{ax}}}=
+\frac{x}{p}-\frac{1}{ap}\ln(p+qe^{ax})
+$$
+<<*>>=
+)clear all
+
+--S 7 of 16
+aa:=integrate(1/(p+q*e^(a*x)),x)
+--R 
+--R
+--R                  a x log(e)
+--R        - log(q %e           + p) + a x log(e)
+--R   (1)  --------------------------------------
+--R                      a p log(e)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.516~~~~~$\displaystyle
+\int{\frac{dx}{(p+qe^{ax})^2}}~dx$}
+$$\int{\frac{dx}{(p+qe^{ax})^2}}=
+\frac{x}{p^2}+\frac{1}{ap(p+qe^{ax})}-\frac{1}{ap^2}\ln(p+qe^{ax})
+$$
+<<*>>=
+)clear all
+
+--S 8 of 16
+aa:=integrate(1/(p+q*e^(a*x)),x)
+--R 
+--R
+--R                  a x log(e)
+--R        - log(q %e           + p) + a x log(e)
+--R   (1)  --------------------------------------
+--R                      a p log(e)
+--R                                          Type: Union(Expression Integer,...)
+--E
+@
+
+\section{\cite{1}:14.517~~~~~$\displaystyle
+\int{\frac{dx}{pe^{ax}+qe^{ax}}}~dx$}
+$$\int{\frac{dx}{pe^{ax}+qe^{ax}}}=
+\left\{
+\begin{array}{l}
+\displaystyle
+\frac{1}{a\sqrt{pq}}\tan^{-1}\left(\sqrt{\frac{p}{q}}e^{ax}\right)\\
+\\
+\displaystyle
+\frac{1}{2a\sqrt{-pq}}
+\ln\left(\frac{e^{ax}-\sqrt{-q/p}}{e^{ax}+\sqrt{-q/p}}\right)
+\end{array}
+\right.
+$$
+<<*>>=
+)clear all
+
+--S 9 of 16
+aa:=integrate(1/(p*e^(a*x)+q*e^(a*x)),x)
+--R 
+--R
+--R                        1
+--R   (1)  - -----------------------------
+--R                             a x log(e)
+--R          (a q + a p)log(e)%e
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.518~~~~~$\displaystyle
+\int{e^{ax}\sin{bx}}~dx$}
+$$\int{e^{ax}\sin{bx}}=
+\frac{e^{ax}(a\sin{bx}-b\cos{bx})}{a^2+b^2}
+$$
+<<*>>=
+)clear all
+
+--S 10 of 16
+aa:=integrate(e^(a*x)*sin(b*x),x)
+--R 
+--R
+--R                                         a x log(e)
+--R        (a log(e)sin(b x) - b cos(b x))%e
+--R   (1)  -------------------------------------------
+--R                        2      2    2
+--R                       a log(e)  + b
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.519~~~~~$\displaystyle
+\int{e^{ax}\cos{bx}}~dx$}
+$$\int{e^{ax}\cos{bx}}=
+\frac{e^{ax}(a\cos{bx}-b\sin{bx})}{a^2+b^2}
+$$
+<<*>>=
+)clear all
+
+--S 11 of 16
+aa:=integrate(e^(a*x)*cos(b*x),x)
+--R 
+--R
+--R                                         a x log(e)
+--R        (b sin(b x) + a cos(b x)log(e))%e
+--R   (1)  -------------------------------------------
+--R                        2      2    2
+--R                       a log(e)  + b
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.520~~~~~$\displaystyle
+\int{xe^{ax}\sin{bx}}~dx$}
+$$\int{xe^{ax}\sin{bx}}=
+\frac{xe^{ax}(a\sin{bx}-b\cos{bx})}{a^2+b^2}
+-\frac{e^{ax}\left((a^2-b^2)\sin{bx}-2ab\cos{bx}\right)}{(a^2+b^2)^2}
+$$
+<<*>>=
+)clear all
+
+--S 12 of 16
+aa:=integrate(x*e^(a*x)*sin(b*x),x)
+--R 
+--R
+--R   (1)
+--R           3        3    2      2      2            2
+--R         (a x log(e)  - a log(e)  + a b x log(e) + b )sin(b x)
+--R       + 
+--R            2                  2                          3
+--R         - a b x cos(b x)log(e)  + 2a b cos(b x)log(e) - b x cos(b x)
+--R    *
+--R         a x log(e)
+--R       %e
+--R  /
+--R      4      4     2 2      2    4
+--R     a log(e)  + 2a b log(e)  + b
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.521~~~~~$\displaystyle
+\int{xe^{ax}\cos{bx}}~dx$}
+$$\int{xe^{ax}\cos{bx}}=
+\frac{xe^{ax}(a\cos{bx}-b\sin{bx})}{a^2+b^2}
+-\frac{e^{ax}\left((a^2-b^2)\cos{bx}-2ab\sin{bx}\right)}{(a^2+b^2)^2}
+$$
+<<*>>=
+)clear all
+
+--S 13 of 16
+aa:=integrate(x*e^(a*x)*cos(b*x),x)
+--R 
+--R
+--R   (1)
+--R           2          2                  3              3                3
+--R         (a b x log(e)  - 2a b log(e) + b x)sin(b x) + a x cos(b x)log(e)
+--R       + 
+--R            2              2      2                    2
+--R         - a cos(b x)log(e)  + a b x cos(b x)log(e) + b cos(b x)
+--R    *
+--R         a x log(e)
+--R       %e
+--R  /
+--R      4      4     2 2      2    4
+--R     a log(e)  + 2a b log(e)  + b
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.522~~~~~$\displaystyle
+\int{e^{ax}\ln{x}}~dx$}
+$$\int{e^{ax}\ln{x}}=
+\frac{e^{ax}\ln{x}}{a}-\frac{1}{a}\int{\frac{e^{ax}}{x}}
+$$
+<<*>>=
+)clear all
+
+--S 14 of 16
+aa:=integrate(e^(a*x)*log(x),x)
+--R 
+--R
+--R           x
+--I         ++          %I a
+--I   (1)   |   log(%I)e    d%I
+--R        ++
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.523~~~~~$\displaystyle
+\int{e^{ax}\sin^n{bx}}~dx$}
+$$\int{e^{ax}\sin^n{bx}}=
+\frac{e^{ax}\sin^{n-1}{bx}}{a^2+n^2b^2}(a\sin{bx}-nb\cos{bx})
++\frac{n(n-1)b^2}{a^2+n^2b^2}\int{e^{ax}\sin^{n-2}{bx}}
+$$
+<<*>>=
+)clear all
+
+--S 15 of 16
+aa:=integrate(e^(a*x)*sin(b*x)^n,x)
+--R 
+--R
+--R           x
+--I         ++   %I a         n
+--I   (1)   |   e    sin(%I b) d%I
+--R        ++
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.524~~~~~$\displaystyle
+\int{e^{ax}\cos^n{bx}}~dx$}
+$$\int{e^{ax}\cos^n{bx}}=
+\frac{e^{ax}\cos^{n-1}{bx}}{a^2+n^2b^2}(a\cos{bx}-nb\sin{bx})
++\frac{n(n-1)b^2}{a^2+n^2b^2}\int{e^{ax}\cos^{n-2}{bx}}
+$$
+<<*>>=
+)clear all
+
+--S 16 of 16
+aa:=integrate(e^(a*x)*cos(b*x)^n,x)
+--R 
+--R
+--R           x
+--I         ++   %I a         n
+--I   (1)   |   e    cos(%I b) d%I
+--R        ++
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+)spool
+)lisp (bye)
+@
+
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} Spiegel, Murray R.
+{\sl Mathematical Handbook of Formulas and Tables}\\
+Schaum's Outline Series McGraw-Hill 1968 p85
+\end{thebibliography}
+\end{document}



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Date: Thu, 10 Apr 2008 04:01:02 -0400
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From: root <daly@axiom-developer.org>
To: "William Sit" <wyscc@sci.ccny.cuny.edu>
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Cc: axiom-developer@nongnu.org
Subject: [Axiom-developer] out of space
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William,

I have been running the input file you posted continuously since
shortly after you posted it on april 3rd. So far it has not 
completed. But it has also not run out of space.

Tim



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Subject: [Axiom-developer] 20080413.01.tpd.patch (CATS integration
	regression testing)
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X-List-Received-Date: Mon, 14 Apr 2008 06:33:52 -0000

More integrals
==========================================================================
diff --git a/changelog b/changelog
index bb20757..26d39fa 100644
--- a/changelog
+++ b/changelog
@@ -1,3 +1,9 @@
+20080413 tpd src/input/Makefile add integration regression testing	
+20080413 tpd src/input/schaum30.input integrals of tanh(ax)
+20080413 tpd src/input/schaum29.input integrals of sinh(ax) and cosh(ax)
+20080413 tpd src/input/schaum28.input integrals of cosh(ax)
+20080413 tpd src/input/schaum27.input integrals of sinh(ax)
+20080413 tpd src/input/schaum26.input integrals of ln x
 20080409 tpd src/input/Makefile add integration regression testing	
 20080409 tpd src/input/schaum25.input integrals of e^(a*x)
 20080409 tpd readme add Max Tegmark
diff --git a/src/input/Makefile.pamphlet b/src/input/Makefile.pamphlet
index 9134ab7..57ff1e9 100644
--- a/src/input/Makefile.pamphlet
+++ b/src/input/Makefile.pamphlet
@@ -361,7 +361,8 @@ REGRES= algaggr.regress algbrbf.regress  algfacob.regress alist.regress  \
     schaum13.regress  schaum14.regress schaum15.regress schaum16.regress \
     schaum17.regress  schaum18.regress schaum19.regress schaum20.regress \
     schaum21.regress  schaum22.regress schaum23.regress schaum24.regress \
-    schaum25.regress \
+    schaum25.regress  schaum26.regress schaum27.regress schaum28.regress \
+    schaum29.regress  schaum30.regress \
     scherk.regress    scope.regress    seccsc.regress \
     segbind.regress   seg.regress \
     series2.regress   series.regress   sersolve.regress set.regress \
@@ -642,6 +643,8 @@ FILES= ${OUT}/algaggr.input  ${OUT}/algbrbf.input    ${OUT}/algfacob.input \
        ${OUT}/schaum17.input ${OUT}/schaum18.input   ${OUT}/schaum19.input \
        ${OUT}/schaum20.input ${OUT}/schaum21.input   ${OUT}/schaum22.input \
        ${OUT}/schaum23.input ${OUT}/schaum24.input   ${OUT}/schaum25.input \
+       ${OUT}/schaum26.input ${OUT}/schaum27.input   ${OUT}/schaum28.input \
+       ${OUT}/schaum29.input ${OUT}/schaum30.input \
        ${OUT}/saddle.input \
        ${OUT}/scherk.input   ${OUT}/scope.input      ${OUT}/seccsc.input \
        ${OUT}/segbind.input  ${OUT}/seg.input        ${OUT}/series2.input \
@@ -952,7 +955,9 @@ DOCFILES= \
   ${DOC}/schaum19.input.dvi    ${DOC}/schaum20.input.dvi \
   ${DOC}/schaum21.input.dvi    ${DOC}/schaum22.input.dvi \
   ${DOC}/schaum23.input.dvi    ${DOC}/schaum24.input.dvi \
-  ${DOC}/schaum25.input.dvi \
+  ${DOC}/schaum25.input.dvi    ${DOC}/schaum26.input.dvi \
+  ${DOC}/schaum27.input.dvi    ${DOC}/schaum28.input.dvi \
+  ${DOC}/schaum29.input.dvi    ${DOC}/schaum30.input.dvi \
   ${DOC}/s01eaf.input.dvi      ${DOC}/s13aaf.input.dvi     \
   ${DOC}/s13acf.input.dvi      ${DOC}/s13adf.input.dvi     \
   ${DOC}/s14aaf.input.dvi      ${DOC}/s14abf.input.dvi     \
diff --git a/src/input/schaum26.input.pamphlet b/src/input/schaum26.input.pamphlet
new file mode 100644
index 0000000..7bf7244
--- /dev/null
+++ b/src/input/schaum26.input.pamphlet
@@ -0,0 +1,324 @@
+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/input schaum26.input}
+\author{Timothy Daly}
+\maketitle
+\eject
+\tableofcontents
+\eject
+\section{\cite{1}:14.525~~~~~$\displaystyle
+\int{ln x}~dx$}
+$$\int{ln x}=
+x\ln{x}-x
+$$
+<<*>>=
+)spool schaum26.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1 of 16
+aa:=integrate(log(x),x)
+--R 
+--R
+--R   (1)  x log(x) - x
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.526~~~~~$\displaystyle
+\int{x\ln{x}}~dx$}
+$$\int{x\ln{x}}=
+\frac{x^2}{2}\left(\ln{x}-\frac{1}{2}\right)
+$$
+<<*>>=
+)clear all
+
+--S 2 of 16
+aa:=integrate(x*log(x),x)
+--R 
+--R
+--R          2          2
+--R        2x log(x) - x
+--R   (1)  --------------
+--R               4
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.527~~~~~$\displaystyle
+\int{x^m\ln{x}}~dx$}
+$$\int{x^m\ln{x}}=
+\frac{x^{m+1}}{m+1}\left(\ln{x}-\frac{1}{m+1}\right)
+$$
+<<*>>=
+)clear all
+
+--S 3 of 16
+aa:=integrate(x^m*log(x),x)
+--R 
+--R
+--R                               m log(x)
+--R        ((m + 1)x log(x) - x)%e
+--R   (1)  -------------------------------
+--R                   2
+--R                  m  + 2m + 1
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.528~~~~~$\displaystyle
+\int{\frac{\ln{x}}{x}}~dx$}
+$$\int{\frac{\ln{x}}{x}}=
+\frac{1}{2}\ln^2{x}
+$$
+<<*>>=
+)clear all
+
+--S 4 of 16
+aa:=integrate(log(x)/x,x)
+--R 
+--R
+--R              2
+--R        log(x)
+--R   (1)  -------
+--R           2
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.529~~~~~$\displaystyle
+\int{\frac{\ln{x}}{x^2}}~dx$}
+$$\int{\frac{\ln{x}}{x^2}}=
+-\frac{\ln{x}}{x}-\frac{1}{x}
+$$
+<<*>>=
+)clear all
+
+--S 5 of 16
+aa:=integrate(log(x)/x^2,x)
+--R 
+--R
+--R        - log(x) - 1
+--R   (1)  ------------
+--R              x
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.530~~~~~$\displaystyle
+\int{\ln^2{x}}~dx$}
+$$\int{\ln^2{x}}=
+x\ln^2{x}-2x\ln{x}+2x
+$$
+<<*>>=
+)clear all
+
+--S 6 of 16
+aa:=integrate(log(x)^2,x)
+--R 
+--R
+--R                2
+--R   (1)  x log(x)  - 2x log(x) + 2x
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.531~~~~~$\displaystyle
+\int{\frac{\ln^n{x}}{x}}~dx$}
+$$\int{\frac{\ln^n{x}}{x}}=
+\frac{ln^{n+1}{x}}{n+1}
+$$
+<<*>>=
+)clear all
+
+--S 7 of 16
+aa:=integrate(log(x)^n/x,x)
+--R 
+--R
+--R                n log(log(x))
+--R        log(x)%e
+--R   (1)  ---------------------
+--R                n + 1
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.532~~~~~$\displaystyle
+\int{\frac{dx}{x\ln{x}}}$}
+$$\int{\frac{1}{x\ln{x}}}=
+\ln(\ln{x})
+$$
+<<*>>=
+)clear all
+
+--S 8 of 16
+aa:=integrate(1/(x*log(x)),x)
+--R 
+--R
+--R   (1)  log(log(x))
+--R                                          Type: Union(Expression Integer,...)
+--E
+@
+
+\section{\cite{1}:14.533~~~~~$\displaystyle
+\int{\frac{dx}{\ln{x}}}$}
+$$\int{\frac{1}{\ln{x}}}=
+\ln(\ln{x})+\ln{x}+\frac{\ln^2{x}}{2\cdot 2!}
++\frac{\ln^3{x}}{3\cdot 3!}+\cdots
+$$
+<<*>>=
+)clear all
+
+--S 9 of 16
+aa:=integrate(1/log(x),x)
+--R 
+--R
+--R   (1)  li(x)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.534~~~~~$\displaystyle
+\int{\frac{x^m}{\ln{x}}}~dx$}
+$$\int{\frac{x^m}{\ln{x}}}=
+\ln(\ln{x})+(m+1)\ln{x}+\frac{(m+1)^2\ln^2{x}}{2\cdot 2!}
++\frac{(m+1)^3\ln^3{x}}{3\cdot 3!}+\cdots
+$$
+<<*>>=
+)clear all
+
+--S 10 of 16
+aa:=integrate(x^m/log(x),x)
+--R 
+--R
+--R           x     m
+--I         ++    %I
+--I   (1)   |   ------- d%I
+--I        ++   log(%I)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.535~~~~~$\displaystyle
+\int{\ln^n{x}}~dx$}
+$$\int{\ln^n{x}}=
+x\ln^n{x}-n\int{\ln^{n-1}{x}}
+$$
+<<*>>=
+)clear all
+
+--S 11 of 16
+aa:=integrate(log(x)^n,x)
+--R 
+--R
+--R           x
+--R         ++         n
+--I   (1)   |   log(%I) d%I
+--R        ++
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.536~~~~~$\displaystyle
+\int{x^m\ln^n{x}}~dx$}
+$$\int{x^m\ln^n{x}}=
+\frac{x^{m+1}\ln^n{x}}{m+1}-\frac{n}{m+1}\int{x^m\ln^{n-1}{x}}
+$$
+<<*>>=
+)clear all
+
+--S 12 of 16
+aa:=integrate(x^m*log(x)^n,x)
+--R 
+--R
+--R           x
+--R         ++    m       n
+--I   (1)   |   %I log(%I) d%I
+--R        ++
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.537~~~~~$\displaystyle
+\int{\ln{(x^2+a^2)}}~dx$}
+$$\int{\ln{(x^2+a^2)}}=
+x\ln(x^2+a^2)-2x+2a\tan^{-1}\frac{x}{a}
+$$
+<<*>>=
+)clear all
+
+--S 13 of 16
+aa:=integrate(log(x^2+a^2),x)
+--R 
+--R
+--R               2    2            x
+--R   (1)  x log(x  + a ) + 2a atan(-) - 2x
+--R                                 a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.538~~~~~$\displaystyle
+\int{\ln(x^2-a^2)}~dx$}
+$$\int{\ln(x^2-a^2)}=
+x\ln(x^2-a^2)-2x+a\ln\left(\frac{x+a}{x-a}\right)
+$$
+<<*>>=
+)clear all
+
+--S 14 of 16
+aa:=integrate(log(x^2-a^2),x)
+--R 
+--R
+--R               2    2
+--R   (1)  x log(x  - a ) + a log(x + a) - a log(x - a) - 2x
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.539~~~~~$\displaystyle
+\int{x^m\ln(x^2\pm a^2)}~dx$}
+$$\int{x^m\ln(x^2\pm a^2)}=
+\frac{x^{m-1}\ln(x^2\pm a^2)}{m+1}
+-\frac{2}{m+1}\int{\frac{x^{m+2}}{x^2\pm a^2}}
+$$
+<<*>>=
+)clear all
+
+--S 15a of 16
+aa:=integrate(x^m*log(x^2+a^2),x)
+--R 
+--R
+--R           x
+--R         ++       2     2   m
+--I   (1)   |   log(a  + %I )%I d%I
+--R        ++
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+)clear all
+
+--S 15b of 16
+aa:=integrate(x^m*log(x^2-a^2),x)
+--R 
+--R
+--R           x
+--R         ++         2     2   m
+--I   (1)   |   log(- a  + %I )%I d%I
+--R        ++
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+)spool
+)lisp (bye)
+@
+
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} Spiegel, Murray R.
+{\sl Mathematical Handbook of Formulas and Tables}\\
+Schaum's Outline Series McGraw-Hill 1968 p86
+\end{thebibliography}
+\end{document}
diff --git a/src/input/schaum27.input.pamphlet b/src/input/schaum27.input.pamphlet
new file mode 100644
index 0000000..bb9f4d2
--- /dev/null
+++ b/src/input/schaum27.input.pamphlet
@@ -0,0 +1,619 @@
+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/input schaum27.input}
+\author{Timothy Daly}
+\maketitle
+\eject
+\tableofcontents
+\eject
+\section{\cite{1}:14.540~~~~~$\displaystyle
+\int{\sinh{ax}}~dx$}
+$$\int{\sinh{ax}}=
+\frac{\cosh{ax}}{a}
+$$
+<<*>>=
+)spool schaum27.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1 of 22
+aa:=integrate(sinh(a*x),x)
+--R
+--R        cosh(a x)
+--R   (1)  ---------
+--R            a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.541~~~~~$\displaystyle
+\int{x\sinh{ax}}~dx$}
+$$\int{x\sinh{ax}}=
+\frac{x*\cosh{ax}}{a}-\frac{\sinh{ax}}{a^2}
+$$
+<<*>>=
+)clear all
+
+--S 2 of 22
+aa:=integrate(x*sinh(a*x),x)
+--R 
+--R
+--R        - sinh(a x) + a x cosh(a x)
+--R   (1)  ---------------------------
+--R                      2
+--R                     a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.542~~~~~$\displaystyle
+\int{x^2\sinh{ax}}~dx$}
+$$\int{x^2\sinh{ax}}=
+\left(\frac{x^2}{a}+\frac{2}{a^3}\right)\cosh{ax}-\frac{2x}{a^2}\sinh{ax}
+$$
+<<*>>=
+)clear all
+
+--S 3 of 22
+aa:=integrate(x^2*sinh(a*x),x)
+--R 
+--R
+--R                             2 2
+--R        - 2a x sinh(a x) + (a x  + 2)cosh(a x)
+--R   (1)  --------------------------------------
+--R                           3
+--R                          a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.543~~~~~$\displaystyle
+\int{\frac{\sinh{ax}}{x}}~dx$}
+$$\int{\frac{\sinh{ax}}{x}}=
+ax+\frac{(ax)^3}{3\cdot 3!}+\frac{(ax)^5}{5\cdot 5!}+\cdots
+$$
+<<*>>=
+)clear all
+
+--S 4 of 22
+aa:=integrate(sinh(a*x)/x,x)
+--R 
+--R
+--R           x
+--I         ++  sinh(%N a)
+--I   (1)   |   ---------- d%N
+--I        ++       %N
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.544~~~~~$\displaystyle
+\int{\frac{\sinh{ax}}{x^2}}~dx$}
+$$\int{\frac{\sinh{ax}}{x^2}}=
+-\frac{\sinh{ax}}{x}+\int{\frac{\cosh{ax}}{x}}
+$$
+<<*>>=
+)clear all
+
+--S 5 of 22
+aa:=integrate(sinh(a*x)/x^2,x)
+--R 
+--R
+--R           x
+--I         ++  sinh(%N a)
+--I   (1)   |   ---------- d%N
+--R        ++         2
+--I                 %N
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.545~~~~~$\displaystyle
+\int{\frac{dx}{\sinh{ax}}}~dx$}
+$$\int{\frac{1}{\sinh{ax}}}=
+\frac{1}{a}\ln\tanh{\frac{ax}{2}}
+$$
+<<*>>=
+)clear all
+
+--S 6 of 22
+aa:=integrate(1/sinh(a*x),x)
+--R 
+--R
+--R        - log(sinh(a x) + cosh(a x) + 1) + log(sinh(a x) + cosh(a x) - 1)
+--R   (1)  -----------------------------------------------------------------
+--R                                        a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.546~~~~~$\displaystyle
+\int{\frac{x~dx}{\sinh{ax}}}~dx$}
+$$\int{\frac{x}{\sinh{ax}}}=
+\frac{1}{a^2}\left\{ax-\frac{(ax)^3}{18}+\frac{7(ax)^5}{1800}-\cdots
++\frac{2(-1)^n(2^{2n-1})B_n(ax)^{2n+1}}{(2n+1)!}+\cdots\right\}
+$$
+<<*>>=
+)clear all
+
+--S 7 of 22
+aa:=integrate(x/sinh(a*x),x)
+--R 
+--R
+--R           x
+--I         ++      %N
+--I   (1)   |   ---------- d%N
+--I        ++   sinh(%N a)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.547~~~~~$\displaystyle
+\int{\sinh^2{ax}}~dx$}
+$$\int{\sinh^2{ax}}=
+\frac{\sinh{ax}\cosh{ax}}{2a}-\frac{x}{2}
+$$
+<<*>>=
+)clear all
+
+--S 8 of 22
+aa:=integrate(sinh(a*x)^2,x)
+--R 
+--R
+--R        cosh(a x)sinh(a x) - a x
+--R   (1)  ------------------------
+--R                   2a
+--R                                          Type: Union(Expression Integer,...)
+--E
+@
+
+\section{\cite{1}:14.548~~~~~$\displaystyle
+\int{x\sinh^2{ax}}~dx$}
+$$\int{x\sinh^2{ax}}=
+\frac{x*\sinh{2ax}}{4a}-\frac{\cosh{2ax}}{8a^2}-\frac{x^2}{4}
+$$
+<<*>>=
+)clear all
+
+--S 9 of 22
+aa:=integrate(x*sinh(a*x)^2,x)
+--R 
+--R
+--R                   2                                      2     2 2
+--R        - sinh(a x)  + 4a x cosh(a x)sinh(a x) - cosh(a x)  - 2a x
+--R   (1)  -----------------------------------------------------------
+--R                                      2
+--R                                    8a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.549~~~~~$\displaystyle
+\int{\frac{dx}{\sinh^2{ax}}}~dx$}
+$$\int{\frac{1}{\sinh^2{ax}}}=
+-\frac{\coth{ax}}{a}
+$$
+<<*>>=
+)clear all
+
+--S 10 of 22
+aa:=integrate(1/sinh(a*x)^2,x)
+--R 
+--R
+--R                                     2
+--R   (1)  - -------------------------------------------------------
+--R                     2                                      2
+--R          a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  - a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.550~~~~~$\displaystyle
+\int{\sinh{ax}\sinh{px}}~dx$}
+$$\int{\sinh{ax}\sinh{px}}=
+\frac{\sinh(a+p)x}{2(a+p)}-\frac{\sinh(a-p)x}{2(a-p)}
+$$
+<<*>>=
+)clear all
+
+--S 11 of 22
+aa:=integrate(sinh(a*x)*sinh(p*x),x)
+--R 
+--R
+--R        a cosh(a x)sinh(p x) - p cosh(p x)sinh(a x)
+--R   (1)  -------------------------------------------
+--R          2    2          2       2    2          2
+--R        (p  - a )sinh(a x)  + (- p  + a )cosh(a x)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.551~~~~~$\displaystyle
+\int{\sinh{ax}\sin{px}}~dx$}
+$$\int{\sinh{ax}\sin{px}}=
+\frac{a\cosh{ax}\sin{px}-p\sinh{ax}\cos{px}}{a^2+p^2}
+$$
+<<*>>=
+)clear all
+
+--S 12 of 22
+aa:=integrate(sinh(a*x)*sin(p*x),x)
+--R 
+--R
+--R   (1)
+--R                                         2
+--R       (a sin(p x) - p cos(p x))sinh(a x)
+--R     + 
+--R       (2a cosh(a x)sin(p x) - 2p cos(p x)cosh(a x))sinh(a x)
+--R     + 
+--R                   2                                   2
+--R       (a cosh(a x)  + a)sin(p x) - p cos(p x)cosh(a x)  + p cos(p x)
+--R  /
+--R        2     2                2     2
+--R     (2p  + 2a )sinh(a x) + (2p  + 2a )cosh(a x)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.552~~~~~$\displaystyle
+\int{\sinh{ax}\cos{px}}~dx$}
+$$\int{\sinh{ax}\cos{px}}=
+\frac{a\cosh{ax}\cos{px}+p\sinh{ax}\sin{px}}{a^2+p^2}
+$$
+<<*>>=
+)clear all
+
+--S 13 of 22
+aa:=integrate(sinh(a*x)*cos(p*x),x)
+--R 
+--R
+--R   (1)
+--R                                         2
+--R       (p sin(p x) + a cos(p x))sinh(a x)
+--R     + 
+--R       (2p cosh(a x)sin(p x) + 2a cos(p x)cosh(a x))sinh(a x)
+--R     + 
+--R                   2                                   2
+--R       (p cosh(a x)  - p)sin(p x) + a cos(p x)cosh(a x)  + a cos(p x)
+--R  /
+--R        2     2                2     2
+--R     (2p  + 2a )sinh(a x) + (2p  + 2a )cosh(a x)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.553~~~~~$\displaystyle
+\int{\frac{dx}{p+q\sinh{ax}}}~dx$}
+$$\int{\frac{1}{p+q\sinh{ax}}}=
+\frac{1}{a\sqrt{p^2+q^2}}
+\ln\left(\frac{qe^{ax}+p-\sqrt{p^2+q^2}}{qe^{ax}+p+\sqrt{p^2+q^2}}\right)
+$$
+<<*>>=
+)clear all
+
+--S 14 of 22
+aa:=integrate(1/(p+q*sinh(a*x)),x)
+--R 
+--R
+--R   (1)
+--R     log
+--R                 2         2      2                              2         2
+--R                q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
+--R              + 
+--R                                  2     2
+--R                2p q cosh(a x) + q  + 2p
+--R           *
+--R               +-------+
+--R               | 2    2
+--R              \|q  + p
+--R          + 
+--R                 3     2                   3     2                  2     3
+--R            (- 2q  - 2p q)sinh(a x) + (- 2q  - 2p q)cosh(a x) - 2p q  - 2p
+--R       /
+--R                       2                                             2
+--R            q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
+--R          + 
+--R            2p cosh(a x) - q
+--R  /
+--R       +-------+
+--R       | 2    2
+--R     a\|q  + p
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.554~~~~~$\displaystyle
+\int{\frac{dx}{(p+q\sinh{ax})^2}}~dx$}
+$$\int{\frac{1}{(p+q\sinh{ax})^2}}=
+\frac{-q\cosh{ax}}{a(p^2+q^2)(p+q\sinh{ax})}
++\frac{p}{p^2+q^2}\int{\frac{1}{p+q\sinh{ax}}}
+$$
+<<*>>=
+)clear all
+
+--S 15 of 22
+aa:=integrate(1/(p*q*sinh(a*x))^2,x)
+--R 
+--R
+--R   (1)
+--R                                         2
+--R   - ------------------------------------------------------------------------
+--R        2 2         2       2 2                        2 2         2      2 2
+--R     a p q sinh(a x)  + 2a p q cosh(a x)sinh(a x) + a p q cosh(a x)  - a p q
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.555~~~~~$\displaystyle
+\int{\frac{dx}{p^2+q^2\sinh^2{ax}}}$}
+$$\int{\frac{1}{p^2+q^2\sinh^2{ax}}}=
+\left\{
+\begin{array}{l}
+\displaystyle
+\frac{1}{ap\sqrt{q^2-p^2}}\tan^{-1}\frac{\sqrt{q^2-p^2}\tanh{ax}}{p}\\
+\\
+\displaystyle
+\frac{1}{2ap\sqrt{p^2-q^2}}\ln\left(\frac{p+\sqrt{p^2-q^2}\tanh{ax}}
+{p-\sqrt{p^2-q^2}\tanh{ax}}\right)
+\end{array}
+\right.
+$$
+<<*>>=
+)clear all
+
+--S 16 of 22
+aa:=integrate(1/(p^2+q^2*sinh(a*x)^2),x)
+--R 
+--R
+--R   (1)
+--R   [
+--R       log
+--R                   4         4     4                  3
+--R                  q sinh(a x)  + 4q cosh(a x)sinh(a x)
+--R                + 
+--R                     4         2     4     2 2          2
+--R                  (6q cosh(a x)  - 2q  + 4p q )sinh(a x)
+--R                + 
+--R                     4         3        4     2 2
+--R                  (4q cosh(a x)  + (- 4q  + 8p q )cosh(a x))sinh(a x)
+--R                + 
+--R                   4         4        4     2 2          2    4     2 2     4
+--R                  q cosh(a x)  + (- 2q  + 4p q )cosh(a x)  + q  - 8p q  + 8p
+--R             *
+--R                 +---------+
+--R                 |   2    2
+--R                \|- q  + p
+--R            + 
+--R                   4     3 2          2        4     3 2
+--R              (4p q  - 4p q )sinh(a x)  + (8p q  - 8p q )cosh(a x)sinh(a x)
+--R            + 
+--R                   4     3 2          2       4      3 2     5
+--R              (4p q  - 4p q )cosh(a x)  - 4p q  + 12p q  - 8p
+--R         /
+--R               2         4     2                  3
+--R              q sinh(a x)  + 4q cosh(a x)sinh(a x)
+--R            + 
+--R                 2         2     2     2          2
+--R              (6q cosh(a x)  - 2q  + 4p )sinh(a x)
+--R            + 
+--R                 2         3        2     2                        2         4
+--R              (4q cosh(a x)  + (- 4q  + 8p )cosh(a x))sinh(a x) + q cosh(a x)
+--R            + 
+--R                   2     2          2    2
+--R              (- 2q  + 4p )cosh(a x)  + q
+--R    /
+--R            +---------+
+--R            |   2    2
+--R       2a p\|- q  + p
+--R     ,
+--R
+--R       atan
+--R                2         2     2                      2         2    2     2
+--R              (q sinh(a x)  + 2q cosh(a x)sinh(a x) + q cosh(a x)  - q  + 2p )
+--R           *
+--R               +-------+
+--R               | 2    2
+--R              \|q  - p
+--R         /
+--R                2     3
+--R            2p q  - 2p
+--R    /
+--R           +-------+
+--R           | 2    2
+--R       a p\|q  - p
+--R     ]
+--R                                     Type: Union(List Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.556~~~~~$\displaystyle
+\int{\frac{dx}{p^2-q^2\sinh^2{ax}}}~dx$}
+$$\int{\frac{1}{p^2-q^2\sinh^2{ax}}}=
+\frac{1}{2ap\sqrt{p^2+q^2}}\ln\left(\frac{p+\sqrt{p^2+q^2}\tanh{ax}}
+{p-\sqrt{p^2+q^2}\tanh{ax}}\right)
+$$
+<<*>>=
+)clear all
+
+--S 17 of 22
+aa:=integrate(1/(p^2+q^2*sinh(a*x)^2),x)
+--R 
+--R
+--R   (1)
+--R   [
+--R       log
+--R                   4         4     4                  3
+--R                  q sinh(a x)  + 4q cosh(a x)sinh(a x)
+--R                + 
+--R                     4         2     4     2 2          2
+--R                  (6q cosh(a x)  - 2q  + 4p q )sinh(a x)
+--R                + 
+--R                     4         3        4     2 2
+--R                  (4q cosh(a x)  + (- 4q  + 8p q )cosh(a x))sinh(a x)
+--R                + 
+--R                   4         4        4     2 2          2    4     2 2     4
+--R                  q cosh(a x)  + (- 2q  + 4p q )cosh(a x)  + q  - 8p q  + 8p
+--R             *
+--R                 +---------+
+--R                 |   2    2
+--R                \|- q  + p
+--R            + 
+--R                   4     3 2          2        4     3 2
+--R              (4p q  - 4p q )sinh(a x)  + (8p q  - 8p q )cosh(a x)sinh(a x)
+--R            + 
+--R                   4     3 2          2       4      3 2     5
+--R              (4p q  - 4p q )cosh(a x)  - 4p q  + 12p q  - 8p
+--R         /
+--R               2         4     2                  3
+--R              q sinh(a x)  + 4q cosh(a x)sinh(a x)
+--R            + 
+--R                 2         2     2     2          2
+--R              (6q cosh(a x)  - 2q  + 4p )sinh(a x)
+--R            + 
+--R                 2         3        2     2                        2         4
+--R              (4q cosh(a x)  + (- 4q  + 8p )cosh(a x))sinh(a x) + q cosh(a x)
+--R            + 
+--R                   2     2          2    2
+--R              (- 2q  + 4p )cosh(a x)  + q
+--R    /
+--R            +---------+
+--R            |   2    2
+--R       2a p\|- q  + p
+--R     ,
+--R
+--R       atan
+--R                2         2     2                      2         2    2     2
+--R              (q sinh(a x)  + 2q cosh(a x)sinh(a x) + q cosh(a x)  - q  + 2p )
+--R           *
+--R               +-------+
+--R               | 2    2
+--R              \|q  - p
+--R         /
+--R                2     3
+--R            2p q  - 2p
+--R    /
+--R           +-------+
+--R           | 2    2
+--R       a p\|q  - p
+--R     ]
+--R                                     Type: Union(List Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.557~~~~~$\displaystyle
+\int{x^m\sinh{ax}}~dx$}
+$$\int{x^m\sinh{ax}}=
+\frac{x^m\cosh{ax}}{a}-\frac{m}{a}\int{x^{m-1}\cosh{ax}}
+$$
+<<*>>=
+)clear all
+
+--S 18 of 22
+aa:=integrate(x^m*sinh(a*x),x)
+--R 
+--R
+--R           x
+--R         ++              m
+--I   (1)   |   sinh(%N a)%N d%N
+--R        ++
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.558~~~~~$\displaystyle
+\int{\sinh^n}~dx$}
+$$\int{\sinh^n}=
+\frac{\sinh^{n-1}{ax}\cosh{ax}}{an}-\frac{n-1}{n}\int{\sinh^{n-2}{ax}}
+$$
+<<*>>=
+)clear all
+
+--S 19 of 22
+aa:=integrate(sinh(a*x)^n,x)
+--R 
+--R
+--R           x
+--R         ++            n
+--I   (1)   |   sinh(%N a) d%N
+--R        ++
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.559~~~~~$\displaystyle
+\int{\frac{\sinh{ax}}{x^n}}~dx$}
+$$\int{\frac{\sinh{ax}}{x^n}}=
+\frac{-\sinh{ax}}{(n-1)x^{n-1}}+\frac{a}{n-1}\int{\frac{\cosh{ax}}{n^{n-1}}}
+$$
+<<*>>=
+)clear all
+
+--S 20 of 22
+aa:=integrate(sinh(a*x)/a^n,x)
+--R
+--R                 2                                  2
+--R        sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  + 1
+--R   (1)  -------------------------------------------------
+--R                                               n
+--R                 (2a sinh(a x) + 2a cosh(a x))a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.560~~~~~$\displaystyle
+\int{\frac{dx}{\sinh^n{ax}}}~dx$}
+$$\int{\frac{1}{\sinh^n{ax}}}=
+\frac{-\cosh{ax}}{a(n-1)\sinh^{n-1}{ax}}
+-\frac{n-2}{n-1}\int{\frac{1}{\sinh^{n-2}{ax}}}
+$$
+<<*>>=
+)clear all
+
+--S 21 of 22
+aa:=integrate(1/sinh(a*x)^n,x)
+--R 
+--R
+--R           x
+--R         ++       1
+--I   (1)   |   ----------- d%N
+--R        ++             n
+--I             sinh(%N a)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.561~~~~~$\displaystyle
+\int{\frac{x~dx}{\sinh^n{ax}}}~dx$}
+$$\int{\frac{x}{\sinh^n{ax}}}=
+\frac{-x\cosh{ax}}{a(n-1)\sinh^{n-1}{ax}}
+-\frac{1}{a^2(n-1)(n-2)\sinh^{n-2}{ax}}
+-\frac{n-2}{n-1}\int{\frac{x}{\sinh^{n-2}{ax}}}
+$$
+<<*>>=
+)clear all
+
+--S 22 of 22
+aa:=integrate(x/sinh(a*x)^n,x)
+--R 
+--R
+--R           x
+--I         ++       %N
+--I   (1)   |   ----------- d%N
+--R        ++             n
+--I             sinh(%N a)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+)spool
+)lisp (bye)
+@
+
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} Spiegel, Murray R.
+{\sl Mathematical Handbook of Formulas and Tables}\\
+Schaum's Outline Series McGraw-Hill 1968 p86
+\end{thebibliography}
+\end{document}
diff --git a/src/input/schaum28.input.pamphlet b/src/input/schaum28.input.pamphlet
new file mode 100644
index 0000000..b3fc3c6
--- /dev/null
+++ b/src/input/schaum28.input.pamphlet
@@ -0,0 +1,846 @@
+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/input schaum28.input}
+\author{Timothy Daly}
+\maketitle
+\eject
+\tableofcontents
+\eject
+\section{\cite{1}:14.562~~~~~$\displaystyle
+\int{\cosh{ax}}~dx$}
+$$\int{\cosh{ax}}=
+\frac{\sinh{ax}}{a}
+$$
+<<*>>=
+)spool schaum28.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1 of 28
+aa:=integrate(cosh(a*x),x)
+--R 
+--R
+--R        sinh(a x)
+--R   (1)  ---------
+--R            a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.563~~~~~$\displaystyle
+\int{x\cosh{ax}}~dx$}
+$$\int{x\cosh{ax}}=
+\frac{x\sinh{ax}}{a}-\frac{\cosh{ax}}{a^2}
+$$
+<<*>>=
+)clear all
+
+--S 2 of 28
+aa:=integrate(x*cosh(a*x),x)
+--R 
+--R
+--R        a x sinh(a x) - cosh(a x)
+--R   (1)  -------------------------
+--R                     2
+--R                    a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.564~~~~~$\displaystyle
+\int{x^2\cosh{ax}}~dx$}
+$$\int{x^2\cosh{ax}}=
+-\frac{2x\cosh{ax}}{a^2}+\left(\frac{x^2}{a}+\frac{2}{a^3}\right)\sinh{ax}
+$$
+<<*>>=
+)clear all
+
+--S 3 of 28
+aa:=integrate(x^2*cosh(a*x),x)
+--R 
+--R
+--R          2 2
+--R        (a x  + 2)sinh(a x) - 2a x cosh(a x)
+--R   (1)  ------------------------------------
+--R                          3
+--R                         a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.565~~~~~$\displaystyle
+\int{\frac{\cosh{ax}}{x}}~dx$}
+$$\int{\frac{\cosh{ax}}{x}}=
+\ln{x}+\frac{(ax)^2}{2\cdot 2!}
++\frac{(ax)^4}{4\cdot 4!}
++\frac{(ax)^6}{6\cdot 6!}+\cdots
+$$
+<<*>>=
+)clear all
+
+--S 4 of 28
+aa:=integrate(cosh(a*x)/x,x)
+--R 
+--R
+--R           x
+--I         ++  cosh(%N a)
+--I   (1)   |   ---------- d%N
+--I        ++       %N
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.566~~~~~$\displaystyle
+\int{\frac{\cosh{ax}}{x^2}}~dx$}
+$$\int{\frac{\cosh{ax}}{x^2}}=
+-\frac{\cosh{ax}}{x}+a\int{\frac{\sinh{ax}}{a}}
+$$
+<<*>>=
+)clear all
+
+--S 5 of 28
+aa:=integrate(cosh(a*x)/x^2,x)
+--R 
+--R
+--R           x
+--I         ++  cosh(%N a)
+--I   (1)   |   ---------- d%N
+--R        ++         2
+--I                 %N
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.567~~~~~$\displaystyle
+\int{\frac{dx}{\cosh{ax}}}~dx$}
+$$\int{\frac{1}{\cosh{ax}}}=
+\frac{2}{a}\tan^{-1}e^{ax}
+$$
+<<*>>=
+)clear all
+
+--S 6 of 28
+aa:=integrate(1/cosh(a*x),x)
+--R 
+--R
+--R        2atan(sinh(a x) + cosh(a x))
+--R   (1)  ----------------------------
+--R                      a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.568~~~~~$\displaystyle
+\int{\frac{x~dx}{\cosh{ax}}}~dx$}
+$$\int{\frac{x}{\cosh{ax}}}=
+\frac{1}{a^2}\left\{\frac{(ax)^2}{2}-\frac{(ax)^4}{8}+\frac{5(ax)^6}{144}
++\cdots+\frac{(-1)^nE_n(ax)^{2n+2}}{(2n+2)(2n)!}+\cdots\right\}
+$$
+<<*>>=
+)clear all
+
+--S 7 of 28
+aa:=integrate(x/cosh(a*x),x)
+--R 
+--R
+--R           x
+--I         ++      %N
+--I   (1)   |   ---------- d%N
+--I        ++   cosh(%N a)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.569~~~~~$\displaystyle
+\int{\cosh^2{ax}}~dx$}
+$$\int{\cosh^2{ax}}=
+\frac{x}{2}+\frac{\sinh{ax}\cosh{ax}}{2}
+$$
+<<*>>=
+)clear all
+
+--S 8 of 28
+aa:=integrate(cosh(a*x)^2,x)
+--R 
+--R
+--R        cosh(a x)sinh(a x) + a x
+--R   (1)  ------------------------
+--R                   2a
+--R                                          Type: Union(Expression Integer,...)
+--E
+@
+
+\section{\cite{1}:14.570~~~~~$\displaystyle
+\int{x\cosh^2{ax}}~dx$}
+$$\int{x\cosh^2{ax}}=
+\frac{x^2}{4}+\frac{x\sinh{2ax}}{4a}-\frac{\cosh{2ax}}{8a^2}
+$$
+<<*>>=
+)clear all
+
+--S 9 of 28
+aa:=integrate(x*cosh(a*x)^2,x)
+--R 
+--R
+--R                   2                                      2     2 2
+--R        - sinh(a x)  + 4a x cosh(a x)sinh(a x) - cosh(a x)  + 2a x
+--R   (1)  -----------------------------------------------------------
+--R                                      2
+--R                                    8a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.571~~~~~$\displaystyle
+\int{\frac{dx}{\cosh^2{ax}}}~dx$}
+$$\int{\frac{1}{\cosh^2{ax}}}=
+\frac{\tanh{ax}}{a}
+$$
+<<*>>=
+)clear all
+
+--S 10 of 28
+aa:=integrate(1/cosh(a*x)^2,x)
+--R 
+--R
+--R                                     2
+--R   (1)  - -------------------------------------------------------
+--R                     2                                      2
+--R          a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  + a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.572~~~~~$\displaystyle
+\int{\cosh{ax}\cosh{px}}~dx$}
+$$\int{\cosh{ax}\cosh{px}}=
+\frac{\sinh(a-p)x}{2(a-p)}+\frac{\sinh(a+p)x}{2(a+p)}
+$$
+<<*>>=
+)clear all
+
+--S 11 of 28
+aa:=integrate(cosh(a*x)*cosh(p*x),x)
+--R 
+--R
+--R        - p cosh(a x)sinh(p x) + a cosh(p x)sinh(a x)
+--R   (1)  ---------------------------------------------
+--R           2    2          2       2    2          2
+--R         (p  - a )sinh(a x)  + (- p  + a )cosh(a x)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.573~~~~~$\displaystyle
+\int{\cosh{ax}\sin{px}}~dx$}
+$$\int{\cosh{ax}\sin{px}}=
+\frac{a\sinh{ax}\sin{px}-p\cosh{ax}\cos{px}}{a^2+p^2}
+$$
+<<*>>=
+)clear all
+
+--S 12 of 28
+aa:=integrate(cosh(a*x)*sin(p*x),x)
+--R 
+--R
+--R   (1)
+--R                                         2
+--R       (a sin(p x) - p cos(p x))sinh(a x)
+--R     + 
+--R       (2a cosh(a x)sin(p x) - 2p cos(p x)cosh(a x))sinh(a x)
+--R     + 
+--R                   2                                   2
+--R       (a cosh(a x)  - a)sin(p x) - p cos(p x)cosh(a x)  - p cos(p x)
+--R  /
+--R        2     2                2     2
+--R     (2p  + 2a )sinh(a x) + (2p  + 2a )cosh(a x)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.574~~~~~$\displaystyle
+\int{\cosh{ax}\cos{px}}~dx$}
+$$\int{\cosh{ax}\cos{px}}=
+\frac{a\sinh{ax}\cos{px}+p\cosh{ax}\sin{px}}{a^2+p^2}
+$$
+<<*>>=
+)clear all
+
+--S 13 of 28
+aa:=integrate(cosh(a*x)*cos(p*x),x)
+--R 
+--R
+--R   (1)
+--R                                         2
+--R       (p sin(p x) + a cos(p x))sinh(a x)
+--R     + 
+--R       (2p cosh(a x)sin(p x) + 2a cos(p x)cosh(a x))sinh(a x)
+--R     + 
+--R                   2                                   2
+--R       (p cosh(a x)  + p)sin(p x) + a cos(p x)cosh(a x)  - a cos(p x)
+--R  /
+--R        2     2                2     2
+--R     (2p  + 2a )sinh(a x) + (2p  + 2a )cosh(a x)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.575~~~~~$\displaystyle
+\int{\frac{dx}{\cosh{ax}+1}}$}
+$$\int{\frac{1}{\cosh{ax}+1}}=
+\frac{1}{a}\tanh{\frac{ax}{2}}
+$$
+<<*>>=
+)clear all
+
+--S 14 of 28
+aa:=integrate(1/(cosh(a*x)+1),x)
+--R 
+--R
+--R                        2
+--R   (1)  - -----------------------------
+--R          a sinh(a x) + a cosh(a x) + a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.576~~~~~$\displaystyle
+\int{\frac{dx}{\cosh{ax}-1}}$}
+$$\int{\frac{1}{\cosh{ax}-1}}=
+-\frac{1}{a}\coth{\frac{ax}{2}}
+$$
+<<*>>=
+)clear all
+
+--S 15 of 28
+aa:=integrate(1/(cosh(a*x)-1),x)
+--R 
+--R
+--R                        2
+--R   (1)  - -----------------------------
+--R          a sinh(a x) + a cosh(a x) - a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.577~~~~~$\displaystyle
+\int{\frac{x~dx}{\cosh{ax}+1}}~dx$}
+$$\int{\frac{x}{\cosh{ax}+1}}=
+\frac{x}{a}\tanh\frac{ax}{2}-\frac{2}{a^2}\ln\cosh\frac{ax}{2}
+$$
+<<*>>=
+)clear all
+
+--S 16 of 28
+aa:=integrate(x/(cosh(a*x)+1),x)
+--R 
+--R
+--R   (1)
+--R       (- 2sinh(a x) - 2cosh(a x) - 2)log(sinh(a x) + cosh(a x) + 1)
+--R     + 
+--R       2a x sinh(a x) + 2a x cosh(a x)
+--R  /
+--R      2             2             2
+--R     a sinh(a x) + a cosh(a x) + a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.578~~~~~$\displaystyle
+\int{\frac{x~dx}{\cosh{ax}-1}}$}
+$$\int{\frac{x}{\cosh{ax}-1}}
+-\frac{x}{a}\coth\frac{ax}{2}+\frac{2}{a^2}\ln\sinh\frac{ax}{2}
+$$
+<<*>>=
+)clear all
+
+--S 17 of 28
+aa:=integrate(x/(cosh(a*x)-1),x)
+--R 
+--R
+--R   (1)
+--R       (2sinh(a x) + 2cosh(a x) - 2)log(sinh(a x) + cosh(a x) - 1)
+--R     + 
+--R       - 2a x sinh(a x) - 2a x cosh(a x)
+--R  /
+--R      2             2             2
+--R     a sinh(a x) + a cosh(a x) - a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.579~~~~~$\displaystyle
+\int{\frac{dx}{(\cosh{ax}+1)^2}}$}
+$$\int{\frac{1}{(\cosh{ax}+1)^2}}=
+\frac{1}{2a}\tanh{\frac{ax}{2}}-\frac{1}{6a}\tanh^3{\frac{ax}{2}}
+$$
+<<*>>=
+)clear all
+
+--S 18 of 28
+aa:=integrate(1/(cosh(a*x)+1)^2,x)
+--R 
+--R
+--R   (1)
+--R     - 6sinh(a x) - 6cosh(a x) - 2
+--R  /
+--R                   3                               2
+--R       3a sinh(a x)  + (9a cosh(a x) + 9a)sinh(a x)
+--R     + 
+--R                    2                                              3
+--R       (9a cosh(a x)  + 18a cosh(a x) + 9a)sinh(a x) + 3a cosh(a x)
+--R     + 
+--R                   2
+--R       9a cosh(a x)  + 9a cosh(a x) + 3a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.580~~~~~$\displaystyle
+\int{\frac{dx}{(\cosh{ax}-1)^2}}$}
+$$\int{\frac{1}{(\cosh{ax}-1)^2}}=
+\frac{1}{2a}\coth{\frac{ax}{2}}-\frac{1}{6a}\coth^3{\frac{ax}{2}}
+$$
+<<*>>=
+)clear all
+
+--S 19 of 28
+aa:=integrate(1/(cosh(a*x)-1)^2,x)
+--R 
+--R
+--R   (1)
+--R     - 6sinh(a x) - 6cosh(a x) + 2
+--R  /
+--R                   3                               2
+--R       3a sinh(a x)  + (9a cosh(a x) - 9a)sinh(a x)
+--R     + 
+--R                    2                                              3
+--R       (9a cosh(a x)  - 18a cosh(a x) + 9a)sinh(a x) + 3a cosh(a x)
+--R     + 
+--R                     2
+--R       - 9a cosh(a x)  + 9a cosh(a x) - 3a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.581~~~~~$\displaystyle
+\int{\frac{dx}{p+q\cosh{ax}}}$}
+$$\int{\frac{1}{p+q\cosh{ax}}}=
+\left\{
+\begin{array}{l}
+\displaystyle
+\frac{2}{a\sqrt{q^2-p^2}}\tan^{-1}\frac{qe^{ax}+p}{\sqrt{q^2-p^2}}\\
+\\
+\displaystyle
+\frac{1}{a\sqrt{p^2-a^2}}\ln\left(\frac{qe^{ax}+p-\sqrt{p^2-q^2}}
+{qe^{ax}+p+\sqrt{p^2-q^2}}\right)
+\end{array}
+\right.
+$$
+<<*>>=
+)clear all
+
+--S 20 of 28
+aa:=integrate(1/(p+q*cosh(a*x)),x)
+--R 
+--R
+--R   (1)
+--R   [
+--R       log
+--R                   2         2      2                              2         2
+--R                  q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
+--R                + 
+--R                                    2     2
+--R                  2p q cosh(a x) - q  + 2p
+--R             *
+--R                 +---------+
+--R                 |   2    2
+--R                \|- q  + p
+--R            + 
+--R                 3     2                 3     2                  2     3
+--R              (2q  - 2p q)sinh(a x) + (2q  - 2p q)cosh(a x) + 2p q  - 2p
+--R         /
+--R                         2                                             2
+--R              q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
+--R            + 
+--R              2p cosh(a x) + q
+--R    /
+--R         +---------+
+--R         |   2    2
+--R       a\|- q  + p
+--R     ,
+--R                                          +-------+
+--R                                          | 2    2
+--R          (q sinh(a x) + q cosh(a x) + p)\|q  - p
+--R    2atan(-----------------------------------------)
+--R                            2    2
+--R                           q  - p
+--R    ------------------------------------------------]
+--R                         +-------+
+--R                         | 2    2
+--R                       a\|q  - p
+--R                                     Type: Union(List Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.582~~~~~$\displaystyle
+\int{\frac{dx}{(p+q\cosh{ax})^2}}~dx$}
+$$\int{\frac{1}{(p+q\cosh{ax})^2}}=
+\frac{q\sinh{ax}}{a(q^2-p^2)(p+q\cosh{ax})}
+-\frac{p}{q^2-p^2}\int{\frac{1}{p+q\cosh{ax}}}
+$$
+<<*>>=
+)clear all
+
+--S 21 of 28
+aa:=integrate(1/(p+q*cosh(a*x))^2,x)
+--R 
+--R
+--R   (1)
+--R   [
+--R                          2                       2                          2
+--R             p q sinh(a x)  + (2p q cosh(a x) + 2p )sinh(a x) + p q cosh(a x)
+--R           + 
+--R               2
+--R             2p cosh(a x) + p q
+--R        *
+--R           log
+--R                       2         2      2
+--R                      q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x)
+--R                    + 
+--R                       2         2                     2     2
+--R                      q cosh(a x)  + 2p q cosh(a x) - q  + 2p
+--R                 *
+--R                     +---------+
+--R                     |   2    2
+--R                    \|- q  + p
+--R                + 
+--R                     3     2                   3     2                  2     3
+--R                (- 2q  + 2p q)sinh(a x) + (- 2q  + 2p q)cosh(a x) - 2p q  + 2p
+--R             /
+--R                             2                                             2
+--R                  q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
+--R                + 
+--R                  2p cosh(a x) + q
+--R       + 
+--R                                              +---------+
+--R                                              |   2    2
+--R         (- 2p sinh(a x) - 2p cosh(a x) - 2q)\|- q  + p
+--R    /
+--R               3      2           2
+--R           (a q  - a p q)sinh(a x)
+--R         + 
+--R                 3       2                    2       3
+--R           ((2a q  - 2a p q)cosh(a x) + 2a p q  - 2a p )sinh(a x)
+--R         + 
+--R               3      2           2          2       3                3      2
+--R           (a q  - a p q)cosh(a x)  + (2a p q  - 2a p )cosh(a x) + a q  - a p q
+--R      *
+--R          +---------+
+--R          |   2    2
+--R         \|- q  + p
+--R     ,
+--R
+--R                             2                         2
+--R             - 2p q sinh(a x)  + (- 4p q cosh(a x) - 4p )sinh(a x)
+--R           + 
+--R                             2     2
+--R             - 2p q cosh(a x)  - 4p cosh(a x) - 2p q
+--R        *
+--R                                                +-------+
+--R                                                | 2    2
+--R                (q sinh(a x) + q cosh(a x) + p)\|q  - p
+--R           atan(-----------------------------------------)
+--R                                  2    2
+--R                                 q  - p
+--R       + 
+--R                                              +-------+
+--R                                              | 2    2
+--R         (- 2p sinh(a x) - 2p cosh(a x) - 2q)\|q  - p
+--R    /
+--R               3      2           2
+--R           (a q  - a p q)sinh(a x)
+--R         + 
+--R                 3       2                    2       3
+--R           ((2a q  - 2a p q)cosh(a x) + 2a p q  - 2a p )sinh(a x)
+--R         + 
+--R               3      2           2          2       3                3      2
+--R           (a q  - a p q)cosh(a x)  + (2a p q  - 2a p )cosh(a x) + a q  - a p q
+--R      *
+--R          +-------+
+--R          | 2    2
+--R         \|q  - p
+--R     ]
+--R                                     Type: Union(List Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.583~~~~~$\displaystyle
+\int{\frac{dx}{p^2-q^2\cosh^2{ax}}}$}
+$$\int{\frac{1}{p^2-q^2\cosh^2{ax}}}=
+\left\{
+\begin{array}{l}
+\displaystyle
+\frac{1}{2ap\sqrt{p^2-q^2}}\ln\left(\frac{p\tanh{ax}+\sqrt{p^2-q^2}}
+{p\tanh{ax}-\sqrt{p^2-q^2}}\right)\\
+\\
+\displaystyle
+\frac{1}{ap\sqrt{q^2-p^2}}\tan^{-1}\frac{p\tanh{ax}}{\sqrt{q^2-p^2}}\\
+\end{array}
+\right.
+$$
+<<*>>=
+)clear all
+
+--S 22 of 28
+aa:=integrate(1/(p^2-q^2*cosh(a*x)^2),x)
+--R 
+--R
+--R   (1)
+--R   [
+--R       log
+--R                   4         4     4                  3
+--R                  q sinh(a x)  + 4q cosh(a x)sinh(a x)
+--R                + 
+--R                     4         2     4     2 2          2
+--R                  (6q cosh(a x)  + 2q  - 4p q )sinh(a x)
+--R                + 
+--R                     4         3      4     2 2
+--R                  (4q cosh(a x)  + (4q  - 8p q )cosh(a x))sinh(a x)
+--R                + 
+--R                   4         4      4     2 2          2    4     2 2     4
+--R                  q cosh(a x)  + (2q  - 4p q )cosh(a x)  + q  - 8p q  + 8p
+--R             *
+--R                 +---------+
+--R                 |   2    2
+--R                \|- q  + p
+--R            + 
+--R                     4     3 2          2          4     3 2
+--R              (- 4p q  + 4p q )sinh(a x)  + (- 8p q  + 8p q )cosh(a x)sinh(a x)
+--R            + 
+--R                     4     3 2          2       4      3 2     5
+--R              (- 4p q  + 4p q )cosh(a x)  - 4p q  + 12p q  - 8p
+--R         /
+--R               2         4     2                  3
+--R              q sinh(a x)  + 4q cosh(a x)sinh(a x)
+--R            + 
+--R                 2         2     2     2          2
+--R              (6q cosh(a x)  + 2q  - 4p )sinh(a x)
+--R            + 
+--R                 2         3      2     2                        2         4
+--R              (4q cosh(a x)  + (4q  - 8p )cosh(a x))sinh(a x) + q cosh(a x)
+--R            + 
+--R                 2     2          2    2
+--R              (2q  - 4p )cosh(a x)  + q
+--R    /
+--R            +---------+
+--R            |   2    2
+--R       2a p\|- q  + p
+--R     ,
+--R
+--R     -
+--R          atan
+--R                      2         2     2                      2         2    2
+--R                     q sinh(a x)  + 2q cosh(a x)sinh(a x) + q cosh(a x)  + q
+--R                   + 
+--R                         2
+--R                     - 2p
+--R              *
+--R                  +-------+
+--R                  | 2    2
+--R                 \|q  - p
+--R            /
+--R                   2     3
+--R               2p q  - 2p
+--R       /
+--R              +-------+
+--R              | 2    2
+--R          a p\|q  - p
+--R     ]
+--R                                     Type: Union(List Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.584~~~~~$\displaystyle
+\int{\frac{dx}{p^2+q^2\cosh^2{ax}}}$}
+$$\int{\frac{1}{p^2+q^2\cosh^2{ax}}}=
+\left\{
+\begin{array}{l}
+\displaystyle
+\frac{1}{2ap\sqrt{p^2+q^2}}\ln\left(\frac{p\tanh{ax}+\sqrt{p^2+q^2}}
+{p\tanh{ax}-\sqrt{p^2+q^2}}\right)\\
+\\
+\displaystyle
+\frac{1}{ap\sqrt{p^2+q^2}}\tan^{-1}\frac{p\tanh{ax}}{\sqrt{p^2+q^2}}\\
+\end{array}
+\right.
+$$
+<<*>>=
+)clear all
+
+--S 23 of 28
+aa:=integrate(1/(p^2+q^2*cosh(a*x)^2),x)
+--R 
+--R
+--R   (1)
+--R     log
+--R                 4         4     4                  3
+--R                q sinh(a x)  + 4q cosh(a x)sinh(a x)
+--R              + 
+--R                   4         2     4     2 2          2
+--R                (6q cosh(a x)  + 2q  + 4p q )sinh(a x)
+--R              + 
+--R                   4         3      4     2 2                        4         4
+--R                (4q cosh(a x)  + (4q  + 8p q )cosh(a x))sinh(a x) + q cosh(a x)
+--R              + 
+--R                   4     2 2          2    4     2 2     4
+--R                (2q  + 4p q )cosh(a x)  + q  + 8p q  + 8p
+--R           *
+--R               +-------+
+--R               | 2    2
+--R              \|q  + p
+--R          + 
+--R                   4     3 2          2          4     3 2
+--R            (- 4p q  - 4p q )sinh(a x)  + (- 8p q  - 8p q )cosh(a x)sinh(a x)
+--R          + 
+--R                   4     3 2          2       4      3 2     5
+--R            (- 4p q  - 4p q )cosh(a x)  - 4p q  - 12p q  - 8p
+--R       /
+--R             2         4     2                  3
+--R            q sinh(a x)  + 4q cosh(a x)sinh(a x)
+--R          + 
+--R               2         2     2     2          2
+--R            (6q cosh(a x)  + 2q  + 4p )sinh(a x)
+--R          + 
+--R               2         3      2     2                        2         4
+--R            (4q cosh(a x)  + (4q  + 8p )cosh(a x))sinh(a x) + q cosh(a x)
+--R          + 
+--R               2     2          2    2
+--R            (2q  + 4p )cosh(a x)  + q
+--R  /
+--R          +-------+
+--R          | 2    2
+--R     2a p\|q  + p
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.585~~~~~$\displaystyle
+\int{x^m\cosh{ax}}~dx$}
+$$\int{x^m\cosh{ax}}=
+\frac{x^m\sinh{ax}}{a}-\frac{m}{a}\int{x^{m-1}\sinh{ax}}
+$$
+<<*>>=
+)clear all
+
+--S 24 of 28
+aa:=integrate(x^m*cosh(a*x),x)
+--R 
+--R
+--R           x
+--R         ++              m
+--I   (1)   |   cosh(%N a)%N d%N
+--R        ++
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.586~~~~~$\displaystyle
+\int{\cosh^n{ax}}~dx$}
+$$\int{\cosh^n{ax}}=
+\frac{\cosh^{n-1}{ax}\sinh{ax}}{an}+\frac{n-1}{n}\int{\cosh^{n-2}{ax}}
+$$
+<<*>>=
+)clear all
+
+--S 25 of 28
+aa:=integrate(cosh(a*x)^n,x)
+--R 
+--R
+--R           x
+--R         ++            n
+--I   (1)   |   cosh(%N a) d%N
+--R        ++
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.587~~~~~$\displaystyle
+\int{\frac{\cosh{ax}}{x^n}}~dx$}
+$$\int{\frac{\cosh{ax}}{x^n}}=
+\frac{-\cosh{ax}}{(n-1)x^{n-1}}
++\frac{a}{n-1}\int{\frac{\sinh{ax}}{x^{n-1}}}
+$$
+<<*>>=
+)clear all
+
+--S 26 of 28
+aa:=integrate(cosh(a*x)/x^n,x)
+--R 
+--R
+--R           x
+--I         ++  cosh(%N a)
+--I   (1)   |   ---------- d%N
+--R        ++         n
+--I                 %N
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.588~~~~~$\displaystyle
+\int{\frac{dx}{\cosh^n{ax}}}~dx$}
+$$\int{\frac{1}{\cosh^n{ax}}}=
+\frac{\sinh{ax}}{a(n-1)\cosh^{n-1}{ax}}
++\frac{n-2}{n-1}\int{\frac{1}{\cosh^{n-2}{ax}}}
+$$
+<<*>>=
+)clear all
+
+--S 27 of 28
+aa:=integrate(1/cosh(a*x)^n,x)
+--R 
+--R
+--R           x
+--R         ++       1
+--I   (1)   |   ----------- d%N
+--R        ++             n
+--I             cosh(%N a)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.589~~~~~$\displaystyle
+\int{\frac{x}{\cosh^n{ax}}}~dx$}
+$$\int{\frac{x}{\cosh^n{ax}}}=
+\frac{x\sinh{ax}}{a(n-1)\cosh^{n-1}{ax}}
++\frac{1}{(n-1)(n-2)a^2\cosh^{n-2}{ax}}
++\frac{n-2}{n-1}\int{\frac{x}{\cosh^{n-2}}}
+$$
+<<*>>=
+)clear all
+
+--S 28 of 28
+aa:=integrate(1/cosh(a*x)^n,x)
+--R 
+--R
+--R           x
+--R         ++       1
+--I   (1)   |   ----------- d%N
+--R        ++             n
+--I             cosh(%N a)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+)spool
+)lisp (bye)
+@
+
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} Spiegel, Murray R.
+{\sl Mathematical Handbook of Formulas and Tables}\\
+Schaum's Outline Series McGraw-Hill 1968 pp88-89
+\end{thebibliography}
+\end{document}
diff --git a/src/input/schaum29.input.pamphlet b/src/input/schaum29.input.pamphlet
new file mode 100644
index 0000000..37e2800
--- /dev/null
+++ b/src/input/schaum29.input.pamphlet
@@ -0,0 +1,365 @@
+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/input schaum29.input}
+\author{Timothy Daly}
+\maketitle
+\eject
+\tableofcontents
+\eject
+\section{\cite{1}:14.590~~~~~$\displaystyle
+\int{\sinh{ax}\cosh{ax}}~dx$}
+$$\int{\sinh{ax}\cosh{ax}}=
+\frac{\sinh^2{ax}}{2a}
+$$
+<<*>>=
+)spool schaum29.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1 of 14
+aa:=integrate(sinh(a*x)*cosh(a*x),x)
+--R 
+--R
+--R                 2            2
+--R        sinh(a x)  + cosh(a x)
+--R   (1)  -----------------------
+--R                   4a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.591~~~~~$\displaystyle
+\int{\sinh{px}\cosh{qx}}~dx$}
+$$\int{\sinh{px}\cosh{qx}}=
+\frac{\cosh(p+q)x}{2(p+q)}+\frac{\cosh(p-q)x}{2(p-q)}
+$$
+<<*>>=
+)clear all
+
+--S 2 of 14
+aa:=integrate(sinh(p*x)*cosh(q*x),x)
+--R 
+--R
+--R        - q sinh(p x)sinh(q x) + p cosh(p x)cosh(q x)
+--R   (1)  ---------------------------------------------
+--R           2    2          2       2    2          2
+--R         (q  - p )sinh(p x)  + (- q  + p )cosh(p x)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.592~~~~~$\displaystyle
+\int{\sinh^n{ax}\cosh{ax}}~dx$}
+$$\int{\sinh^n{ax}\cosh{ax}}=
+\frac{\sinh^{n+1}{ax}}{(n+1)a}
+$$
+<<*>>=
+)clear all
+
+--S 3 of 14
+aa:=integrate(sinh(a*x)^n*cosh(a*x),x)
+--R 
+--R
+--R        - sinh(a x)sinh(n log(sinh(a x))) - sinh(a x)cosh(n log(sinh(a x)))
+--R   (1)  -------------------------------------------------------------------
+--R                                      2                       2
+--R                    (a n + a)sinh(a x)  + (- a n - a)cosh(a x)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.593~~~~~$\displaystyle
+\int{\cosh^n{ax}\sinh{ax}}~dx$}
+$$\int{\cosh^n{ax}\sinh{ax}}=
+\frac{\cosh^{n+1}{ax}}{(n+1)a}
+$$
+<<*>>=
+)clear all
+
+--S 4 of 14
+aa:=integrate(cosh(a*x)^n*sinh(a*x),x)
+--R 
+--R
+--R        - cosh(a x)sinh(n log(cosh(a x))) - cosh(a x)cosh(n log(cosh(a x)))
+--R   (1)  -------------------------------------------------------------------
+--R                                      2                       2
+--R                    (a n + a)sinh(a x)  + (- a n - a)cosh(a x)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.594~~~~~$\displaystyle
+\int{\sinh^2{ax}\cosh^2{ax}}~dx$}
+$$\int{\sinh^2{ax}\cosh^2{ax}}=
+\frac{\sinh{4ax}}{32a}-\frac{x}{8}
+$$
+<<*>>=
+)clear all
+
+--S 5 of 14
+aa:=integrate(sinh(a*x)^2*cosh(a*x)^2,x)
+--R 
+--R
+--R                          3            3
+--R        cosh(a x)sinh(a x)  + cosh(a x) sinh(a x) - a x
+--R   (1)  -----------------------------------------------
+--R                               8a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.595~~~~~$\displaystyle
+\int{\frac{dx}{\sinh{ax}\cosh{ax}}}$}
+$$\int{\frac{1}{\sinh{ax}\cosh{ax}}}=
+\frac{1}{a}\ln\tanh{ax}
+$$
+<<*>>=
+)clear all
+
+--S 6 of 14
+aa:=integrate(1/(sinh(a*x)*cosh(a*x)),x)
+--R 
+--R
+--R                      2cosh(a x)                     2sinh(a x)
+--R        - log(- ---------------------) + log(- ---------------------)
+--R                sinh(a x) - cosh(a x)          sinh(a x) - cosh(a x)
+--R   (1)  -------------------------------------------------------------
+--R                                      a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.596~~~~~$\displaystyle
+\int{\frac{dx}{\sinh^2{ax}\cosh{ax}}}$}
+$$\int{\frac{1}{\sinh^2{ax}\cosh{ax}}}=
+-\frac{1}{a}\tan^{-1}\sinh{ax}-\frac{{\rm csch~}{ax}}{a}
+$$
+<<*>>=
+)clear all
+
+--S 7 of 14
+aa:=integrate(1/(sinh(a*x)^2*cos(a*x)),x)
+--R 
+--R
+--R           x
+--R         ++            1
+--I   (1)   |   -------------------- d%R
+--R        ++                      2
+--I             cos(%R a)sinh(%R a)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.597~~~~~$\displaystyle
+\int{\frac{dx}{\sinh{ax}\cosh^2{ax}}}$}
+$$\int{\frac{1}{\sinh{ax}\cosh^2{ax}}}=
+\frac{{\rm sech~}{ax}}{a}+\frac{1}{a}\ln\tanh{\frac{ax}{2}}
+$$
+<<*>>=
+)clear all
+
+--S 8 of 14
+aa:=integrate(1/(sinh(a*x)*cosh(a*x)^2),x)
+--R 
+--R
+--R   (1)
+--R                     2                                  2
+--R         (- sinh(a x)  - 2cosh(a x)sinh(a x) - cosh(a x)  - 1)
+--R      *
+--R         log(sinh(a x) + cosh(a x) + 1)
+--R     + 
+--R                   2                                  2
+--R         (sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  + 1)
+--R      *
+--R         log(sinh(a x) + cosh(a x) - 1)
+--R     + 
+--R       2sinh(a x) + 2cosh(a x)
+--R  /
+--R                2                                      2
+--R     a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  + a
+--R                                          Type: Union(Expression Integer,...)
+--E
+@
+
+\section{\cite{1}:14.598~~~~~$\displaystyle
+\int{\frac{dx}{\sinh^2{ax}\cosh^2{ax}}}$}
+$$\int{\frac{1}{\sinh^2{ax}\cosh^2{ax}}}=
+-\frac{2\coth{2ax}}{a}
+$$
+<<*>>=
+)clear all
+
+--S 9 of 14
+aa:=integrate(1/(sinh(a*x)^2*cosh(a*x)^2),x)
+--R 
+--R
+--R   (1)
+--R   -
+--R        4
+--R     /
+--R                     4                        3               2         2
+--R          a sinh(a x)  + 4a cosh(a x)sinh(a x)  + 6a cosh(a x) sinh(a x)
+--R        + 
+--R                      3                       4
+--R          4a cosh(a x) sinh(a x) + a cosh(a x)  - a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.599~~~~~$\displaystyle
+\int{\frac{\sinh^2{ax}}{\cosh{ax}}}~dx$}
+$$\int{\frac{\sinh^2{ax}}{\cosh{ax}}}~dx=
+\frac{\sinh{ax}}{a}-\frac{1}{a}\tan^{-1}\sinh{ax}
+$$
+<<*>>=
+)clear all
+
+--S 10 of 14
+aa:=integrate(sinh(a*x)^2/cosh(a*x),x)
+--R 
+--R
+--R   (1)
+--R                                                                         2
+--R       (- 4sinh(a x) - 4cosh(a x))atan(sinh(a x) + cosh(a x)) + sinh(a x)
+--R     + 
+--R                                      2
+--R       2cosh(a x)sinh(a x) + cosh(a x)  - 1
+--R  /
+--R     2a sinh(a x) + 2a cosh(a x)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.600~~~~~$\displaystyle
+\int{\frac{\cosh^2{ax}}{\sinh{ax}}}~dx$}
+$$\int{\frac{\cosh^2{ax}}{\sinh{ax}}}=
+\frac{\cosh{ax}}{a}+\frac{1}{a}\ln\tanh{\frac{ax}{2}}
+$$
+<<*>>=
+)clear all
+
+--S 11 of 14
+aa:=integrate(cosh(a*x)^2/sinh(a*x),x)
+--R 
+--R
+--R   (1)
+--R       (- 2sinh(a x) - 2cosh(a x))log(sinh(a x) + cosh(a x) + 1)
+--R     + 
+--R                                                                          2
+--R       (2sinh(a x) + 2cosh(a x))log(sinh(a x) + cosh(a x) - 1) + sinh(a x)
+--R     + 
+--R                                      2
+--R       2cosh(a x)sinh(a x) + cosh(a x)  + 1
+--R  /
+--R     2a sinh(a x) + 2a cosh(a x)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.601~~~~~$\displaystyle
+\int{\frac{dx}{\cosh{ax}(1+\sinh{ax})}}$}
+$$\int{\frac{1}{\cosh{ax}(1+\sinh{ax})}}=
+\frac{1}{2a}\ln\left(\frac{1+\sinh{ax}}{\cosh{ax}}\right)
++\frac{1}{a}\tan^{-1}{e^{ax}}
+$$
+<<*>>=
+)clear all
+
+--S 12 of 14
+aa:=integrate(1/(cosh(a*x)*(1+sinh(a*x))),x)
+--R 
+--R
+--R   (1)
+--R                     2cosh(a x)                - 2sinh(a x) - 2
+--R       - log(- ---------------------) + log(---------------------)
+--R               sinh(a x) - cosh(a x)        sinh(a x) - cosh(a x)
+--R     + 
+--R       2atan(sinh(a x) + cosh(a x))
+--R  /
+--R     2a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.602~~~~~$\displaystyle
+\int{\frac{dx}{\sinh{ax}(\cosh{ax}+1)}}$}
+$$\int{\frac{1}{\sinh{ax}(\cosh{ax}+1)}}=
+\frac{1}{2a}\ln\tanh\frac{ax}{2}+\frac{1}{2a(\cosh{ax}+1)}
+$$
+<<*>>=
+)clear all
+
+--S 13 of 14
+aa:=integrate(1/(sinh(a*x)*(cosh(a*x)+1)),x)
+--R 
+--R
+--R   (1)
+--R                      2                                          2
+--R           - sinh(a x)  + (- 2cosh(a x) - 2)sinh(a x) - cosh(a x)  - 2cosh(a x)
+--R         + 
+--R           - 1
+--R      *
+--R         log(sinh(a x) + cosh(a x) + 1)
+--R     + 
+--R                   2                                        2
+--R         (sinh(a x)  + (2cosh(a x) + 2)sinh(a x) + cosh(a x)  + 2cosh(a x) + 1)
+--R      *
+--R         log(sinh(a x) + cosh(a x) - 1)
+--R     + 
+--R       2sinh(a x) + 2cosh(a x)
+--R  /
+--R                   2                                              2
+--R       2a sinh(a x)  + (4a cosh(a x) + 4a)sinh(a x) + 2a cosh(a x)
+--R     + 
+--R       4a cosh(a x) + 2a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.603~~~~~$\displaystyle
+\int{\frac{dx}{\sinh{ax}(\cosh{ax}-1)}}$}
+$$\int{\frac{1}{\sinh{ax}(\cosh{ax}-1)}}=
+-\frac{1}{2a}\ln\tanh\frac{ax}{2}-\frac{1}{2a(cosh{ax}-1)}
+$$
+<<*>>=
+)clear all
+
+--S 14 of 14
+aa:=integrate(1/(sinh(a*x)*(cosh(a*x)-1)),x)
+--R 
+--R
+--R   (1)
+--R                   2                                        2
+--R         (sinh(a x)  + (2cosh(a x) - 2)sinh(a x) + cosh(a x)  - 2cosh(a x) + 1)
+--R      *
+--R         log(sinh(a x) + cosh(a x) + 1)
+--R     + 
+--R                      2                                          2
+--R           - sinh(a x)  + (- 2cosh(a x) + 2)sinh(a x) - cosh(a x)  + 2cosh(a x)
+--R         + 
+--R           - 1
+--R      *
+--R         log(sinh(a x) + cosh(a x) - 1)
+--R     + 
+--R       - 2sinh(a x) - 2cosh(a x)
+--R  /
+--R                   2                                              2
+--R       2a sinh(a x)  + (4a cosh(a x) - 4a)sinh(a x) + 2a cosh(a x)
+--R     + 
+--R       - 4a cosh(a x) + 2a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+)spool
+)lisp (bye)
+@
+
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} Spiegel, Murray R.
+{\sl Mathematical Handbook of Formulas and Tables}\\
+Schaum's Outline Series McGraw-Hill 1968 pp89-90
+\end{thebibliography}
+\end{document}
diff --git a/src/input/schaum30.input.pamphlet b/src/input/schaum30.input.pamphlet
new file mode 100644
index 0000000..0e1aaf4
--- /dev/null
+++ b/src/input/schaum30.input.pamphlet
@@ -0,0 +1,286 @@
+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/input schaum30.input}
+\author{Timothy Daly}
+\maketitle
+\eject
+\tableofcontents
+\eject
+\section{\cite{1}:14.604~~~~~$\displaystyle
+\int{\tanh{ax}}~dx$}
+$$\int{\tanh{ax}}=
+\frac{1}{a}\ln\cosh{ax}
+$$
+<<*>>=
+)spool schaum30.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1 of 11
+aa:=integrate(tanh(a*x),x)
+--R 
+--R
+--R                    2cosh(a x)
+--R        log(- ---------------------) - a x
+--R              sinh(a x) - cosh(a x)
+--R   (1)  ----------------------------------
+--R                         a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.605~~~~~$\displaystyle
+\int{\tanh^2{ax}}~dx$}
+$$\int{\tanh^2{ax}}=
+x-\frac{\tanh{ax}}{a}
+$$
+<<*>>=
+)clear all
+
+--S 2 of 11
+aa:=integrate(tanh(a*x)^2,x)
+--R 
+--R
+--R        - sinh(a x) + (a x + 1)cosh(a x)
+--R   (1)  --------------------------------
+--R                   a cosh(a x)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.606~~~~~$\displaystyle
+\int{\tanh^3{ax}}~dx$}
+$$\int{\tanh^3{ax}}=
+\frac{1}{a}\ln\cosh{ax}-\frac{\tanh^2{ax}}{2a}
+$$
+<<*>>=
+)clear all
+
+--S 3 of 11
+aa:=integrate(tanh(a*x)^3,x)
+--R 
+--R
+--R   (1)
+--R                    4                      3              2              2
+--R           sinh(a x)  + 4cosh(a x)sinh(a x)  + (6cosh(a x)  + 2)sinh(a x)
+--R         + 
+--R                      3                                   4             2
+--R           (4cosh(a x)  + 4cosh(a x))sinh(a x) + cosh(a x)  + 2cosh(a x)  + 1
+--R      *
+--R                     2cosh(a x)
+--R         log(- ---------------------)
+--R               sinh(a x) - cosh(a x)
+--R     + 
+--R                      4                          3
+--R       - a x sinh(a x)  - 4a x cosh(a x)sinh(a x)
+--R     + 
+--R                        2                     2
+--R       (- 6a x cosh(a x)  - 2a x + 2)sinh(a x)
+--R     + 
+--R                        3                                                  4
+--R       (- 4a x cosh(a x)  + (- 4a x + 4)cosh(a x))sinh(a x) - a x cosh(a x)
+--R     + 
+--R                            2
+--R       (- 2a x + 2)cosh(a x)  - a x
+--R  /
+--R                  4                        3                2               2
+--R       a sinh(a x)  + 4a cosh(a x)sinh(a x)  + (6a cosh(a x)  + 2a)sinh(a x)
+--R     + 
+--R                  3                                       4               2
+--R     (4a cosh(a x)  + 4a cosh(a x))sinh(a x) + a cosh(a x)  + 2a cosh(a x)  + a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.607~~~~~$\displaystyle
+\int{\tanh^n{ax}{{\rm ~sech}^2{ax}}}~dx$}
+$$\int{\tanh^n{ax}{{\rm ~sech}^2{ax}}}=
+\frac{\tanh^{n+1}{ax}}{(n+1)a}
+$$
+<<*>>=
+)clear all
+
+--S 4 of 11
+aa:=integrate(tanh(a*x)^n*sech(a*x)^2,x)
+--R 
+--R
+--R                            sinh(a x)                         sinh(a x)
+--R        sinh(a x)sinh(n log(---------)) + sinh(a x)cosh(n log(---------))
+--R                            cosh(a x)                         cosh(a x)
+--R   (1)  -----------------------------------------------------------------
+--R                                (a n + a)cosh(a x)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.608~~~~~$\displaystyle
+\int{\frac{{\rm sech}^2{ax}}{\tanh{ax}}}~dx$}
+$$\int{\frac{{\rm sech}^2{ax}}{\tanh{ax}}}=
+\frac{1}{a}\ln\tanh{ax}
+$$
+<<*>>=
+)clear all
+
+--S 5 of 11
+aa:=integrate(sech(a*x)^2/tanh(a*x),x)
+--R 
+--R
+--R                      2cosh(a x)                     2sinh(a x)
+--R        - log(- ---------------------) + log(- ---------------------)
+--R                sinh(a x) - cosh(a x)          sinh(a x) - cosh(a x)
+--R   (1)  -------------------------------------------------------------
+--R                                      a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.609~~~~~$\displaystyle
+\int{\frac{dx}{\tanh{ax}}}~dx$}
+$$\int{\frac{1}{\tanh{ax}}}=
+\frac{1}{a}\ln\sinh{ax}
+$$
+<<*>>=
+)clear all
+
+--S 6 of 11
+aa:=integrate(1/tanh(a*x),x)
+--R 
+--R
+--R                    2sinh(a x)
+--R        log(- ---------------------) - a x
+--R              sinh(a x) - cosh(a x)
+--R   (1)  ----------------------------------
+--R                         a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.610~~~~~$\displaystyle
+\int{x\tanh{ax}}~dx$}
+$$\int{x\tanh{ax}}=
+\frac{1}{a^2}\left\{
+\frac{(ax)^3}{3}-\frac{(ax)^5}{15}+\frac{2(ax)^7}{105}-\cdots
+\frac{(-1)^{n-1}2^{2n}(2^{2n}-1)B_n(ax)^{2n+1}}{(2n+1)!}+\cdots\right\}
+$$
+<<*>>=
+)clear all
+
+--S 7 of 11
+aa:=integrate(x*tanh(a*x),x)
+--R 
+--R
+--R           x
+--R         ++
+--I   (1)   |   %O tanh(%O a)d%O
+--R        ++
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.611~~~~~$\displaystyle
+\int{x\tanh^2{ax}}~dx$}
+$$\int{x\tanh^2{ax}}=
+\frac{x^2}{2}-\frac{x\tanh{ax}}{a}+\frac{1}{a^2}\ln\cosh{ax}
+$$
+<<*>>=
+)clear all
+
+--S 8 of 11
+aa:=integrate(x*tanh(a*x)^2,x)
+--R 
+--R
+--R   (1)
+--R                    2                                   2
+--R         (2sinh(a x)  + 4cosh(a x)sinh(a x) + 2cosh(a x)  + 2)
+--R      *
+--R                     2cosh(a x)
+--R         log(- ---------------------)
+--R               sinh(a x) - cosh(a x)
+--R     + 
+--R         2 2                 2      2 2
+--R       (a x  - 4a x)sinh(a x)  + (2a x  - 8a x)cosh(a x)sinh(a x)
+--R     + 
+--R         2 2                 2    2 2
+--R       (a x  - 4a x)cosh(a x)  + a x
+--R  /
+--R       2         2     2                       2         2     2
+--R     2a sinh(a x)  + 4a cosh(a x)sinh(a x) + 2a cosh(a x)  + 2a
+--R                                          Type: Union(Expression Integer,...)
+--E
+@
+
+\section{\cite{1}:14.612~~~~~$\displaystyle
+\int{\frac{\tanh{ax}}{x}}~dx$}
+$$\int{\frac{\tanh{ax}}{x}}=
+ax-\frac{(ax)^3}{9}+\frac{2(ax)^5}{75}-\cdots
+\frac{(-1)^{n-1}2^{2n}(2^{2n}-1)B_n(ax)^{2n-1}}{(2n-1)(2n)!}+\cdots
+$$
+<<*>>=
+)clear all
+
+--S 9 of 11
+aa:=integrate(tanh(a*x)/x,x)
+--R 
+--R
+--R           x
+--I         ++  tanh(%O a)
+--I   (1)   |   ---------- d%O
+--I        ++       %O
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.613~~~~~$\displaystyle
+\int{\frac{dx}{p+q\tanh{ax}}}~dx$}
+$$\int{\frac{1}{p+q\tanh{ax}}}=
+\frac{px}{p^2-q^2}-\frac{q}{a(p^2-q^2)}\ln(q\sinh{ax}+p\cosh{ax})
+$$
+<<*>>=
+)clear all
+
+--S 10 of 11
+aa:=integrate(1/(p+q*tanh(a*x)),x)
+--R 
+--R
+--R              - 2q sinh(a x) - 2p cosh(a x)
+--R        q log(-----------------------------) + (- a q - a p)x
+--R                  sinh(a x) - cosh(a x)
+--R   (1)  -----------------------------------------------------
+--R                                2      2
+--R                             a q  - a p
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.614~~~~~$\displaystyle
+\int{\tanh^n{ax}}~dx$}
+$$\int{\tanh^n{ax}}=
+\frac{-\tanh^{n-1}{ax}}{a(n-1)}+\int{\tanh^{n-2}{ax}}
+$$
+<<*>>=
+)clear all
+
+--S 11 of 11
+aa:=integrate(tanh(a*x)^n,x)
+--R 
+--R
+--R           x
+--R         ++            n
+--I   (1)   |   tanh(%O a) d%O
+--R        ++
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+)spool
+)lisp (bye)
+@
+
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} Spiegel, Murray R.
+{\sl Mathematical Handbook of Formulas and Tables}\\
+Schaum's Outline Series McGraw-Hill 1968 pp89-90
+\end{thebibliography}
+\end{document}



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The last of the indefinite integrals
=======================================================================
diff --git a/changelog b/changelog
index 26d39fa..d3ccbf9 100644
--- a/changelog
+++ b/changelog
@@ -1,3 +1,8 @@
+20080414 tpd src/input/Makefile add integration regression testing	
+20080414 tpd src/input/schaum34.input integrals of csch(ax)
+20080414 tpd src/input/schaum33.input integrals of csch(ax)
+20080414 tpd src/input/schaum32.input integrals of sech(ax)
+20080414 tpd src/input/schaum31.input integrals of coth(ax)
 20080413 tpd src/input/Makefile add integration regression testing	
 20080413 tpd src/input/schaum30.input integrals of tanh(ax)
 20080413 tpd src/input/schaum29.input integrals of sinh(ax) and cosh(ax)
diff --git a/src/input/Makefile.pamphlet b/src/input/Makefile.pamphlet
index 57ff1e9..fdf2fff 100644
--- a/src/input/Makefile.pamphlet
+++ b/src/input/Makefile.pamphlet
@@ -362,7 +362,8 @@ REGRES= algaggr.regress algbrbf.regress  algfacob.regress alist.regress  \
     schaum17.regress  schaum18.regress schaum19.regress schaum20.regress \
     schaum21.regress  schaum22.regress schaum23.regress schaum24.regress \
     schaum25.regress  schaum26.regress schaum27.regress schaum28.regress \
-    schaum29.regress  schaum30.regress \
+    schaum29.regress  schaum30.regress schaum31.regress schaum32.regress \
+    schaum33.regress  schaum34.regress \
     scherk.regress    scope.regress    seccsc.regress \
     segbind.regress   seg.regress \
     series2.regress   series.regress   sersolve.regress set.regress \
@@ -644,7 +645,8 @@ FILES= ${OUT}/algaggr.input  ${OUT}/algbrbf.input    ${OUT}/algfacob.input \
        ${OUT}/schaum20.input ${OUT}/schaum21.input   ${OUT}/schaum22.input \
        ${OUT}/schaum23.input ${OUT}/schaum24.input   ${OUT}/schaum25.input \
        ${OUT}/schaum26.input ${OUT}/schaum27.input   ${OUT}/schaum28.input \
-       ${OUT}/schaum29.input ${OUT}/schaum30.input \
+       ${OUT}/schaum29.input ${OUT}/schaum30.input   ${OUT}/schaum31.input \
+       ${OUT}/schaum32.input ${OUT}/schaum33.input   ${OUT}/schaum34.input \
        ${OUT}/saddle.input \
        ${OUT}/scherk.input   ${OUT}/scope.input      ${OUT}/seccsc.input \
        ${OUT}/segbind.input  ${OUT}/seg.input        ${OUT}/series2.input \
@@ -958,6 +960,8 @@ DOCFILES= \
   ${DOC}/schaum25.input.dvi    ${DOC}/schaum26.input.dvi \
   ${DOC}/schaum27.input.dvi    ${DOC}/schaum28.input.dvi \
   ${DOC}/schaum29.input.dvi    ${DOC}/schaum30.input.dvi \
+  ${DOC}/schaum31.input.dvi    ${DOC}/schaum32.input.dvi \
+  ${DOC}/schaum33.input.dvi    ${DOC}/schaum34.input.dvi \
   ${DOC}/s01eaf.input.dvi      ${DOC}/s13aaf.input.dvi     \
   ${DOC}/s13acf.input.dvi      ${DOC}/s13adf.input.dvi     \
   ${DOC}/s14aaf.input.dvi      ${DOC}/s14abf.input.dvi     \
diff --git a/src/input/schaum31.input.pamphlet b/src/input/schaum31.input.pamphlet
new file mode 100644
index 0000000..3e81bf2
--- /dev/null
+++ b/src/input/schaum31.input.pamphlet
@@ -0,0 +1,286 @@
+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/input schaum31.input}
+\author{Timothy Daly}
+\maketitle
+\eject
+\tableofcontents
+\eject
+\section{\cite{1}:14.615~~~~~$\displaystyle
+\int{\coth{ax}}~dx$}
+$$\int{\coth{ax}}=
+\frac{1}{a}\ln\sinh{ax}
+$$
+<<*>>=
+)spool schaum31.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1 of 11
+aa:=integrate(coth(a*x),x)
+--R 
+--R
+--R                    2sinh(a x)
+--R        log(- ---------------------) - a x
+--R              sinh(a x) - cosh(a x)
+--R   (1)  ----------------------------------
+--R                         a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.616~~~~~$\displaystyle
+\int{\coth^2{ax}}~dx$}
+$$\int{\coth^2{ax}}=
+x-\frac{\coth{ax}}{a}
+$$
+<<*>>=
+)clear all
+
+--S 2 of 11
+aa:=integrate(coth(a*x)^2,x)
+--R 
+--R
+--R        (a x + 1)sinh(a x) - cosh(a x)
+--R   (1)  ------------------------------
+--R                  a sinh(a x)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.617~~~~~$\displaystyle
+\int{\coth^3{ax}}~dx$}
+$$\int{\coth^3{ax}}=
+\frac{1}{a}\ln\sinh{ax}-\frac{\coth^2{ax}}{2a}
+$$
+<<*>>=
+)clear all
+
+--S 3 of 11
+aa:=integrate(coth(a*x)^3,x)
+--R 
+--R
+--R   (1)
+--R                    4                      3              2              2
+--R           sinh(a x)  + 4cosh(a x)sinh(a x)  + (6cosh(a x)  - 2)sinh(a x)
+--R         + 
+--R                      3                                   4             2
+--R           (4cosh(a x)  - 4cosh(a x))sinh(a x) + cosh(a x)  - 2cosh(a x)  + 1
+--R      *
+--R                     2sinh(a x)
+--R         log(- ---------------------)
+--R               sinh(a x) - cosh(a x)
+--R     + 
+--R                      4                          3
+--R       - a x sinh(a x)  - 4a x cosh(a x)sinh(a x)
+--R     + 
+--R                        2                     2
+--R       (- 6a x cosh(a x)  + 2a x - 2)sinh(a x)
+--R     + 
+--R                        3                                                4
+--R       (- 4a x cosh(a x)  + (4a x - 4)cosh(a x))sinh(a x) - a x cosh(a x)
+--R     + 
+--R                          2
+--R       (2a x - 2)cosh(a x)  - a x
+--R  /
+--R                  4                        3                2               2
+--R       a sinh(a x)  + 4a cosh(a x)sinh(a x)  + (6a cosh(a x)  - 2a)sinh(a x)
+--R     + 
+--R                  3                                       4               2
+--R     (4a cosh(a x)  - 4a cosh(a x))sinh(a x) + a cosh(a x)  - 2a cosh(a x)  + a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.618~~~~~$\displaystyle
+\int{\coth^n{ax}{{\rm ~csch}^2{ax}}}~dx$}
+$$\int{\coth^n{ax}{{\rm ~csch}^2{ax}}}=
+-\frac{\coth^{n+1}{ax}}{(n+1)a}
+$$
+<<*>>=
+)clear all
+
+--S 4 of 11
+aa:=integrate(coth(a*x)^n*csch(a*x)^2,x)
+--R 
+--R
+--R                              cosh(a x)                         cosh(a x)
+--R        - cosh(a x)sinh(n log(---------)) - cosh(a x)cosh(n log(---------))
+--R                              sinh(a x)                         sinh(a x)
+--R   (1)  -------------------------------------------------------------------
+--R                                 (a n + a)sinh(a x)
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.619~~~~~$\displaystyle
+\int{\frac{{\rm csch}^2{ax}}{\coth{ax}}}~dx$}
+$$\int{\frac{{\rm csch}^2{ax}}{\coth{ax}}}=
+-\frac{1}{a}\ln\coth{ax}
+$$
+<<*>>=
+)clear all
+
+--S 5 of 11
+aa:=integrate(csch(a*x)^2/coth(a*x),x)
+--R 
+--R
+--R                      2cosh(a x)                     2sinh(a x)
+--R        - log(- ---------------------) + log(- ---------------------)
+--R                sinh(a x) - cosh(a x)          sinh(a x) - cosh(a x)
+--R   (1)  -------------------------------------------------------------
+--R                                      a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.620~~~~~$\displaystyle
+\int{\frac{dx}{\coth{ax}}}~dx$}
+$$\int{\frac{1}{\coth{ax}}}=
+\frac{1}{a}\ln\cosh{ax}
+$$
+<<*>>=
+)clear all
+
+--S 6 of 11
+aa:=integrate(1/coth(a*x),x)
+--R 
+--R
+--R                    2cosh(a x)
+--R        log(- ---------------------) - a x
+--R              sinh(a x) - cosh(a x)
+--R   (1)  ----------------------------------
+--R                         a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.621~~~~~$\displaystyle
+\int{x\coth{ax}}~dx$}
+$$\int{x\coth{ax}}=
+\frac{1}{a^2}\left\{
+ax+\frac{(ax)^3}{9}-\frac{(ax)^5}{225}+\cdots
+\frac{(-1)^{n-1}2^{2n}B_n(ax)^{2n+1}}{(2n+1)!}+\cdots\right\}
+$$
+<<*>>=
+)clear all
+
+--S 7 of 11
+aa:=integrate(x*coth(a*x),x)
+--R 
+--R
+--R           x
+--R         ++
+--I   (1)   |   %O coth(%O a)d%O
+--R        ++
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.622~~~~~$\displaystyle
+\int{x\coth^2{ax}}~dx$}
+$$\int{x\coth^2{ax}}=
+\frac{x^2}{2}-\frac{x\coth{ax}}{a}+\frac{1}{a^2}\ln\sinh{ax}
+$$
+<<*>>=
+)clear all
+
+--S 8 of 11
+aa:=integrate(x*coth(a*x)^2,x)
+--R 
+--R
+--R   (1)
+--R                    2                                   2
+--R         (2sinh(a x)  + 4cosh(a x)sinh(a x) + 2cosh(a x)  - 2)
+--R      *
+--R                     2sinh(a x)
+--R         log(- ---------------------)
+--R               sinh(a x) - cosh(a x)
+--R     + 
+--R         2 2                 2      2 2
+--R       (a x  - 4a x)sinh(a x)  + (2a x  - 8a x)cosh(a x)sinh(a x)
+--R     + 
+--R         2 2                 2    2 2
+--R       (a x  - 4a x)cosh(a x)  - a x
+--R  /
+--R       2         2     2                       2         2     2
+--R     2a sinh(a x)  + 4a cosh(a x)sinh(a x) + 2a cosh(a x)  - 2a
+--R                                          Type: Union(Expression Integer,...)
+--E
+@
+
+\section{\cite{1}:14.623~~~~~$\displaystyle
+\int{\frac{\coth{ax}}{x}}~dx$}
+$$\int{\frac{\coth{ax}}{x}}=
+-\frac{1}{ax}+\frac{(ax)}{3}-\frac{(ax)^3}{135}+\cdots
+\frac{(-1)^{n}2^{2n}B_n(ax)^{2n-1}}{(2n-1)(2n)!}+\cdots
+$$
+<<*>>=
+)clear all
+
+--S 9 of 11
+aa:=integrate(coth(a*x)/x,x)
+--R 
+--R
+--R           x
+--I         ++  coth(%O a)
+--I   (1)   |   ---------- d%O
+--I        ++       %O
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.624~~~~~$\displaystyle
+\int{\frac{dx}{p+q\coth{ax}}}~dx$}
+$$\int{\frac{1}{p+q\coth{ax}}}=
+\frac{px}{p^2-q^2}-\frac{q}{a(p^2-q^2)}\ln(p\sinh{ax}+q\cosh{ax})
+$$
+<<*>>=
+)clear all
+
+--S 10 of 11
+aa:=integrate(1/(p+q*coth(a*x)),x)
+--R 
+--R
+--R              - 2p sinh(a x) - 2q cosh(a x)
+--R        q log(-----------------------------) + (- a q - a p)x
+--R                  sinh(a x) - cosh(a x)
+--R   (1)  -----------------------------------------------------
+--R                                2      2
+--R                             a q  - a p
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.625~~~~~$\displaystyle
+\int{\coth^n{ax}}~dx$}
+$$\int{\coth^n{ax}}=
+-\frac{\coth^{n-1}{ax}}{a(n-1)}+\int{\coth^{n-1}{ax}}
+$$
+<<*>>=
+)clear all
+
+--S 11 of 11
+aa:=integrate(coth(a*x)^n,x)
+--R 
+--R
+--R           x
+--R         ++            n
+--I   (1)   |   coth(%O a) d%O
+--R        ++
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+)spool
+)lisp (bye)
+@
+
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} Spiegel, Murray R.
+{\sl Mathematical Handbook of Formulas and Tables}\\
+Schaum's Outline Series McGraw-Hill 1968 pp90-91
+\end{thebibliography}
+\end{document}
diff --git a/src/input/schaum32.input.pamphlet b/src/input/schaum32.input.pamphlet
new file mode 100644
index 0000000..085ddf0
--- /dev/null
+++ b/src/input/schaum32.input.pamphlet
@@ -0,0 +1,294 @@
+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/input schaum32.input}
+\author{Timothy Daly}
+\maketitle
+\eject
+\tableofcontents
+\eject
+\section{\cite{1}:14.626~~~~~$\displaystyle
+\int{{\rm sech~}{ax}}~dx$}
+$$\int{{\rm sech~}{ax}}=
+\frac{2}{a}\tanh^{-1}{e^{ax}}
+$$
+<<*>>=
+)spool schaum32.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1 of 10
+aa:=integrate(sech(a*x),x)
+--R 
+--R
+--R        2atan(sinh(a x) + cosh(a x))
+--R   (1)  ----------------------------
+--R                      a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.627~~~~~$\displaystyle
+\int{{\rm sech}^2~{ax}}~dx$}
+$$\int{{\rm sech}^2~{ax}}=
+\frac{\tanh{ax}}{a}
+$$
+<<*>>=
+)clear all
+
+--S 2 of 10
+aa:=integrate(sech(a*x)^2,x)
+--R 
+--R
+--R                                     2
+--R   (1)  - -------------------------------------------------------
+--R                     2                                      2
+--R          a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  + a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.628~~~~~$\displaystyle
+\int{{\rm sech}^3~{ax}}~dx$}
+$$\int{{\rm sech}^3~{ax}}=
+\frac{{\rm sech}~{ax}~\tanh{ax}}{2a}+\frac{1}{2a}\tan^{-1}{\rm ~sech~}{ax}
+$$
+<<*>>=
+)clear all
+
+--S 3 of 10
+aa:=integrate(sech(a*x)^3,x)
+--R 
+--R
+--R   (1)
+--R                    4                      3              2              2
+--R           sinh(a x)  + 4cosh(a x)sinh(a x)  + (6cosh(a x)  + 2)sinh(a x)
+--R         + 
+--R                      3                                   4             2
+--R           (4cosh(a x)  + 4cosh(a x))sinh(a x) + cosh(a x)  + 2cosh(a x)  + 1
+--R      *
+--R         atan(sinh(a x) + cosh(a x))
+--R     + 
+--R                3                      2              2
+--R       sinh(a x)  + 3cosh(a x)sinh(a x)  + (3cosh(a x)  - 1)sinh(a x)
+--R     + 
+--R                3
+--R       cosh(a x)  - cosh(a x)
+--R  /
+--R                  4                        3                2               2
+--R       a sinh(a x)  + 4a cosh(a x)sinh(a x)  + (6a cosh(a x)  + 2a)sinh(a x)
+--R     + 
+--R                  3                                       4               2
+--R     (4a cosh(a x)  + 4a cosh(a x))sinh(a x) + a cosh(a x)  + 2a cosh(a x)  + a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.629~~~~~$\displaystyle
+\int{{\rm sech}^n~{ax}~{\tanh{ax}}}~dx$}
+$$\int{{\rm sech~}^n{ax}~{\tanh{ax}}}=
+-\frac{{\rm sech~}^{n}{ax}}{na}
+$$
+<<*>>=
+)clear all
+
+--S 4 of 10
+aa:=integrate(sech(a*x)^n*tanh(a*x),x)
+--R 
+--R
+--R   (1)
+--R                                 2sinh(a x) + 2cosh(a x)
+--R       - sinh(n log(-------------------------------------------------))
+--R                             2                                  2
+--R                    sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  + 1
+--R     + 
+--R                                 2sinh(a x) + 2cosh(a x)
+--R       - cosh(n log(-------------------------------------------------))
+--R                             2                                  2
+--R                    sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  + 1
+--R  /
+--R     a n
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.630~~~~~$\displaystyle
+\int{\frac{dx}{{\rm sech~}{ax}}}~dx$}
+$$\int{\frac{1}{{\rm sech~}{ax}}}=
+\frac{{\rm sech}~{ax}}{a}
+$$
+<<*>>=
+)clear all
+
+--S 5 of 10
+aa:=integrate(1/sech(a*x),x)
+--R 
+--R
+--R        sinh(a x)
+--R   (1)  ---------
+--R            a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.631~~~~~$\displaystyle
+\int{x{\rm ~sech~}{ax}}~dx$}
+$$\int{x{\rm ~sech~}{ax}}=
+\frac{1}{a^2}\left\{
+\frac{(ax)^2}{2}-\frac{(ax)^4}{8}+\frac{5(ax)^6}{144}+\cdots
+\frac{(-1)^{n}E_n(ax)^{2n+2}}{(2n+2)(2n)!}+\cdots\right\}
+$$
+<<*>>=
+)clear all
+
+--S 6 of 10
+aa:=integrate(x*sech(a*x),x)
+--R 
+--R
+--R           x
+--R         ++
+--I   (1)   |   %O sech(%O a)d%O
+--R        ++
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.632~~~~~$\displaystyle
+\int{x~{\rm sech}^2~{ax}}~dx$}
+$$\int{x~{\rm sech}^2~{ax}}=
+\frac{x\tanh{ax}}{a}-\frac{1}{a^2}\ln\cosh{ax}
+$$
+<<*>>=
+)clear all
+
+--S 7 of 10
+aa:=integrate(x*sech(a*x)^2,x)
+--R 
+--R
+--R   (1)
+--R                     2                                  2
+--R         (- sinh(a x)  - 2cosh(a x)sinh(a x) - cosh(a x)  - 1)
+--R      *
+--R                     2cosh(a x)
+--R         log(- ---------------------)
+--R               sinh(a x) - cosh(a x)
+--R     + 
+--R                     2                                           2
+--R       2a x sinh(a x)  + 4a x cosh(a x)sinh(a x) + 2a x cosh(a x)
+--R  /
+--R      2         2     2                      2         2    2
+--R     a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  + a
+--R                                          Type: Union(Expression Integer,...)
+--E
+@
+
+\section{\cite{1}:14.633~~~~~$\displaystyle
+\int{\frac{{\rm sech~}{ax}}{x}}~dx$}
+$$\int{\frac{{\rm sech~}{ax}}{x}}=
+\ln{x}-\frac{(ax)^2}{4}+\frac{5(ax)^4}{96}-\frac{61(ax)^6}{4320}+\cdots
+\frac{(-1)^{n}E_n(ax)^{2n}}{2n(2n)!}+\cdots
+$$
+<<*>>=
+)clear all
+
+--S 8 of 10
+aa:=integrate(sech(a*x)/x,x)
+--R 
+--R
+--R           x
+--I         ++  sech(%O a)
+--I   (1)   |   ---------- d%O
+--I        ++       %O
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.634~~~~~$\displaystyle
+\int{\frac{dx}{q+p{\rm ~sech~}{ax}}}~dx$}
+$$\int{\frac{1}{q+p{\rm ~sech~}{ax}}}=
+\frac{x}{q}-\frac{p}{q}\int{\frac{dx}{p+q\cosh{ax}}}
+$$
+<<*>>=
+)clear all
+
+--S 9 of 10
+aa:=integrate(1/(q+p*sech(a*x)),x)
+--R 
+--R
+--R   (1)
+--R   [
+--R           p
+--R        *
+--R           log
+--R                       2         2      2
+--R                      q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x)
+--R                    + 
+--R                       2         2                     2     2
+--R                      q cosh(a x)  + 2p q cosh(a x) - q  + 2p
+--R                 *
+--R                     +---------+
+--R                     |   2    2
+--R                    \|- q  + p
+--R                + 
+--R                     3     2                   3     2                  2     3
+--R                (- 2q  + 2p q)sinh(a x) + (- 2q  + 2p q)cosh(a x) - 2p q  + 2p
+--R             /
+--R                             2                                             2
+--R                  q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
+--R                + 
+--R                  2p cosh(a x) + q
+--R       + 
+--R             +---------+
+--R             |   2    2
+--R         a x\|- q  + p
+--R    /
+--R           +---------+
+--R           |   2    2
+--R       a q\|- q  + p
+--R     ,
+--R                                              +-------+
+--R                                              | 2    2         +-------+
+--R              (q sinh(a x) + q cosh(a x) + p)\|q  - p          | 2    2
+--R    - 2p atan(-----------------------------------------) + a x\|q  - p
+--R                                2    2
+--R                               q  - p
+--R    --------------------------------------------------------------------]
+--R                                    +-------+
+--R                                    | 2    2
+--R                                a q\|q  - p
+--R                                     Type: Union(List Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.635~~~~~$\displaystyle
+\int{{\rm sech}^n~{ax}}~dx$}
+$$\int{{\rm sech}^n~{ax}}=
+\frac{{\rm sech}^{n-2}~{ax}~\tanh{ax}}{a(n-1)}
++\frac{n-2}{n-1}\int{{\rm sech}^{n-2}~{ax}}
+$$
+<<*>>=
+)clear all
+
+--S 10 of 10
+aa:=integrate(sech(a*x)^n,x)
+--R 
+--R
+--R           x
+--R         ++            n
+--I   (1)   |   sech(%O a) d%O
+--R        ++
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+)spool
+)lisp (bye)
+@
+
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} Spiegel, Murray R.
+{\sl Mathematical Handbook of Formulas and Tables}\\
+Schaum's Outline Series McGraw-Hill 1968 p91
+\end{thebibliography}
+\end{document}
diff --git a/src/input/schaum33.input.pamphlet b/src/input/schaum33.input.pamphlet
new file mode 100644
index 0000000..c5ee6a2
--- /dev/null
+++ b/src/input/schaum33.input.pamphlet
@@ -0,0 +1,292 @@
+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/input schaum33.input}
+\author{Timothy Daly}
+\maketitle
+\eject
+\tableofcontents
+\eject
+\section{\cite{1}:14.636~~~~~$\displaystyle
+\int{{\rm csch~}{ax}}~dx$}
+$$\int{{\rm csch~}{ax}}=
+\frac{1}{a}\ln\tanh{\frac{ax}{2}}
+$$
+<<*>>=
+)spool schaum33.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1 of 10
+aa:=integrate(csch(a*x),x)
+--R 
+--R
+--R        - log(sinh(a x) + cosh(a x) + 1) + log(sinh(a x) + cosh(a x) - 1)
+--R   (1)  -----------------------------------------------------------------
+--R                                        a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.637~~~~~$\displaystyle
+\int{{\rm csch}^2~{ax}}~dx$}
+$$\int{{\rm csch}^2~{ax}}=
+-\frac{\coth{ax}}{a}
+$$
+<<*>>=
+)clear all
+
+--S 2 of 10
+aa:=integrate(csch(a*x)^2,x)
+--R 
+--R
+--R                                     2
+--R   (1)  - -------------------------------------------------------
+--R                     2                                      2
+--R          a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  - a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.638~~~~~$\displaystyle
+\int{{\rm csch}^3~{ax}}~dx$}
+$$\int{{\rm csch}^3~{ax}}=
+-\frac{{\rm csch~}{ax}\coth{ax}}{2a}-\frac{1}{2a}\ln\tanh\frac{ax}{2}
+$$
+<<*>>=
+)clear all
+
+--S 3 of 10
+aa:=integrate(csch(a*x)^3,x)
+--R 
+--R
+--R   (1)
+--R                    4                      3              2              2
+--R           sinh(a x)  + 4cosh(a x)sinh(a x)  + (6cosh(a x)  - 2)sinh(a x)
+--R         + 
+--R                      3                                   4             2
+--R           (4cosh(a x)  - 4cosh(a x))sinh(a x) + cosh(a x)  - 2cosh(a x)  + 1
+--R      *
+--R         log(sinh(a x) + cosh(a x) + 1)
+--R     + 
+--R                      4                      3                2              2
+--R           - sinh(a x)  - 4cosh(a x)sinh(a x)  + (- 6cosh(a x)  + 2)sinh(a x)
+--R         + 
+--R                        3                                   4             2
+--R           (- 4cosh(a x)  + 4cosh(a x))sinh(a x) - cosh(a x)  + 2cosh(a x)  - 1
+--R      *
+--R         log(sinh(a x) + cosh(a x) - 1)
+--R     + 
+--R                   3                      2                2
+--R       - 2sinh(a x)  - 6cosh(a x)sinh(a x)  + (- 6cosh(a x)  - 2)sinh(a x)
+--R     + 
+--R                   3
+--R       - 2cosh(a x)  - 2cosh(a x)
+--R  /
+--R                   4                        3                 2               2
+--R       2a sinh(a x)  + 8a cosh(a x)sinh(a x)  + (12a cosh(a x)  - 4a)sinh(a x)
+--R     + 
+--R                    3                                        4               2
+--R       (8a cosh(a x)  - 8a cosh(a x))sinh(a x) + 2a cosh(a x)  - 4a cosh(a x)
+--R     + 
+--R       2a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.639~~~~~$\displaystyle
+\int{{\rm csch}^n~{ax}~{\coth{ax}}}~dx$}
+$$\int{{\rm csch~}^n{ax}~{\coth{ax}}}=
+-\frac{{\rm csch~}^{n}{ax}}{na}
+$$
+<<*>>=
+)clear all
+
+--S 4 of 10
+aa:=integrate(csch(a*x)^n*coth(a*x),x)
+--R 
+--R
+--R   (1)
+--R                                 2sinh(a x) + 2cosh(a x)
+--R       - sinh(n log(-------------------------------------------------))
+--R                             2                                  2
+--R                    sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  - 1
+--R     + 
+--R                                 2sinh(a x) + 2cosh(a x)
+--R       - cosh(n log(-------------------------------------------------))
+--R                             2                                  2
+--R                    sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  - 1
+--R  /
+--R     a n
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.640~~~~~$\displaystyle
+\int{\frac{dx}{{\rm csch~}{ax}}}~dx$}
+$$\int{\frac{1}{{\rm csch~}{ax}}}=
+\frac{1}{a}{\rm cosh}~{ax}
+$$
+<<*>>=
+)clear all
+
+--S 5 of 10
+aa:=integrate(1/csch(a*x),x)
+--R 
+--R
+--R        cosh(a x)
+--R   (1)  ---------
+--R            a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.641~~~~~$\displaystyle
+\int{x{\rm ~csch~}{ax}}~dx$}
+$$\int{x{\rm ~csch~}{ax}}=
+\frac{1}{a^2}\left\{
+ax-\frac{(ax)^3}{18}+\frac{7(ax)^5}{1800}+\cdots+
+\frac{2(-1)^n(2^{2n-1}-1)B_n(ax)^{2n+1}}{(2n+1)!}+\cdots\right\}
+$$
+<<*>>=
+)clear all
+
+--S 6 of 10
+aa:=integrate(x*csch(a*x),x)
+--R 
+--R
+--R           x
+--R         ++
+--I   (1)   |   %O csch(%O a)d%O
+--R        ++
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.642~~~~~$\displaystyle
+\int{x~{\rm csch}^2~{ax}}~dx$}
+$$\int{x~{\rm csch}^2~{ax}}=
+-\frac{x\coth{ax}}{a}+\frac{1}{a^2}\ln\sinh{ax}
+$$
+<<*>>=
+)clear all
+
+--S 7 of 10
+aa:=integrate(x*csch(a*x)^2,x)
+--R 
+--R
+--R   (1)
+--R                   2                                  2
+--R         (sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  - 1)
+--R      *
+--R                     2sinh(a x)
+--R         log(- ---------------------)
+--R               sinh(a x) - cosh(a x)
+--R     + 
+--R                       2                                           2
+--R       - 2a x sinh(a x)  - 4a x cosh(a x)sinh(a x) - 2a x cosh(a x)
+--R  /
+--R      2         2     2                      2         2    2
+--R     a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  - a
+--R                                          Type: Union(Expression Integer,...)
+--E
+@
+
+\section{\cite{1}:14.643~~~~~$\displaystyle
+\int{\frac{{\rm csch~}{ax}}{x}}~dx$}
+$$\int{\frac{{\rm csch~}{ax}}{x}}=
+-\frac{1}{ax}-\frac{ax}{6}+\frac{7(ax)^3}{1080}+\cdots
+\frac{(-1)^n2(2^{2n-1}-1)B_n(ax)^{2n-1}}{(2n-1)(2n)!}+\cdots
+$$
+<<*>>=
+)clear all
+
+--S 8 of 10
+aa:=integrate(csch(a*x)/x,x)
+--R 
+--R
+--R           x
+--I         ++  csch(%O a)
+--I   (1)   |   ---------- d%O
+--I        ++       %O
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.644~~~~~$\displaystyle
+\int{\frac{dx}{q+p{\rm ~csch~}{ax}}}~dx$}
+$$\int{\frac{1}{q+p{\rm ~csch~}{ax}}}=
+\frac{x}{q}-\frac{p}{q}\int{\frac{dx}{p+q\sinh{ax}}}
+$$
+<<*>>=
+)clear all
+
+--S 9 of 10
+aa:=integrate(1/(q+p*csch(a*x)),x)
+--R 
+--R
+--R   (1)
+--R         p
+--R      *
+--R         log
+--R                     2         2      2                              2         2
+--R                    q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
+--R                  + 
+--R                                      2     2
+--R                    2p q cosh(a x) + q  + 2p
+--R               *
+--R                   +-------+
+--R                   | 2    2
+--R                  \|q  + p
+--R              + 
+--R                   3     2                 3     2                  2     3
+--R                (2q  + 2p q)sinh(a x) + (2q  + 2p q)cosh(a x) + 2p q  + 2p
+--R           /
+--R                           2                                             2
+--R                q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
+--R              + 
+--R                2p cosh(a x) - q
+--R     + 
+--R           +-------+
+--R           | 2    2
+--R       a x\|q  + p
+--R  /
+--R         +-------+
+--R         | 2    2
+--R     a q\|q  + p
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.645~~~~~$\displaystyle
+\int{{\rm csch}^n~{ax}}~dx$}
+$$\int{{\rm csch}^n~{ax}}=
+\frac{-{\rm csch}^{n-2}~{ax}~\coth{ax}}{a(n-1)}
+-\frac{n-2}{n-1}\int{{\rm csch}^{n-2}~{ax}}
+$$
+<<*>>=
+)clear all
+
+--S 10 of 10
+aa:=integrate(csch(a*x)^n,x)
+--R 
+--R
+--R           x
+--R         ++            n
+--I   (1)   |   csch(%O a) d%O
+--R        ++
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+)spool
+)lisp (bye)
+@
+
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} Spiegel, Murray R.
+{\sl Mathematical Handbook of Formulas and Tables}\\
+Schaum's Outline Series McGraw-Hill 1968 pp91-92
+\end{thebibliography}
+\end{document}
diff --git a/src/input/schaum34.input.pamphlet b/src/input/schaum34.input.pamphlet
new file mode 100644
index 0000000..1a5c359
--- /dev/null
+++ b/src/input/schaum34.input.pamphlet
@@ -0,0 +1,901 @@
+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/input schaum34.input}
+\author{Timothy Daly}
+\maketitle
+\eject
+\tableofcontents
+\eject
+\section{\cite{1}:14.646~~~~~$\displaystyle
+\int{\sinh^{-1}\frac{x}{a}}~dx$}
+$$\int{\sinh^{-1}\frac{x}{a}}=
+x\sinh^{-1}\frac{x}{a}-\sqrt{x^2+a^2}
+$$
+<<*>>=
+)spool schaum34.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1 of 32
+aa:=integrate(asinh(x/a),x)
+--R 
+--R
+--R                               +-------+
+--R           +-------+           | 2    2           +-------+
+--R           | 2    2     2     \|x  + a   + x      | 2    2     2    2
+--R        (x\|x  + a   - x )log(--------------) + x\|x  + a   - x  - a
+--R                                     a
+--R   (1)  -------------------------------------------------------------
+--R                                 +-------+
+--R                                 | 2    2
+--R                                \|x  + a   - x
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.647~~~~~$\displaystyle
+\int{x\sinh^{-1}\frac{x}{a}}~dx$}
+$$\int{x\sinh^{-1}\frac{x}{a}}=
+\left(\frac{x^2}{2}+\frac{a^2}{4}\right)\sinh^{-1}\frac{x}{a}
+-\frac{x\sqrt{x^2+a^2}}{4}
+$$
+<<*>>=
+)clear all
+
+--S 2 of 32
+aa:=integrate(x*asinh(x/a),x)
+--R 
+--R
+--R   (1)
+--R                                                       +-------+
+--R                     +-------+                         | 2    2
+--R           3     2   | 2    2      4     2 2    4     \|x  + a   + x
+--R       ((4x  + 2a x)\|x  + a   - 4x  - 4a x  - a )log(--------------)
+--R                                                             a
+--R     + 
+--R                   +-------+
+--R          3    2   | 2    2      4     2 2
+--R       (2x  + a x)\|x  + a   - 2x  - 2a x
+--R  /
+--R        +-------+
+--R        | 2    2      2     2
+--R     8x\|x  + a   - 8x  - 4a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.648~~~~~$\displaystyle
+\int{x^2\sinh^{-1}\frac{x}{a}}~dx$}
+$$\int{x^2\sinh^{-1}\frac{x}{a}}=
+\frac{x^3}{3}\sinh^{-1}\frac{x}{a}+\frac{(2a^2-x^2)\sqrt{x^2+a^2}}{9}
+$$
+<<*>>=
+)clear all
+
+--S 3 of 32
+aa:=integrate(x^2*asinh(x/a),x)
+--R 
+--R
+--R   (1)
+--R                                                     +-------+
+--R                       +-------+                     | 2    2
+--R            5     2 3  | 2    2       6     2 4     \|x  + a   + x
+--R       ((12x  + 3a x )\|x  + a   - 12x  - 9a x )log(--------------)
+--R                                                           a
+--R     + 
+--R                            +-------+
+--R          5     2 3     4   | 2    2      6     2 4     4 2     6
+--R       (4x  - 5a x  - 6a x)\|x  + a   - 4x  + 3a x  + 9a x  + 2a
+--R  /
+--R                  +-------+
+--R         2     2  | 2    2       3      2
+--R     (36x  + 9a )\|x  + a   - 36x  - 27a x
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.649~~~~~$\displaystyle
+\int{\frac{\sinh^{-1}(x/a)}{x}}~dx$}
+$$\int{\frac{\sinh^{-1}(x/a)}{x}}=
+\left\{
+\begin{array}{lr}
+\displaystyle
+\frac{x}{a}-\frac{(x/a)^3}{2\cdot 3\cdot 3}
++\frac{1\cdot 3(x/a)^5}{2\cdot 4\cdot 5\cdot 5}
+-\frac{1\cdot 3\cdot 5(x/a)^7}{2\cdot 4\cdot 6\cdot 7\cdot 7}+\cdots&
+|x|<a\\
+\\
+\displaystyle
+\frac{\ln^2(2x/a)}{2}-\frac{(a/x)^2}{2\cdot 2\cdot 2}
++\frac{1\cdot 3(a/x)^4}{2\cdot 4\cdot 4\cdot 4}
+-\frac{1\cdot 3\cdot 5(a/x)^6}{2\cdot 4\cdot 6\cdot 6\cdot 6}+\cdots&
+x > a\\
+\\
+\displaystyle
+-\frac{\ln^2(-2x/a)}{2}+\frac{(a/x)^2}{2\cdot 2\cdot 2}
+-\frac{1\cdot 3(a/x)^4}{2\cdot 4\cdot 4\cdot 4}
++\frac{1\cdot 3\cdot 5(a/x)^6}{2\cdot 4\cdot 6\cdot 6\cdot 6}-\cdots&
+x<-a\\
+\end{array}
+\right.
+$$
+<<*>>=
+)clear all
+
+--S 4 of 32
+aa:=integrate(asinh(x/a)/x,x)
+--R 
+--R
+--I                   %P
+--R           x asinh(--)
+--R         ++         a
+--I   (1)   |   --------- d%P
+--I        ++       %P
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.650~~~~~$\displaystyle
+\int{\frac{\sinh^{-1}(x/a)}{x^2}}~dx$}
+$$\int{\frac{\sinh^{-1}(x/a)}{x^2}}=
+-\frac{\sinh^{-1}(x/a)}{x}
+-\frac{1}{a}\ln\left(\frac{a+\sqrt{x^2+a^2}}{x}\right)
+$$
+<<*>>=
+)clear all
+
+--S 5 of 32
+aa:=integrate(asinh(x/a)/x^2,x)
+--R 
+--R
+--R   (1)
+--R                +-------+                   +-------+
+--R                | 2    2                    | 2    2
+--R       - x log(\|x  + a   - x + a) + x log(\|x  + a   - x - a)
+--R     + 
+--R                +-------+
+--R                | 2    2
+--R               \|x  + a   + x
+--R       - a log(--------------)
+--R                      a
+--R  /
+--R     a x
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.651~~~~~$\displaystyle
+\int{\cosh^{-1}\frac{x}{a}}~dx$}
+$$\int{\cosh^{-1}\frac{x}{a}}=
+\left\{
+\begin{array}{l}
+\displaystyle
+x\cosh^{-1}(x/a)-\sqrt{x^2-a^2},\quad\cosh^{-1}\frac{x}{a} > 0\\
+\\
+\displaystyle
+x\cosh^{-1}(x/a)+\sqrt{x^2-a^2},\quad\cosh^{-1}\frac{x}{a} < 0\\
+\end{array}
+\right.
+$$
+<<*>>=
+)clear all
+
+--S 6 of 32
+aa:=integrate(acosh(x/a),x)
+--R 
+--R
+--R                               +-------+
+--R           +-------+           | 2    2           +-------+
+--R           | 2    2     2     \|x  - a   + x      | 2    2     2    2
+--R        (x\|x  - a   - x )log(--------------) + x\|x  - a   - x  + a
+--R                                     a
+--R   (1)  -------------------------------------------------------------
+--R                                 +-------+
+--R                                 | 2    2
+--R                                \|x  - a   - x
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.652~~~~~$\displaystyle
+\int{x\cosh^{-1}\frac{x}{a}}~dx$}
+$$\int{x\cosh^{-1}\frac{x}{a}}=
+\left\{
+\begin{array}{l}
+\displaystyle
+\frac{1}{4}(2x^2-a^2)\cosh^{-1}(x/a)-\frac{1}{4}x\sqrt{x^2-a^2},
+\quad\cosh^{-1}(x/a)>0\\
+\\
+\displaystyle
+\frac{1}{4}(2x^2-a^2)\cosh^{-1}(x/a)+\frac{1}{4}x\sqrt{x^2-a^2},
+\quad\cosh^{-1}(x/a)<0\\
+\end{array}
+\right.
+$$
+<<*>>=
+)clear all
+
+--S 7 of 32
+aa:=integrate(x*acosh(x/a),x)
+--R 
+--R
+--R   (1)
+--R                                                       +-------+
+--R                     +-------+                         | 2    2
+--R           3     2   | 2    2      4     2 2    4     \|x  - a   + x
+--R       ((4x  - 2a x)\|x  - a   - 4x  + 4a x  - a )log(--------------)
+--R                                                             a
+--R     + 
+--R                   +-------+
+--R          3    2   | 2    2      4     2 2
+--R       (2x  - a x)\|x  - a   - 2x  + 2a x
+--R  /
+--R        +-------+
+--R        | 2    2      2     2
+--R     8x\|x  - a   - 8x  + 4a
+--R                                          Type: Union(Expression Integer,...)
+--E
+@
+
+\section{\cite{1}:14.653~~~~~$\displaystyle
+\int{x^2\cosh^{-1}\frac{x}{a}}~dx$}
+$$\int{x^2\cosh^{-1}\frac{x}{a}}=
+\left\{
+\begin{array}{l}
+\displaystyle
+\frac{1}{3}x^3\cosh^{-1}(x/a)-\frac{1}{9}(x^2+2a^2)\sqrt{x^2-a^2},
+\quad\cosh^{-1}(x/a)>0\\
+\\
+\displaystyle
+\frac{1}{3}x^3\cosh^{-1}(x/a)+\frac{1}{9}(x^2+2a^2)\sqrt{x^2-a^2},
+\quad\cosh^{-1}(x/a)<0\\
+\end{array}
+\right.
+$$
+<<*>>=
+)clear all
+
+--S 8 of 32
+aa:=integrate(x^2*acosh(x/a),x)
+--R 
+--R
+--R   (1)
+--R                                                     +-------+
+--R                       +-------+                     | 2    2
+--R            5     2 3  | 2    2       6     2 4     \|x  - a   + x
+--R       ((12x  - 3a x )\|x  - a   - 12x  + 9a x )log(--------------)
+--R                                                           a
+--R     + 
+--R                            +-------+
+--R          5     2 3     4   | 2    2      6     2 4     4 2     6
+--R       (4x  + 5a x  - 6a x)\|x  - a   - 4x  - 3a x  + 9a x  - 2a
+--R  /
+--R                  +-------+
+--R         2     2  | 2    2       3      2
+--R     (36x  - 9a )\|x  - a   - 36x  + 27a x
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.654~~~~~$\displaystyle
+\int{\frac{\cosh^{-1}(x/a)}{x}}~dx$}
+$$\int{\frac{\cosh^{-1}(x/a)}{x}}=
+\begin{array}{l}
+\displaystyle
+\pm\left[\frac{1}{2}\ln^2(2x/a)+\frac{(a/x)^2}{2\cdot 2\cdot 2}
++\frac{1\cdot 3(a/x)^4}{2\cdot 4\cdot 4\cdot 4}
++\frac{1\cdot 3\cdot 5(a/x)^6}{2\cdot 4\cdot 6\cdot 6\cdot 6}+\cdots\right]\\
+\\
+\displaystyle
+\hbox{\hskip 2cm}+{\rm if\ }\cosh^{-1}(x/a)>0,
+\quad -{\rm if\ }\cosh^{-1}(x/a)<0,
+\end{array}
+$$
+<<*>>=
+)clear all
+
+--S 9 of 32
+aa:=integrate(acosh(x/a)/x,x)
+--R 
+--R
+--I                   %P
+--R           x acosh(--)
+--R         ++         a
+--I   (1)   |   --------- d%P
+--I        ++       %P
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.655~~~~~$\displaystyle
+\int{\frac{\cosh^{-1}(x/a)}{x^2}}~dx$}
+$$\int{\frac{\cosh^{-1}(x/a)}{x^2}}=
+\begin{array}{l}
+\displaystyle
+-\frac{\cosh^{-1}(x/a)}{x}
+\mp\frac{1}{a}\ln\left(\frac{a+\sqrt{x^2+a^2}}{x}\right)\\
+\\
+\displaystyle
+\hbox{\hskip 1cm}-{\rm if\ }\cosh^{-1}(x/a)>0,
+\quad +{\rm if\ }\cosh^{-1}(x/a)<0,
+\end{array}
+$$
+<<*>>=
+)clear all
+
+--S 10 of 32
+aa:=integrate(acosh(x/a)/x^2,x)
+--R 
+--R
+--R                 +-------+                 +-------+
+--R                 | 2    2                  | 2    2
+--R                \|x  - a   + x            \|x  - a   - x
+--R        - a log(--------------) + 2x atan(--------------)
+--R                       a                         a
+--R   (1)  -------------------------------------------------
+--R                               a x
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.656~~~~~$\displaystyle
+\int{\tanh^{-1}\frac{x}{a}}~dx$}
+$$\int{\tanh^{-1}\frac{x}{a}}=
+x\tanh^{-1}\frac{x}{a}+\frac{a}{2}\ln(a^2-x^2)
+$$
+<<*>>=
+)clear all
+
+--S 11 of 32
+aa:=integrate(atanh(x/a),x)
+--R 
+--R
+--R               2    2          - x - a
+--R        a log(x  - a ) + x log(-------)
+--R                                x - a
+--R   (1)  -------------------------------
+--R                       2
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.657~~~~~$\displaystyle
+\int{x*\tanh^{-1}\frac{x}{a}}~dx$}
+$$\int{x*\tanh^{-1}\frac{x}{a}}=
+\frac{ax}{2}+\frac{1}{2}(x^2-a^2)\tanh^{-1}\frac{x}{a}
+$$
+<<*>>=
+)clear all
+
+--S 12 of 32
+aa:=integrate(x*atanh(x/a),x)
+--R 
+--R
+--R          2    2     - x - a
+--R        (x  - a )log(-------) + 2a x
+--R                      x - a
+--R   (1)  ----------------------------
+--R                      4
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.658~~~~~$\displaystyle
+\int{x^2\tanh^{-1}\frac{x}{a}}~dx$}
+$$\int{x^2\tanh^{-1}\frac{x}{a}}=
+\frac{ax^2}{6}+\frac{x^3}{3}\tanh^{-1}\frac{x}{a}
++\frac{a^3}{6}\ln(a^2-x^2)
+$$
+<<*>>=
+)clear all
+
+--S 13 of 32
+aa:=integrate(x^2*atanh(x/a),x)
+--R 
+--R
+--R         3     2    2     3    - x - a       2
+--R        a log(x  - a ) + x log(-------) + a x
+--R                                x - a
+--R   (1)  --------------------------------------
+--R                           6
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.659~~~~~$\displaystyle
+\int{\frac{\tanh^{-1}(x/a)}{a}}~dx$}
+$$\int{\frac{\tanh^{-1}(x/a)}{a}}=
+\frac{x}{a}+\frac{(x/a)^3}{3^2}+\frac{(x/a)^5}{5^2}+\cdots
+$$
+<<*>>=
+)clear all
+
+--S 14 of 32
+aa:=integrate(atanh(x/a)/x,x)
+--R 
+--R
+--I                   %P
+--R           x atanh(--)
+--R         ++         a
+--I   (1)   |   --------- d%P
+--I        ++       %P
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.660~~~~~$\displaystyle
+\int{\frac{tanh^{-1}(x/a)}{x^2}}~dx$}
+$$\int{\frac{tanh^{-1}(x/a)}{x^2}}=
+-\frac{\tanh^{-1}(x/a)}{x}+\frac{1}{2a}\ln\left(\frac{x^2}{a^2-x^2}\right)
+$$
+<<*>>=
+)clear all
+
+--S 15 of 32
+aa:=integrate(atanh(x/a)/x^2,x)
+--R 
+--R
+--R                 2    2                      - x - a
+--R        - x log(x  - a ) + 2x log(x) - a log(-------)
+--R                                              x - a
+--R   (1)  ---------------------------------------------
+--R                             2a x
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.661~~~~~$\displaystyle
+\int{\coth^{-1}\frac{x}{a}}~dx$}
+$$\int{\coth^{-1}\frac{x}{a}}=
+x\coth^{-1}{x}+\frac{a}{2}\ln(x^2-a^2)
+$$
+<<*>>=
+)clear all
+
+--S 16 of 32
+aa:=integrate(acoth(x/a),x)
+--R 
+--R
+--R               2    2          x + a
+--R        a log(x  - a ) + x log(-----)
+--R                               x - a
+--R   (1)  -----------------------------
+--R                      2
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.662~~~~~$\displaystyle
+\int{x\coth^{-1}\frac{x}{a}}~dx$}
+$$\int{x\coth^{-1}\frac{x}{a}}=
+\frac{ax}{2}+\frac{1}{2}(x^2-a^2)\coth^{-1}\frac{x}{a}
+$$
+<<*>>=
+)clear all
+
+--S 17 of 32
+aa:=integrate(x*acoth(x/a),x)
+--R 
+--R
+--R          2    2     x + a
+--R        (x  - a )log(-----) + 2a x
+--R                     x - a
+--R   (1)  --------------------------
+--R                     4
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.663~~~~~$\displaystyle
+\int{x^2\coth^{-1}\frac{x}{a}}~dx$}
+$$\int{x^2\coth^{-1}\frac{x}{a}}=
+\frac{ax^2}{6}+\frac{x^3}{3}\coth^{-1}\frac{x}{a}
++\frac{a^3}{6}\ln(x^2-a^2)
+$$
+<<*>>=
+)clear all
+
+--S 18 of 32
+aa:=integrate(x^2*acoth(x/a),x)
+--R 
+--R
+--R         3     2    2     3    x + a       2
+--R        a log(x  - a ) + x log(-----) + a x
+--R                               x - a
+--R   (1)  ------------------------------------
+--R                          6
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.664~~~~~$\displaystyle
+\int{\frac{\coth^{-1}(x/a)}{x}}~dx$}
+$$\int{\frac{\coth^{-1}(x/a)}{x}}=
+-\left(\frac{a}{x}+\frac{(a/x)^3}{3^2}+\frac{(a/x)^5}{5^2}+\cdots\right)
+$$
+<<*>>=
+)clear all
+
+--S 19 of 32
+aa:=integrate(acoth(x/a)/x,x)
+--R 
+--R
+--I                   %P
+--R           x acoth(--)
+--R         ++         a
+--I   (1)   |   --------- d%P
+--I        ++       %P
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.665~~~~~$\displaystyle
+\int{\frac{\coth^{-1}(x/a)}{x^2}}~dx$}
+$$\int{\frac{\coth^{-1}(x/a)}{x^2}}=
+-\frac{\coth^{-1}(x/a)}{x}+\frac{1}{2a}\ln\left(\frac{x^2}{x^2-a^2}\right)
+$$
+<<*>>=
+)clear all
+
+--S 20 of 32
+aa:=integrate(acoth(x/a)/x^2,x)
+--R 
+--R
+--R                 2    2                      x + a
+--R        - x log(x  - a ) + 2x log(x) - a log(-----)
+--R                                             x - a
+--R   (1)  -------------------------------------------
+--R                            2a x
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.666~~~~~$\displaystyle
+\int{{\rm sech}^{-1}\frac{x}{a}}~dx$}
+$$\int{{\rm sech}^{-1}\frac{x}{a}}=
+\left\{
+\begin{array}{l}
+\displaystyle
+x{\rm ~sech}^{-1}(x/a)+a\sin^{-1}(x/a),\quad{\rm sech}^{-1}(x/a)>0\\
+\\
+\displaystyle
+x{\rm ~sech}^{-1}(x/a)-a\sin^{-1}(x/a),\quad{\rm sech}^{-1}(x/a)<0\\
+\end{array}
+\right.
+$$
+<<*>>=
+)clear all
+
+--S 21 of 32
+aa:=integrate(asech(x/a),x)
+--R 
+--R
+--R               +---------+                 +---------+
+--R               |   2    2                  |   2    2
+--R              \|- x  + a   + a            \|- x  + a   - a
+--R   (1)  x log(----------------) - 2a atan(----------------)
+--R                      x                           x
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.667~~~~~$\displaystyle
+\int{x{\rm ~sech}^{-1}\frac{x}{a}}~dx$}
+$$\int{x{\rm ~sech}^{-1}\frac{x}{a}}=
+\left\{
+\begin{array}{l}
+\displaystyle
+\frac{1}{2}x^2{\rm ~sech}^{-1}(x/a)-\frac{1}{2}a\sqrt{a^2-x^2},
+\quad{\rm sech}^{-1}(x/a)>0\\
+\\
+\displaystyle
+\frac{1}{2}x^2{\rm ~sech}^{-1}(x/a)+\frac{1}{2}a\sqrt{a^2-x^2},
+\quad{\rm sech}^{-1}(x/a)<0\\
+\end{array}
+\right.
+$$
+<<*>>=
+)clear all
+
+--S 22 of 32
+aa:=integrate(x*asech(x/a),x)
+--R 
+--R
+--R                                    +---------+
+--R            +---------+             |   2    2
+--R          2 |   2    2       2     \|- x  + a   + a       2
+--R        (x \|- x  + a   - a x )log(----------------) + a x
+--R                                           x
+--R   (1)  ---------------------------------------------------
+--R                           +---------+
+--R                           |   2    2
+--R                         2\|- x  + a   - 2a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.668~~~~~$\displaystyle
+\int{\frac{{\rm sech}^{-1}(x/a)}{x}}~dx$}
+$$\int{\frac{{\rm sech}^{-1}(x/a)}{x}}=
+\left\{
+\begin{array}{l}
+\displaystyle
+-\frac{1}{2}\ln(a/x)\ln(4a/x)-\frac{(x/a)^2}{2\cdot 2\cdot 2}
+-\frac{1\cdot 3(x/a)^4}{2\cdot 4\cdot 4\cdot 4}
+-\cdots,\quad{\rm sech}^{-1}(x/a)>0\\
+\\
+\displaystyle
+\frac{1}{2}\ln(a/x)\ln(4a/x)+\frac{(x/a)^2}{2\cdot 2\cdot 2}
++\frac{1\cdot 3(x/a)^4}{2\cdot 4\cdot 4\cdot 4}
++\cdots,\quad{\rm sech}^{-1}(x/a)<0\\
+\end{array}
+\right.
+$$
+<<*>>=
+)clear all
+
+--S 23 of 32
+aa:=integrate(asech(x/a)/x,x)
+--R 
+--R
+--R                           +---------+     2
+--R           +---------+     |   2    2
+--R           |   2    2     \|- x  + a   + a
+--R          \|- x  + a  log(----------------)
+--R                                  x
+--R   (1)  - ----------------------------------
+--R                          2a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.669~~~~~$\displaystyle
+\int{{\rm csch}^{-1}\frac{x}{a}}~dx$}
+$$\int{{\rm csch}^{-1}\frac{x}{a}}=
+x{\rm ~csch}^{-1}\frac{x}{a}\pm a\sinh^{-1}\frac{x}{a}
+\quad +{\rm if\ }x>0, -{\rm if\ }x<0
+$$
+<<*>>=
+)clear all
+
+--S 24 of 32
+aa:=integrate(acsch(x/a),x)
+--R 
+--R
+--R                                         +-------+
+--R                 +-------+               | 2    2
+--R                 | 2    2               \|x  + a   + a
+--R   (1)  - a log(\|x  + a   - x) + x log(--------------)
+--R                                               x
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.670~~~~~$\displaystyle
+\int{x{\rm ~csch}^{-1}\frac{x}{a}}~dx$}
+$$\int{x{\rm ~csch}^{-1}\frac{x}{a}}=
+\frac{x^2}{2}{\rm ~csch}^{-1}\frac{x}{a}\pm \frac{a\sqrt{x^2+a^2}}{2}
+\quad +{\rm if\ }x>0, -{\rm if\ }x<0
+$$
+<<*>>=
+)clear all
+
+--S 25 of 32
+aa:=integrate(x*acsch(x/a),x)
+--R 
+--R
+--R                                +-------+
+--R            +-------+           | 2    2             +-------+
+--R          2 | 2    2     3     \|x  + a   + a        | 2    2       2    3
+--R        (x \|x  + a   - x )log(--------------) - a x\|x  + a   + a x  + a
+--R                                      x
+--R   (1)  ------------------------------------------------------------------
+--R                                   +-------+
+--R                                   | 2    2
+--R                                 2\|x  + a   - 2x
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.671~~~~~$\displaystyle
+\int{\frac{{\rm csch}^{-1}(x/a)}{x}}~dx$}
+$$\int{\frac{{\rm csch}^{-1}(x/a)}{x}}=
+\left\{
+\begin{array}{lr}
+\displaystyle
+\frac{1}{2}\ln(x/a)\ln(4a/x)+\frac{1(x/a)^2}{2\cdot 2\cdot 2}
+-\frac{1\cdot 3(x/a)^4}{2\cdot 4\cdot 4\cdot 4}+\cdots&
+0<x<a\\
+\\
+\displaystyle
+\frac{1}{2}\ln(-x/a)\ln(-x/4a)-\frac{(x/a)^2}{2\cdot 2\cdot 2}
++\frac{1\cdot 3(x/a)^4}{2\cdot 4\cdot 4\cdot 4}-\cdots&
+-a<x<0\\
+\\
+\displaystyle
+-\frac{a}{x}+\frac{(a/x)^3}{2\cdot 3\cdot 3}
+-\frac{1\cdot 3(a/x)^5}{2\cdot 4\cdot 5\cdot 5}+\cdots&
+|x|>a
+\end{array}
+\right.
+$$
+<<*>>=
+)clear all
+
+--S 26 of 32
+aa:=integrate(acsch(x/a)/x,x)
+--R 
+--R
+--R                         +-------+     2
+--R           +-------+     | 2    2
+--R           | 2    2     \|x  + a   + a
+--R          \|x  + a  log(--------------)
+--R                               x
+--R   (1)  - ------------------------------
+--R                        2a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.672~~~~~$\displaystyle
+\int{x^m\sinh^{-1}\frac{x}{a}}~dx$}
+$$\int{x^m\sinh^{-1}\frac{x}{a}}=
+\frac{x^{m+1}}{m+1}\sinh^{-1}\frac{x}{a}
+-\frac{1}{m+1}\int{\frac{x^{m+1}}{\sqrt{x^2+a^2}}}
+$$
+<<*>>=
+)clear all
+
+--S 27 of 32
+aa:=integrate(x^m*asinh(x/a),x)
+--R 
+--R
+--R           x
+--I         ++        %P   m
+--I   (1)   |   asinh(--)%P d%P
+--R        ++          a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.673~~~~~$\displaystyle
+\int{x^m\cosh^{-1}\frac{x}{a}}~dx$}
+$$\int{x^m\cosh^{-1}\frac{x}{a}}=
+\left\{
+\begin{array}{lr}
+\displaystyle
+\frac{x^{m+1}}{m+1}\cosh^{-1}\frac{x}{a}
+-\frac{1}{m+1}\int{\frac{x^{m+1}}{\sqrt{x^2-a^2}}},&
+\quad\cosh^{-1}(x/a)>0\\
+\\
+\displaystyle
+\frac{x^{m+1}}{m+1}\cosh^{-1}\frac{x}{a}
++\frac{1}{m+1}\int{\frac{x^{m+1}}{\sqrt{x^2-a^2}}},&
+\quad\cosh^{-1}(x/a)<0\\
+\end{array}
+\right.
+$$
+<<*>>=
+)clear all
+
+--S 28 of 32
+aa:=integrate(x^m*acosh(x/a),x)
+--R 
+--R
+--R           x
+--I         ++        %P   m
+--I   (1)   |   acosh(--)%P d%P
+--R        ++          a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.674~~~~~$\displaystyle
+\int{x^m\tanh^{-1}\frac{x}{a}}~dx$}
+$$\int{x^m\tanh^{-1}\frac{x}{a}}=
+\frac{x^{m+1}}{m+1}\tanh^{-1}\frac{x}{a}
+-\frac{a}{m+1}\int{\frac{x^{m+1}}{a^2-x^2}}
+$$
+<<*>>=
+)clear all
+
+--S 29 of 32
+aa:=integrate(x^m*atanh(x/a),x)
+--R 
+--R
+--R           x
+--I         ++        %P   m
+--I   (1)   |   atanh(--)%P d%P
+--R        ++          a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.675~~~~~$\displaystyle
+\int{x^m\coth^{-1}\frac{x}{a}}~dx$}
+$$\int{x^m\coth^{-1}\frac{x}{a}}=
+\frac{x^{m+1}}{m+1}\coth^{-1}\frac{x}{a}
+-\frac{a}{m+1}\int{\frac{x^{m+1}}{a^2-x^2}}
+$$
+<<*>>=
+)clear all
+
+--S 30 of 32
+aa:=integrate(x^m*acoth(x/a),x)
+--R 
+--R
+--R           x
+--I         ++        %P   m
+--I   (1)   |   acoth(--)%P d%P
+--R        ++          a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.676~~~~~$\displaystyle
+\int{x^m{\rm ~sech}^{-1}\frac{x}{a}}~dx$}
+$$\int{x^m{\rm ~sech}^{-1}\frac{x}{a}}=
+\left\{
+\begin{array}{lr}
+\displaystyle
+\frac{x^{m+1}}{m+1}{\rm ~sech}^{-1}\frac{x}{a}
++\frac{a}{m+1}\int{\frac{x^m}{\sqrt{a^2-x^2}}}&
+{\rm sech}^{-1}(x/a)>0\\
+\\
+\displaystyle
+\frac{x^{m+1}}{m+1}{\rm ~sech}^{-1}\frac{x}{a}
+-\frac{a}{m+1}\int{\frac{x^m}{\sqrt{a^2-x^2}}}&
+{\rm sech}^{-1}(x/a)<0\\
+\end{array}
+\right.
+$$
+<<*>>=
+)clear all
+
+--S 31 of 32
+aa:=integrate(x^m*asech(x/a),x)
+--R 
+--R
+--R           x
+--I         ++        %P   m
+--I   (1)   |   asech(--)%P d%P
+--R        ++          a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+@
+
+\section{\cite{1}:14.677~~~~~$\displaystyle
+\int{x^m{\rm ~csch}^{-1}\frac{x}{a}}~dx$}
+$$\int{x^m{\rm ~csch}^{-1}\frac{x}{a}}=
+\frac{x^{m+1}}{m+1}{\rm ~csch}^{-1}\frac{x}{a}
+\pm\frac{a}{m+1}\int{\frac{x^m}{\sqrt{x^2+a^2}}}
+\quad+{\rm if\ }x>0
+~-{\rm if\ }x<0
+$$
+<<*>>=
+)clear all
+
+--S 32 of 32
+aa:=integrate(x^m*acsch(x/a),x)
+--R 
+--R
+--R           x
+--I         ++        %P   m
+--I   (1)   |   acsch(--)%P d%P
+--R        ++          a
+--R                                          Type: Union(Expression Integer,...)
+--E 
+
+)spool
+)lisp (bye)
+@
+
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} Spiegel, Murray R.
+{\sl Mathematical Handbook of Formulas and Tables}\\
+Schaum's Outline Series McGraw-Hill 1968 pp92-93
+\end{thebibliography}
+\end{document}



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Subject: [Axiom-developer] 20080415.01.tpd.patch (CATS Schaums-Axiom
	equivalence testing (1))
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This patch covers schaum1.input.pamphlet which are integrals involving
a*x+b. We attempt to determine if the results from Schaums and Axiom
are equal. If the results differ by a constant, the constant is
determined. The detailed results are:

14:59 Schaums and Axiom agree
14:60 Schaums and Axiom agree
14:61 Schaums and Axiom differ by a constant
14:62 Schaums and Axiom differ by a constant
14:63 Schaums and Axiom agree
14:64 Schaums and Axiom agree
14:65 Schaums and Axiom agree
14:66 Schaums and Axiom agree
14:67 Schaums and Axiom agree
14:68 Schaums and Axiom differ by a constant
14:69 Schaums and Axiom differ by a constant
14:70 Schaums and Axiom agree
14:71 Schaums and Axiom agree
14:72 Schaums and Axiom differ by a constant
14:73 Schaums and Axiom differ by a constant
14:74 Schaums and Axiom agree
14:75 Schaums and Axiom agree
14:76 Schaums and Axiom agree
14:77 Schaums and Axiom differ by a constant
14:78 Schaums and Axiom agree
14:79 Schaums and Axiom agree
14:80 Schaums and Axiom agree
14:81 Schaums and Axiom agreement cannot be determined
14:82 Schaums and Axiom agreement cannot be determined
14:83 Axiom cannot do this integration

This has uncovered one obvious weakness in Axiom related to 
indeterminants, shown in 14:81 and 14:82

Tim

==================================================================
diff --git a/changelog b/changelog
index d3ccbf9..346e9f2 100644
--- a/changelog
+++ b/changelog
@@ -1,3 +1,4 @@
+20080415 tpd src/input/schaum1.input show Schaums-Axiom equivalence
 20080414 tpd src/input/Makefile add integration regression testing	
 20080414 tpd src/input/schaum34.input integrals of csch(ax)
 20080414 tpd src/input/schaum33.input integrals of csch(ax)
diff --git a/src/input/schaum1.input.pamphlet b/src/input/schaum1.input.pamphlet
index 8507428..7e7e8c4 100644
--- a/src/input/schaum1.input.pamphlet
+++ b/src/input/schaum1.input.pamphlet
@@ -7,8 +7,11 @@
 \eject
 \tableofcontents
 \eject
-\section{\cite{1}:14.59~~~~~$\displaystyle\int{\frac{dx}{ax+b}~dx}$}
-$$\int{\frac{dx}{ax+b}~dx}==\frac{1}{a}~\ln(ax+b)$$
+\section{\cite{1}:14.59~~~~~$\displaystyle
+\int{\frac{dx}{ax+b}}$}
+$$\int{\frac{1}{ax+b}}=
+\frac{1}{a}~\ln(ax+b)
+$$
 <<*>>=
 )spool schaum1.output
 )set message test on
@@ -16,21 +19,40 @@ $$\int{\frac{dx}{ax+b}~dx}==\frac{1}{a}~\ln(ax+b)$$
 )clear all
 
 --S 1
-integrate(1/(a*x+b),x)
+aa:=integrate(1/(a*x+b),x)
 --R
 --R        log(a x + b)
 --R   (1)  ------------
 --R              a
 --R                                          Type: Union(Expression Integer,...)
 --E 1
+
+--S 2
+bb:=1/a*log(a*x+b)
+--R
+--R        log(a x + b)
+--R   (2)  ------------
+--R              a
+--R                                                     Type: Expression Integer
+--E
+
+--S 3      14:59 Schaums and Axiom agree
+cc:=bb-aa
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
 @
-\section{\cite{1}:14.60~~~~~$\displaystyle\int{\frac{x~dx}{ax+b}}$}
-$$\int{\frac{x~dx}{ax+b}}=\frac{x}{a}-\frac{b}{a^2}~\ln(ax+b)$$
+\section{\cite{1}:14.60~~~~~$\displaystyle
+\int{\frac{x~dx}{ax+b}}$}
+$$\int{\frac{x}{ax+b}}=
+\frac{x}{a}-\frac{b}{a^2}~\ln(ax+b)
+$$
 <<*>>=
 )clear all
 
---S 2
-integrate(x/(a*x+b),x)
+--S 4
+aa:=integrate(x/(a*x+b),x)
 --R 
 --R
 --R        - b log(a x + b) + a x
@@ -38,16 +60,36 @@ integrate(x/(a*x+b),x)
 --R                   2
 --R                  a
 --R                                          Type: Union(Expression Integer,...)
---E 2
+--E 
+
+--S 5
+bb:=x/a-b/a^2*log(a*x+b)
+--R
+--R        - b log(a x + b) + a x
+--R   (2)  ----------------------
+--R                   2
+--R                  a
+--R                                                     Type: Expression Integer
+--E
+
+--S 6      14:60 Schaums and Axiom agree
+cc:=bb-aa
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
 @
-\section{\cite{1}:14.61~~~~~$\displaystyle\int{\frac{x^2~dx}{ax+b}}$}
-$$\int{\frac{x^2~dx}{ax+b}}=
-\frac{(ax+b)^2}{2a^3}-\frac{2b(ax+b)}{a^3}+\frac{b^2}{a^3}~\ln(ax+b)$$
+
+\section{\cite{1}:14.61~~~~~$\displaystyle
+\int{\frac{x^2~dx}{ax+b}}$}
+$$\int{\frac{x^2}{ax+b}}=
+\frac{(ax+b)^2}{2a^3}-\frac{2b(ax+b)}{a^3}+\frac{b^2}{a^3}~\ln(ax+b)
+$$
 <<*>>=
 )clear all
 
---S 3
-nn:=integrate(x^2/(a*x+b),x)
+--S 7
+aa:=integrate(x^2/(a*x+b),x)
 --R
 --R          2                2 2
 --R        2b log(a x + b) + a x  - 2a b x
@@ -55,13 +97,10 @@ nn:=integrate(x^2/(a*x+b),x)
 --R                        3
 --R                      2a
 --R                                          Type: Union(Expression Integer,...)
---E 3
-@
-To see that these are the same answers we put the prior result over
-a common fraction:
-<<*>>=
---S 4
-mm:=((a*x+b)^2-2*2*b*(a*x+b)+2*b^2*log(a*x+b))/(2*a^3)
+--E 
+
+--S 8
+bb:=(a*x+b)^2/(2*a^3)-(2*b*(a*x+b))/a^3+b^2/a^3*log(a*x+b)
 --R
 --R          2                2 2              2
 --R        2b log(a x + b) + a x  - 2a b x - 3b
@@ -69,12 +108,10 @@ mm:=((a*x+b)^2-2*2*b*(a*x+b)+2*b^2*log(a*x+b))/(2*a^3)
 --R                           3
 --R                         2a
 --R                                                     Type: Expression Integer
---E 4
-@
-and we take their difference:
-<<*>>=
---S 5
-pp:=mm-nn
+--E
+
+--S 9
+cc:=bb-aa
 --R
 --R            2
 --R          3b
@@ -82,50 +119,28 @@ pp:=mm-nn
 --R            3
 --R          2a
 --R                                                     Type: Expression Integer
---E 5
+--E
 @
-which is a constant with respect to x, and thus the constant C.
+This factor is constant with respect to $x$ as shown by taking the
+derivative. It is a constant of integration.
 <<*>>=
---S 6
-D(pp,x)
+--S 10     14:61 Schaums and Axiom differ by a constant
+differentiate(cc,x)
 --R
 --R   (4)  0
 --R                                                     Type: Expression Integer
---E 6
-@
-Alternatively we can differentiate the answers with respect to x:
-<<*>>=
---S 7
-D(nn,x)
---R
---R            2
---R           x
---R   (5)  -------
---R        a x + b
---R                                                     Type: Expression Integer
---E 7
+--E
 @
-<<*>>=
---S 8
-D(mm,x)
---R
---R            2
---R           x
---R   (6)  -------
---R        a x + b
---R                                                     Type: Expression Integer
---E 8
-@
-and see that they are indeed the same.
-
-\section{\cite{1}:14.62~~~~~$\displaystyle\int{\frac{x^3~dx}{ax+b}}$}
-$$\int{\frac{x^3~dx}{ax+b}}=
+\section{\cite{1}:14.62~~~~~$\displaystyle
+\int{\frac{x^3~dx}{ax+b}}$}
+$$\int{\frac{x^3}{ax+b}}=
 \frac{(ax+b)^3}{3a^4}-\frac{3b(ax+b)^2}{2a^4}+
-\frac{3b^2(ax+b)}{a^4}-\frac{b^3}{a^4}~\ln(ax+b)$$
+\frac{3b^2(ax+b)}{a^4}-\frac{b^3}{a^4}~\ln(ax+b)
+$$
 <<*>>=
 )clear all
 
---S 9
+--S 11
 aa:=integrate(x^3/(a*x+b),x)
 --R
 --R            3                 3 3     2   2       2
@@ -134,11 +149,11 @@ aa:=integrate(x^3/(a*x+b),x)
 --R                               4
 --R                             6a
 --R                                          Type: Union(Expression Integer,...)
---E 9
+--E
 @
 and the book expression is:
 <<*>>=
---S 10
+--S 12
 bb:=(a*x+b)^3/(3*a^4)-(3*b*(a*x+b)^2)/(2*a^4)+(3*b^2*(a*x+b))/a^4-(b^3/a^4)*log(a*x+b)
 --R
 --R            3                 3 3     2   2       2       3
@@ -147,13 +162,13 @@ bb:=(a*x+b)^3/(3*a^4)-(3*b*(a*x+b)^2)/(2*a^4)+(3*b^2*(a*x+b))/a^4-(b^3/a^4)*log(
 --R                                  4
 --R                                6a
 --R                                                     Type: Expression Integer
---E 10
+--E 
 @
 
 The difference is a constant with respect to x:
 <<*>>=
---S 11
-aa-bb
+--S 13
+cc:=aa-bb
 --R
 --R             3
 --R          11b
@@ -161,90 +176,92 @@ aa-bb
 --R             4
 --R           6a
 --R                                                     Type: Expression Integer
---E 11
+--E 
 @
 
-If we differentiate each expression we see
+If we differentiate each expression we see that this is the integration
+constant.
 <<*>>=
---S 12
-cc:=D(aa,x)
+--S 14     14:62 Schaums and Axiom differ by a constant
+dd:=D(cc,x)
 --R
---R            3
---R           x
---R   (4)  -------
---R        a x + b
---R                                                     Type: Expression Integer
---E 12
-@
-<<*>>=
---S 13
-dd:=D(bb,x)
---R
---R            3
---R           x
---R   (5)  -------
---R        a x + b
---R                                                     Type: Expression Integer
---E 13
-@
-<<*>>=
---S 14
-cc-dd
---R
---R   (6)  0
+--R   (4)  0
 --R                                                     Type: Expression Integer
---E 14
+--E 
 @
 
-\section{\cite{1}:14.63~~~~~$\displaystyle\int{\frac{dx}{x~(ax+b)}}$}
-$$\int{\frac{dx}{x~(ax+b)}}=\frac{1}{b}~\ln\left(\frac{x}{ax+b}\right)$$
+\section{\cite{1}:14.63~~~~~$\displaystyle
+\int{\frac{dx}{x~(ax+b)}}$}
+$$\int{\frac{1}{x~(ax+b)}}=
+\frac{1}{b}~\ln\left(\frac{x}{ax+b}\right)
+$$
 <<*>>=
 )clear all
 
 --S 15
-ff:=integrate(1/(x*(a*x+b)),x)
+aa:=integrate(1/(x*(a*x+b)),x)
 --R
 --R        - log(a x + b) + log(x)
 --R   (1)  -----------------------
 --R                   b
 --R                                          Type: Union(Expression Integer,...)
---E 15
+--E 
+
+--S 16
+bb:=1/b*log(x/(a*x+b))
+--R
+--R               x
+--R        log(-------)
+--R            a x + b
+--R   (2)  ------------
+--R              b
+--R                                                     Type: Expression Integer
+--E
+
+--S 17
+cc:=aa-bb
+--R
+--R                                         x
+--R        - log(a x + b) + log(x) - log(-------)
+--R                                      a x + b
+--R   (3)  --------------------------------------
+--R                           b
+--R                                                     Type: Expression Integer
+--E
 @
 but we know that $$\log(a)-\log(b)=\log(\frac{a}{b})$$
 
 We can express this fact as a rule:
 <<*>>=
---S 16
+--S 18
 logdiv:=rule(log(a)-log(b) == log(a/b))
 --R
 --R                                      a
---I   (2)  - log(b) + log(a) + %I == log(-) + %I
+--I   (4)  - log(b) + log(a) + %I == log(-) + %I
 --R                                      b
 --R                        Type: RewriteRule(Integer,Integer,Expression Integer)
---E 16
+--E 
 @
 and use this rule to rewrite the logs into divisions:
 <<*>>=
---S 17
-logdiv ff
+--S 19     14:63 Schaums and Axiom agree
+dd:=logdiv cc
 --R
---R               x
---R        log(-------)
---R            a x + b
---R   (3)  ------------
---R              b
+--R   (5)  0
 --R                                                     Type: Expression Integer
---E 17
+--E
 @
 so we can see the equivalence directly.
 
-\section{\cite{1}:14.64~~~~~$\displaystyle\int{\frac{dx}{x^2~(ax+b)}}$}
-$$\int{\frac{dx}{x^2~(ax+b)}}=
--\frac{1}{bx}+\frac{a}{b^2}~\ln\left(\frac{ax+b}{x}\right)$$
+\section{\cite{1}:14.64~~~~~$\displaystyle
+\int{\frac{dx}{x^2~(ax+b)}}$}
+$$\int{\frac{1}{x^2~(ax+b)}}=
+-\frac{1}{bx}+\frac{a}{b^2}~\ln\left(\frac{ax+b}{x}\right)
+$$
 <<*>>=
 )clear all
 
---S 18
+--S 20
 aa:=integrate(1/(x^2*(a*x+b)),x)
 --R
 --R        a x log(a x + b) - a x log(x) - b
@@ -252,12 +269,12 @@ aa:=integrate(1/(x^2*(a*x+b)),x)
 --R                        2
 --R                       b x
 --R                                          Type: Union(Expression Integer,...)
---E 18
+--E 
 @
 
 The original form given in the book expands to:
 <<*>>=
---S 19
+--S 21
 bb:=-1/(b*x)+a/b^2*log((a*x+b)/x)
 --R
 --R                a x + b
@@ -267,48 +284,50 @@ bb:=-1/(b*x)+a/b^2*log((a*x+b)/x)
 --R                  2
 --R                 b x
 --R                                                     Type: Expression Integer
---E 19
+--E 
+
+--S 22
+cc:=aa-bb
+--R
+--R                                          a x + b
+--R        a log(a x + b) - a log(x) - a log(-------)
+--R                                             x
+--R   (3)  ------------------------------------------
+--R                             2
+--R                            b
+--R                                                     Type: Expression Integer
+--E
 @
 
 We can define the following rule to expand log forms:
 <<*>>=
---S 20
+--S 23
 divlog:=rule(log(a/b) == log(a) - log(b))
 --R
 --R            a
---R   (3)  log(-) == - log(b) + log(a)
+--R   (4)  log(-) == - log(b) + log(a)
 --R            b
 --R                        Type: RewriteRule(Integer,Integer,Expression Integer)
---E 20
-@
-and apply it to the book form:
-<<*>>=
---S 21
-cc:= divlog bb
---R
---R        a x log(a x + b) - a x log(x) - b
---R   (4)  ---------------------------------
---R                        2
---R                       b x
---R                                                     Type: Expression Integer
---E 21
+--E 
 @
-and we can now see that the results are identical.
+and apply it to the difference
 <<*>>=
---S 22
-aa-cc
+--S 24     14:64 Schaums and Axiom agree
+divlog cc
 --R
 --R   (5)  0
 --R                                                     Type: Expression Integer
---E 22
+--E
 @
 
-\section{\cite{1}:14.65~~~~~$\displaystyle\int{\frac{dx}{x^3~(ax+b)}}$}
-$$\int{\frac{dx}{x^3~(ax+b)}}=
-\frac{2ax-b}{2b^2x^2}+\frac{a^2}{b^3}~\ln\left(\frac{x}{ax+b}\right)$$
+\section{\cite{1}:14.65~~~~~$\displaystyle
+\int{\frac{dx}{x^3~(ax+b)}}$}
+$$\int{\frac{1}{x^3~(ax+b)}}=
+\frac{2ax-b}{2b^2x^2}+\frac{a^2}{b^3}~\ln\left(\frac{x}{ax+b}\right)
+$$
 <<*>>=
 )clear all
---S 23
+--S 25
 aa:=integrate(1/(x^3*(a*x+b)),x)
 --R
 --R            2 2                 2 2                   2
@@ -317,11 +336,9 @@ aa:=integrate(1/(x^3*(a*x+b)),x)
 --R                               3 2
 --R                             2b x
 --R                                          Type: Union(Expression Integer,...)
---E 23
-@
+--E
 
-<<*>>=
---S 24
+--S 26
 bb:=(2*a*x-b)/(2*b^2*x^2)+a^2/b^3*log(x/(a*x+b))
 --R
 --R          2 2       x                 2
@@ -331,95 +348,121 @@ bb:=(2*a*x-b)/(2*b^2*x^2)+a^2/b^3*log(x/(a*x+b))
 --R                       3 2
 --R                     2b x
 --R                                                     Type: Expression Integer
---E 24
-@
+--E
 
-<<*>>=
---S 25
+--S 27
+cc:=aa-bb
+--R
+--R           2                2          2       x
+--R        - a log(a x + b) + a log(x) - a log(-------)
+--R                                            a x + b
+--R   (3)  --------------------------------------------
+--R                              3
+--R                             b
+--R                                                     Type: Expression Integer
+--E
+
+--S 28
 divlog:=rule(log(a/b) == log(a) - log(b))
 --R
 --R            a
---R   (3)  log(-) == - log(b) + log(a)
+--R   (4)  log(-) == - log(b) + log(a)
 --R            b
 --R                        Type: RewriteRule(Integer,Integer,Expression Integer)
---E 25
-@
+--E
 
-<<*>>=
---S 26
-cc:=divlog bb
---R
---R            2 2                 2 2                   2
---R        - 2a x log(a x + b) + 2a x log(x) + 2a b x - b
---R   (4)  -----------------------------------------------
---R                               3 2
---R                             2b x
---R                                                     Type: Expression Integer
---E 26
-@
-
-<<*>>=
---S 27
-cc-aa
+--S 29     14:65 Schaums and Axiom agree
+dd:=divlog cc
 --R
 --R   (5)  0
 --R                                                     Type: Expression Integer
---E 27
+--E 
 @
 
-\section{\cite{1}:14.66~~~~~$\displaystyle\int{\frac{dx}{(ax+b)^2}}$}
-$$\int{\frac{dx}{(ax+b)^2}}=\frac{-1}{a~(ax+b)}$$
+\section{\cite{1}:14.66~~~~~$\displaystyle
+\int{\frac{dx}{(ax+b)^2}}$}
+$$\int{\frac{1}{(ax+b)^2}}=
+\frac{-1}{a~(ax+b)}
+$$
 <<*>>=
 )clear all
 
---S 28
-integrate(1/(a*x+b)^2,x)
+--S 30
+aa:=integrate(1/(a*x+b)^2,x)
 --R
 --R              1
 --R   (1)  - ---------
 --R           2
 --R          a x + a b
 --R                                          Type: Union(Expression Integer,...)
---E 28
+--E 
+
+--S 31
+bb:=-1/(a*(a*x+b))
+--R
+--R              1
+--R   (2)  - ---------
+--R           2
+--R          a x + a b
+--R                                            Type: Fraction Polynomial Integer
+--E
+
+--S 32     14:66 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
+
 @
 
-\section{\cite{1}:14.67~~~~~$\displaystyle\int{\frac{x~dx}{(ax+b)^2}}$}
-$$\int{\frac{x~dx}{(ax+b)^2}}=
-\frac{b}{a^2~(ax+b)}+\frac{1}{a^2}~\ln(ax+b)$$
+\section{\cite{1}:14.67~~~~~$\displaystyle
+\int{\frac{x~dx}{(ax+b)^2}}$}
+$$\int{\frac{x}{(ax+b)^2}}=
+\frac{b}{a^2~(ax+b)}+\frac{1}{a^2}~\ln(ax+b)
+$$
 <<*>>=
 )clear all
 
---S 29
-integrate(x/(a*x+b)^2,x)
+--S 33
+aa:=integrate(x/(a*x+b)^2,x)
 --R
 --R        (a x + b)log(a x + b) + b
 --R   (1)  -------------------------
 --R                 3     2
 --R                a x + a b
 --R                                          Type: Union(Expression Integer,...)
---E 29
-@
-and the book form expands to:
-<<*>>=
---S 30
-b/(a^2*(a*x+b))+(1/a^2)*log(a*x+b)
+--E 
+
+--S 34
+bb:=b/(a^2*(a*x+b))+1/a^2*log(a*x+b)
 --R
 --R        (a x + b)log(a x + b) + b
 --R   (2)  -------------------------
 --R                 3     2
 --R                a x + a b
 --R                                                     Type: Expression Integer
---E 30
+--E
+
+--S 35     14:67 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
+
 @
 
-\section{\cite{1}:14.68~~~~~$\displaystyle\int{\frac{x^2~dx}{(ax+b)^2}}$}
-$$\int{\frac{x^2~dx}{(ax+b)^2}}=
+\section{\cite{1}:14.68~~~~~$\displaystyle
+\int{\frac{x^2~dx}{(ax+b)^2}}$}
+$$\int{\frac{x^2}{(ax+b)^2}}=
 \frac{ax+b}{a^3}-\frac{b^2}{a^3~(ax+b)}
--\frac{2b}{a^3}~\ln(ax+b)$$
+-\frac{2b}{a^3}~\ln(ax+b)
+$$
 <<*>>=
 )clear all
 
---S 31
+--S 36
 aa:=integrate(x^2/(a*x+b)^2,x)
 --R
 --R                      2                 2 2            2
@@ -428,11 +471,11 @@ aa:=integrate(x^2/(a*x+b)^2,x)
 --R                             4     3
 --R                            a x + a b
 --R                                          Type: Union(Expression Integer,...)
---E 31
+--E 
 @
 and the book expression expands into
 <<*>>=
---S 32
+--S 37
 bb:=(a*x+b)/a^3-b^2/(a^3*(a*x+b))-((2*b)/a^3)*log(a*x+b)
 --R
 --R                      2                 2 2
@@ -441,57 +484,42 @@ bb:=(a*x+b)/a^3-b^2/(a^3*(a*x+b))-((2*b)/a^3)*log(a*x+b)
 --R                           4     3
 --R                          a x + a b
 --R                                                     Type: Expression Integer
---E 32
+--E 
 @
 
 These two expressions differ by the constant
 <<*>>=
---S 33
-aa-bb
+--S 38
+cc:=aa-bb
 --R
 --R           b
 --R   (3)  - --
 --R           3
 --R          a
 --R                                                     Type: Expression Integer
---E 33
+--E 
 @
 
-These are the same integrands as can be shown by differentiation:
+That this expression is constant can be shown by differentiation:
 <<*>>=
---S 34
-D(aa,x)
+--S 39     14:68 Schaums and Axiom differ by a constant
+D(cc,x)
 --R
---R                 2
---R                x
---R   (4)  ------------------
---R         2 2             2
---R        a x  + 2a b x + b
---R                                                     Type: Expression Integer
---E 34
-@
-
-<<*>>=
---S 35
-D(bb,x)
---R
---R                 2
---R                x
---R   (5)  ------------------
---R         2 2             2
---R        a x  + 2a b x + b
+--R   (4)  0
 --R                                                     Type: Expression Integer
---E 35
+--E 
 @
 
-\section{\cite{1}:14.69~~~~~$\displaystyle\int{\frac{x^3~dx}{(ax+b)^2}}$}
-$$\int{\frac{x^3~dx}{(ax+b)^2}}=
+\section{\cite{1}:14.69~~~~~$\displaystyle
+\int{\frac{x^3~dx}{(ax+b)^2}}$}
+$$\int{\frac{x^3}{(ax+b)^2}}=
 \frac{(ax+b)^2}{2a^4}-\frac{3b(ax+b)}{a^4}+\frac{b^3}{a^4(ax+b)}
-+\frac{3b^2}{a^4}~\ln(ax+b)$$
++\frac{3b^2}{a^4}~\ln(ax+b)
+$$
 <<*>>=
 )clear all
 
---S 36
+--S 40
 aa:=integrate(x^3/(a*x+b)^2,x)
 --R
 --R             2      3                 3 3     2   2       2      3
@@ -500,11 +528,9 @@ aa:=integrate(x^3/(a*x+b)^2,x)
 --R                                  5      4
 --R                                2a x + 2a b
 --R                                          Type: Union(Expression Integer,...)
---E 36
-@
+--E
 
-<<*>>=
---S 37
+--S 41
 bb:=(a*x+b)^2/(2*a^4)-(3*b*(a*x+b))/a^4+b^3/(a^4*(a*x+b))+(3*b^2/a^4)*log(a*x+b)
 --R
 --R             2      3                 3 3     2   2       2      3
@@ -513,12 +539,10 @@ bb:=(a*x+b)^2/(2*a^4)-(3*b*(a*x+b))/a^4+b^3/(a^4*(a*x+b))+(3*b^2/a^4)*log(a*x+b)
 --R                                  5      4
 --R                                2a x + 2a b
 --R                                                     Type: Expression Integer
---E 37
-@
+--E
 
-<<*>>=
---S 38
-aa-bb
+--S 42
+cc:=aa-bb
 --R
 --R          2
 --R        5b
@@ -526,51 +550,24 @@ aa-bb
 --R          4
 --R        2a
 --R                                                     Type: Expression Integer
---E 38
-@
+--E
 
-<<*>>=
---S 39
-cc:=D(aa,x)
+--S 43     14:69 Schaums and Axiom differ by a constant
+dd:=D(cc,x)
 --R
---R                 3
---R                x
---R   (4)  ------------------
---R         2 2             2
---R        a x  + 2a b x + b
---R                                                     Type: Expression Integer
---E 39
-@
-
-<<*>>=
---S 40
-dd:=D(bb,x)
---R
---R                 3
---R                x
---R   (5)  ------------------
---R         2 2             2
---R        a x  + 2a b x + b
---R                                                     Type: Expression Integer
---E 40
-@
-
-<<*>>=
---S 41
-cc-dd
---R
---R   (6)  0
+--R   (4)  0
 --R                                                     Type: Expression Integer
---E 41
+--E
 @
-
-\section{\cite{1}:14.70~~~~~$\displaystyle\int{\frac{dx}{x~(ax+b)^2}}$}
-$$\int{\frac{dx}{x~(ax+b)^2}}=
-\frac{1}{b~(ax+b)}+\frac{1}{b^2}~\ln\left(\frac{x}{ax+b}\right)$$
+\section{\cite{1}:14.70~~~~~$\displaystyle
+\int{\frac{dx}{x~(ax+b)^2}}$}
+$$\int{\frac{1}{x~(ax+b)^2}}=
+\frac{1}{b~(ax+b)}+\frac{1}{b^2}~\ln\left(\frac{x}{ax+b}\right)
+$$
 <<*>>=
 )clear all
 
---S 42
+--S 44
 aa:=integrate(1/(x*(a*x+b)^2),x)
 --R
 --R        (- a x - b)log(a x + b) + (a x + b)log(x) + b
@@ -578,11 +575,11 @@ aa:=integrate(1/(x*(a*x+b)^2),x)
 --R                             2     3
 --R                          a b x + b
 --R                                          Type: Union(Expression Integer,...)
---E 42
+--E
 @
 and the book says:
 <<*>>=
---S 43
+--S 45
 bb:=(1/(b*(a*x+b))+(1/b^2)*log(x/(a*x+b)))
 --R
 --R                        x
@@ -592,51 +589,52 @@ bb:=(1/(b*(a*x+b))+(1/b^2)*log(x/(a*x+b)))
 --R                   2     3
 --R                a b x + b
 --R                                                     Type: Expression Integer
---E 43
-@
+--E
 
+--S 46
+cc:=aa-bb
+--R
+--R                                         x
+--R        - log(a x + b) + log(x) - log(-------)
+--R                                      a x + b
+--R   (3)  --------------------------------------
+--R                           2
+--R                          b
+--R                                                     Type: Expression Integer
+--E
+@
 So we look at the divlog rule again:
 <<*>>=
---S 44
+--S 47
 divlog:=rule(log(a/b) == log(a) - log(b))
 --R
 --R            a
---R   (3)  log(-) == - log(b) + log(a)
+--R   (4)  log(-) == - log(b) + log(a)
 --R            b
 --R                        Type: RewriteRule(Integer,Integer,Expression Integer)
---E 44
+--E
 @
 
 we apply it:
 <<*>>=
---S 45
-cc:=divlog bb
---R
---R        (- a x - b)log(a x + b) + (a x + b)log(x) + b
---R   (4)  ---------------------------------------------
---R                             2     3
---R                          a b x + b
---R                                                     Type: Expression Integer
---E 45
-@
-and we difference the two to find they are identical:
-<<*>>=
---S 46
-cc-aa
+--S 48     14:70 Schaums and Axiom agree
+dd:=divlog cc
 --R
 --R   (5)  0
 --R                                                     Type: Expression Integer
---E 46
+--E
 @
 
-\section{\cite{1}:14.71~~~~~$\displaystyle\int{\frac{dx}{x^2~(ax+b)^2}}$}
-$$\int{\frac{dx}{x^2~(ax+b)^2}}=
+\section{\cite{1}:14.71~~~~~$\displaystyle
+\int{\frac{dx}{x^2~(ax+b)^2}}$}
+$$\int{\frac{1}{x^2~(ax+b)^2}}=
 \frac{-a}{b^2~(ax+b)}-\frac{1}{b^2~x}+
-\frac{2a}{b^3}~\ln\left(\frac{ax+b}{x}\right)$$
+\frac{2a}{b^3}~\ln\left(\frac{ax+b}{x}\right)
+$$
 <<*>>=
 )clear all
 
---S 47
+--S 49
 aa:=integrate(1/(x^2*(a*x+b)^2),x)
 --R
 --R           2 2                              2 2                             2
@@ -645,11 +643,11 @@ aa:=integrate(1/(x^2*(a*x+b)^2),x)
 --R                                        3 2    4
 --R                                     a b x  + b x
 --R                                          Type: Union(Expression Integer,...)
---E 47
+--E
 @
 and the book says:
 <<*>>=
---S 48
+--S 50
 bb:=(-a/(b^2*(a*x+b)))-(1/(b^2*x))+((2*a)/b^3)*log((a*x+b)/x)
 --R
 --R           2 2              a x + b              2
@@ -659,50 +657,50 @@ bb:=(-a/(b^2*(a*x+b)))-(1/(b^2*x))+((2*a)/b^3)*log((a*x+b)/x)
 --R                          3 2    4
 --R                       a b x  + b x
 --R                                                     Type: Expression Integer
---E 48
+--E
+
+--S 51
+cc:=aa-bb
+--R
+--R                                             a x + b
+--R        2a log(a x + b) - 2a log(x) - 2a log(-------)
+--R                                                x
+--R   (3)  ---------------------------------------------
+--R                               3
+--R                              b
+--R                                                     Type: Expression Integer
+--E
 @
 which calls for our divlog rule:
 <<*>>=
---S 49
+--S 52
 divlog:=rule(log(a/b) == log(a) - log(b))
 --R
 --R            a
---R   (3)  log(-) == - log(b) + log(a)
+--R   (4)  log(-) == - log(b) + log(a)
 --R            b
 --R                        Type: RewriteRule(Integer,Integer,Expression Integer)
---E 49
+--E
 @
 which we use to transform the result:
 <<*>>=
---S 50
-cc:=divlog bb
---R
---R           2 2                              2 2                             2
---R        (2a x  + 2a b x)log(a x + b) + (- 2a x  - 2a b x)log(x) - 2a b x - b
---R   (4)  ---------------------------------------------------------------------
---R                                        3 2    4
---R                                     a b x  + b x
---R                                                     Type: Expression Integer
---E 50
-@
-and we show they are identical:
-<<*>>=
---S 51
-dd:=aa-cc
+--S 53     14:71 Schaums and Axiom agree
+dd:=divlog cc
 --R
 --R   (5)  0
 --R                                                     Type: Expression Integer
---E 51
+--E
 @
-
-\section{\cite{1}:14.72~~~~~$\displaystyle\int{\frac{dx}{x^3~(ax+b)^2}}$}
-$$\int{\frac{dx}{x^3~(ax+b)^2}}=
+\section{\cite{1}:14.72~~~~~$\displaystyle
+\int{\frac{dx}{x^3~(ax+b)^2}}$}
+$$\int{\frac{1}{x^3~(ax+b)^2}}=
 -\frac{(ax+b)^2}{2b^4x^2}+\frac{3a(ax+b)}{b^4x}-
-\frac{a^3x}{b^4(ax+b)}-\frac{3a^2}{b^4}~\ln\left(\frac{ax+b}{x}\right)$$
+\frac{a^3x}{b^4(ax+b)}-\frac{3a^2}{b^4}~\ln\left(\frac{ax+b}{x}\right)
+$$
 <<*>>=
 )clear all
 
---S 52
+--S 54
 aa:=integrate(1/(x^3*(a*x+b)^2),x)
 --R
 --R   (1)
@@ -715,11 +713,9 @@ aa:=integrate(1/(x^3*(a*x+b)^2),x)
 --R         4 3     5 2
 --R     2a b x  + 2b x
 --R                                          Type: Union(Expression Integer,...)
---E 52
-@
+--E
 
-<<*>>=
---S 53
+--S 55
 bb:=-(a*x+b)^2/(2*b^4*x^2)+(3*a*(a*x+b))/(b^4*x)-(a^3*x)/(b^4*(a*x+b))-((3*a^2)/b^4)*log((a*x+b)/x)
 --R
 --R             3 3     2   2     a x + b      3 3     2   2       2     3
@@ -729,85 +725,53 @@ bb:=-(a*x+b)^2/(2*b^4*x^2)+(3*a*(a*x+b))/(b^4*x)-(a^3*x)/(b^4*(a*x+b))-((3*a^2)/
 --R                                    4 3     5 2
 --R                                2a b x  + 2b x
 --R                                                     Type: Expression Integer
---E 53
-@
-
-<<*>>=
---S 54
-divlog:=rule(log(a/b) == log(a) - log(b))
---R
---R            a
---R   (3)  log(-) == - log(b) + log(a)
---R            b
---R                        Type: RewriteRule(Integer,Integer,Expression Integer)
---E 54
-@
-
-<<*>>=
---S 55
-cc:=divlog bb
---R
---R   (4)
---R            3 3     2   2                   3 3     2   2            3 3
---R       (- 6a x  - 6a b x )log(a x + b) + (6a x  + 6a b x )log(x) + 3a x
---R     + 
---R         2   2       2     3
---R       9a b x  + 3a b x - b
---R  /
---R         4 3     5 2
---R     2a b x  + 2b x
---R                                                     Type: Expression Integer
---E 55
-@
+--E
 
-<<*>>=
 --S 56
-cc-aa
+cc:=aa-bb
 --R
---R          2
---R        3a
---R   (5)  ---
---R          4
---R        2b
+--R            2                 2           2    a x + b      2
+--R        - 6a log(a x + b) + 6a log(x) + 6a log(-------) - 3a
+--R                                                  x
+--R   (3)  -----------------------------------------------------
+--R                                   4
+--R                                 2b
 --R                                                     Type: Expression Integer
---E 56
-@
+--E
 
-<<*>>=
 --S 57
-dd:=D(aa,x)
+divlog:=rule(log(a/b) == log(a) - log(b))
 --R
---R                  1
---R   (6)  ---------------------
---R         2 5         4    2 3
---R        a x  + 2a b x  + b x
---R                                                     Type: Expression Integer
---E 57
-@
+--R            a
+--R   (4)  log(-) == - log(b) + log(a)
+--R            b
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
 
-<<*>>=
 --S 58
-ee:=D(bb,x)
+dd:=divlog cc
 --R
---R                  1
---R   (7)  ---------------------
---R         2 5         4    2 3
---R        a x  + 2a b x  + b x
+--R            2
+--R          3a
+--R   (5)  - ---
+--R            4
+--R          2b
 --R                                                     Type: Expression Integer
---E 58
-@
+--E
 
-<<*>>=
---S 59
-dd-ee
+--S 59     14:72 Schaums and Axiom differ by a constant
+ee:=D(dd,x)
 --R
---R   (8)  0
+--R   (6)  0
 --R                                                     Type: Expression Integer
---E 59
+--E
 @
 
-\section{\cite{1}:14.73~~~~~$\displaystyle\int{\frac{dx}{(ax+b)^3}}$}
-$$\int{\frac{dx}{(ax+b)^3}}=\frac{-1}{2a(ax+b)^2}$$
+\section{\cite{1}:14.73~~~~~$\displaystyle
+\int{\frac{dx}{(ax+b)^3}}$}
+$$\int{\frac{1}{(ax+b)^3}}=
+\frac{-1}{2a(ax+b)^2}
+$$
 <<*>>=
 )clear all
 
@@ -819,39 +783,54 @@ aa:=integrate(1/(a*x+b)^3,x)
 --R            3 2     2          2
 --R          2a x  + 4a b x + 2a b
 --R                                          Type: Union(Expression Integer,...)
---E 60
-@
+--E
 
-{\bf NOTE: }There is a missing factor of $1/a$ in the published book.
-This factor has been inserted here.
-<<*>>=
 --S 61
-bb:=-1/(2*a*(a*x+b)^2)
+bb:=-1/(2*(a*x+b)^2)
 --R
---R                     1
---R   (2)  - ----------------------
---R            3 2     2          2
---R          2a x  + 4a b x + 2a b
+--R                    1
+--R   (2)  - --------------------
+--R            2 2              2
+--R          2a x  + 4a b x + 2b
 --R                                            Type: Fraction Polynomial Integer
---E 61
-@
+--E
 
-<<*>>=
 --S 62
-aa-bb
+cc:=aa-bb
 --R
---R   (3)  0
+--R                 a - 1
+--R   (3)  ----------------------
+--R          3 2     2          2
+--R        2a x  + 4a b x + 2a b
+--R                                                     Type: Expression Integer
+--E
+
+--S 63
+dd:=aa/bb
+--R
+--R        1
+--R   (4)  -
+--R        a
+--R                                                     Type: Expression Integer
+--E
+
+--S 64     14:73 Schaums and Axiom differ by a constant
+ee:=D(dd,x)
+--R
+--R   (5)  0
 --R                                                     Type: Expression Integer
---E 62
+--E
 @
 
-\section{\cite{1}:14.74~~~~~$\displaystyle\int{\frac{x~dx}{(ax+b)^3}}$}
-$$\int{\frac{x~dx}{(ax+b)^3}}=
-\frac{-1}{a^2(ax+b)}+\frac{b}{2a^2(ax+b)^2}$$
+\section{\cite{1}:14.74~~~~~$\displaystyle
+\int{\frac{x~dx}{(ax+b)^3}}$}
+$$\int{\frac{x}{(ax+b)^3}}=
+\frac{-1}{a^2(ax+b)}+\frac{b}{2a^2(ax+b)^2}
+$$
 <<*>>=
 )clear all
 
---S 63
+--S 65
 aa:=integrate(x/(a*x+b)^3,x)
 --R
 --R              - 2a x - b
@@ -859,11 +838,9 @@ aa:=integrate(x/(a*x+b)^3,x)
 --R          4 2     3        2 2
 --R        2a x  + 4a b x + 2a b
 --R                                          Type: Union(Expression Integer,...)
---E 63
-@
+--E
 
-<<*>>=
---S 64
+--S 66
 bb:=-1/(a^2*(a*x+b))+b/(2*a^2*(a*x+b)^2)
 --R
 --R              - 2a x - b
@@ -871,26 +848,26 @@ bb:=-1/(a^2*(a*x+b))+b/(2*a^2*(a*x+b)^2)
 --R          4 2     3        2 2
 --R        2a x  + 4a b x + 2a b
 --R                                            Type: Fraction Polynomial Integer
---E 64
-@
+--E
 
-<<*>>=
---S 65
-aa-bb
+--S 67     14:74 Schaums and Axiom agree
+cc:=aa-bb
 --R
 --R   (3)  0
 --R                                                     Type: Expression Integer
---E 65
+--E
 @
 
-\section{\cite{1}:14.75~~~~~$\displaystyle\int{\frac{x^2~dx}{(ax+b)^3}}$}
-$$\int{\frac{x^2~dx}{(ax+b)^3}}=
+\section{\cite{1}:14.75~~~~~$\displaystyle
+\int{\frac{x^2~dx}{(ax+b)^3}}$}
+$$\int{\frac{x^2}{(ax+b)^3}}=
 \frac{2b}{a^3(ax+b)}-\frac{b^2}{2a^3(ax+b)^2}+
-\frac{1}{a^3}~\ln(ax+b)$$
+\frac{1}{a^3}~\ln(ax+b)
+$$
 <<*>>=
 )clear all
 
---S 66
+--S 68
 aa:=integrate(x^2/(a*x+b)^3,x)
 --R
 --R           2 2              2                           2
@@ -899,11 +876,9 @@ aa:=integrate(x^2/(a*x+b)^3,x)
 --R                        5 2     4        3 2
 --R                      2a x  + 4a b x + 2a b
 --R                                          Type: Union(Expression Integer,...)
---E 66
-@
+--E
 
-<<*>>=
---S 67
+--S 69
 bb:=(2*b)/(a^3*(a*x+b))-(b^2)/(2*a^3*(a*x+b)^2)+1/a^3*log(a*x+b)
 --R
 --R           2 2              2                           2
@@ -912,25 +887,25 @@ bb:=(2*b)/(a^3*(a*x+b))-(b^2)/(2*a^3*(a*x+b)^2)+1/a^3*log(a*x+b)
 --R                        5 2     4        3 2
 --R                      2a x  + 4a b x + 2a b
 --R                                                     Type: Expression Integer
---E 67
-@
+--E
 
-<<*>>=
---S 68
-aa-bb
+--S 70     14:75 Schaums and Axiom agree
+cc:=aa-bb
 --R
 --R   (3)  0
 --R                                                     Type: Expression Integer
---E 68
+--E
 @
 
-\section{\cite{1}:14.76~~~~~$\displaystyle\int{\frac{x^3~dx}{(ax+b)^3}}$}
-$$\int{\frac{x^3~dx}{(ax+b)^3}}=
+\section{\cite{1}:14.76~~~~~$\displaystyle
+\int{\frac{x^3~dx}{(ax+b)^3}}$}
+$$\int{\frac{x^3}{(ax+b)^3}}=
 \frac{x}{a^3}-\frac{3b^2}{a^4(ax+b)}+\frac{b^3}{2a^4(ax+b)^2}-
-\frac{3b}{a^4}~\ln(ax+b)$$
+\frac{3b}{a^4}~\ln(ax+b)
+$$
 <<*>>=
 )clear all
---S 69
+--S 71
 aa:=integrate(x^3/(a*x+b)^3,x)
 --R
 --R   (1)
@@ -940,11 +915,9 @@ aa:=integrate(x^3/(a*x+b)^3,x)
 --R                              6 2     5        4 2
 --R                            2a x  + 4a b x + 2a b
 --R                                          Type: Union(Expression Integer,...)
---E 69
-@
+--E
 
-<<*>>=
---S 70
+--S 72
 bb:=(x/a^3)-(3*b^2)/(a^4*(a*x+b))+b^3/(2*a^4*(a*x+b)^2)-(3*b)/a^4*log(a*x+b)
 --R
 --R   (2)
@@ -954,29 +927,27 @@ bb:=(x/a^3)-(3*b^2)/(a^4*(a*x+b))+b^3/(2*a^4*(a*x+b)^2)-(3*b)/a^4*log(a*x+b)
 --R                              6 2     5        4 2
 --R                            2a x  + 4a b x + 2a b
 --R                                                     Type: Expression Integer
---E 70
-@
+--E
 
-<<*>>=
---S 71
-aa-bb
+--S 73     14:76 Schaums and Axiom agree
+cc:=aa-bb
 --R
 --R   (3)  0
 --R                                                     Type: Expression Integer
---E 71
+--E
 @
 
-\section{\cite{1}:14.77~~~~~$\displaystyle\int{\frac{dx}{x(ax+b)^3}}$}
-$$\int{\frac{dx}{x(ax+b)^3}}=
+\section{\cite{1}:14.77~~~~~$\displaystyle
+\int{\frac{dx}{x(ax+b)^3}}$}
+$$\int{\frac{1}{x(ax+b)^3}}=
 \frac{3}{2b(ax+b)^2}+\frac{2ax}{2b^2(ax+b)^2}-
-\frac{1}{b^3}*\ln\left(\frac{ax+b}{x}\right)$$
-
-{\bf NOTE: }The equation given in the book is wrong. This is correct.
+\frac{1}{b^3}*\ln\left(\frac{ax+b}{x}\right)
+$$
 
 <<*>>=
 )clear all
 
---S 72
+--S 74
 aa:=integrate(1/(x*(a*x+b)^3),x)
 --R
 --R   (1)
@@ -989,68 +960,69 @@ aa:=integrate(1/(x*(a*x+b)^3),x)
 --R       2 3 2       4      5
 --R     2a b x  + 4a b x + 2b
 --R                                          Type: Union(Expression Integer,...)
---E 72
-@
+--E
 
-<<*>>=
---S 73
-bb:=3/(2*b*(a*x+b)^2)+(2*a*x)/(2*b^2*(a*x+b)^2)-1/b^3*log((a*x+b)/x)
+--S 75
+bb:=(a^2*x^2)/(2*b^3*(a*x+b)^2)-(2*a*x)/(b^3*(a*x+b))-(1/b^3)*log((a*x+b)/x)
 --R
---R             2 2              2     a x + b               2
---R        (- 2a x  - 4a b x - 2b )log(-------) + 2a b x + 3b
+--R             2 2              2     a x + b      2 2
+--R        (- 2a x  - 4a b x - 2b )log(-------) - 3a x  - 4a b x
 --R                                       x
---R   (2)  ---------------------------------------------------
---R                         2 3 2       4      5
---R                       2a b x  + 4a b x + 2b
+--R   (2)  -----------------------------------------------------
+--R                          2 3 2       4      5
+--R                        2a b x  + 4a b x + 2b
 --R                                                     Type: Expression Integer
---E 73
-@
+--E
 
-<<*>>=
---S 74
+--S 76
+cc:=aa-bb
+--R
+--R                                         a x + b
+--R        - 2log(a x + b) + 2log(x) + 2log(-------) + 3
+--R                                            x
+--R   (3)  ---------------------------------------------
+--R                               3
+--R                             2b
+--R                                                     Type: Expression Integer
+--E
+
+--S 77
 divlog:=rule(log(a/b) == log(a) - log(b))
 --R
 --R            a
---R   (3)  log(-) == - log(b) + log(a)
+--R   (4)  log(-) == - log(b) + log(a)
 --R            b
 --R                        Type: RewriteRule(Integer,Integer,Expression Integer)
---E 74
-@
+--E
 
-<<*>>=
---S 75
-cc:=divlog bb
+--S 78
+dd:=divlog cc
 --R
---R   (4)
---R            2 2              2                   2 2              2
---R       (- 2a x  - 4a b x - 2b )log(a x + b) + (2a x  + 4a b x + 2b )log(x)
---R     + 
---R                  2
---R       2a b x + 3b
---R  /
---R       2 3 2       4      5
---R     2a b x  + 4a b x + 2b
+--R         3
+--R   (5)  ---
+--R          3
+--R        2b
 --R                                                     Type: Expression Integer
---E 75
-@
+--E
 
-<<*>>=
---S 76
-aa-cc
+--S 79     14:77 Schaums and Axiom differ by a constant
+ee:=D(dd,x)
 --R
---R   (5)  0
+--R   (6)  0
 --R                                                     Type: Expression Integer
---E 76
+--E
 @
 
-\section{\cite{1}:14.78~~~~~$\displaystyle\int{\frac{dx}{x^2(ax+b)^3}}$}
-$$\int{\frac{dx}{x^2(ax+b)^3}}=
+\section{\cite{1}:14.78~~~~~$\displaystyle
+\int{\frac{dx}{x^2(ax+b)^3}}$}
+$$\int{\frac{1}{x^2(ax+b)^3}}=
 \frac{-a}{2b^2(ax+b)^2}-\frac{2a}{b^3(ax+b)}-
-\frac{1}{b^3x}+\frac{3a}{b^4}~\ln\left(\frac{ax+b}{x}\right)$$
+\frac{1}{b^3x}+\frac{3a}{b^4}~\ln\left(\frac{ax+b}{x}\right)
+$$
 <<*>>=
 )clear all
 
---S 77
+--S 80
 aa:=integrate(1/(x^2*(a*x+b)^3),x)
 --R
 --R   (1)
@@ -1063,11 +1035,9 @@ aa:=integrate(1/(x^2*(a*x+b)^3),x)
 --R       2 4 3       5 2     6
 --R     2a b x  + 4a b x  + 2b x
 --R                                          Type: Union(Expression Integer,...)
---E 77
-@
+--E
 
-<<*>>=
---S 78
+--S 81
 bb:=-a/(2*b^2*(a*x+b)^2)-(2*a)/(b^3*(a*x+b))-1/(b^3*x)+((3*a)/b^4)*log((a*x+b)/x)
 --R
 --R           3 3      2   2       2      a x + b      2   2       2      3
@@ -1077,60 +1047,50 @@ bb:=-a/(2*b^2*(a*x+b)^2)-(2*a)/(b^3*(a*x+b))-1/(b^3*x)+((3*a)/b^4)*log((a*x+b)/x
 --R                              2 4 3       5 2     6
 --R                            2a b x  + 4a b x  + 2b x
 --R                                                     Type: Expression Integer
---E 78
-@
+--E
 
-<<*>>=
---S 79
+--S 82
+cc:=aa-bb
+--R
+--R                                             a x + b
+--R        3a log(a x + b) - 3a log(x) - 3a log(-------)
+--R                                                x
+--R   (3)  ---------------------------------------------
+--R                               4
+--R                              b
+--R                                                     Type: Expression Integer
+--E
+
+--S 83
 divlog:=rule(log(a/b) == log(a) - log(b))
 --R
 --R            a
---R   (3)  log(-) == - log(b) + log(a)
+--R   (4)  log(-) == - log(b) + log(a)
 --R            b
 --R                        Type: RewriteRule(Integer,Integer,Expression Integer)
---E 79
-@
+--E
 
-<<*>>=
---S 80
-cc:=divlog bb
---R
---R   (4)
---R          3 3      2   2       2
---R       (6a x  + 12a b x  + 6a b x)log(a x + b)
---R     + 
---R            3 3      2   2       2             2   2       2      3
---R       (- 6a x  - 12a b x  - 6a b x)log(x) - 6a b x  - 9a b x - 2b
---R  /
---R       2 4 3       5 2     6
---R     2a b x  + 4a b x  + 2b x
---R                                                     Type: Expression Integer
---E 80
-@
-
-<<*>>=
---S 81
-cc-aa
+--S 84     14:78 Schaums and Axiom agree
+dd:=divlog cc
 --R
 --R   (5)  0
 --R                                                     Type: Expression Integer
---E 81
+--E
 @
 
-\section{\cite{1}:14.79~~~~~$\displaystyle\int{\frac{dx}{x^3(ax+b)^3}}$}
-$$\int{\frac{dx}{x^3(ax+b)^3}}=$$
-$$-\frac{1}{2bx^2(ax+b)^2}+
+\section{\cite{1}:14.79~~~~~$\displaystyle
+\int{\frac{dx}{x^3(ax+b)^3}}$}
+$$\int{\frac{1}{x^3(ax+b)^3}}=
+-\frac{1}{2bx^2(ax+b)^2}+
 \frac{2a}{b^2x(ax+b)^2}+
 \frac{9a^2}{b^3(ax+b)^2}+
 \frac{6a^3x}{b^4(ax+b)^2}-
 \frac{6a^2}{b^5}~\ln\left(\frac{ax+b}{x}\right)$$
 
-{\bf NOTE: }The equation given in the book is wrong. This is correct.
-
 <<*>>=
 )clear all
 
---S 82
+--S 85
 aa:=integrate(1/(x^3*(a*x+b)^3),x)
 --R
 --R   (1)
@@ -1143,11 +1103,9 @@ aa:=integrate(1/(x^3*(a*x+b)^3),x)
 --R       2 5 4       6 3     7 2
 --R     2a b x  + 4a b x  + 2b x
 --R                                          Type: Union(Expression Integer,...)
---E 82
-@
+--E
 
-<<*>>=
---S 83
+--S 86
 bb:=-1/(2*b*x^2*(a*x+b)^2)_
     +(2*a)/(b^2*x*(a*x+b)^2)_
     +(9*a^2)/(b^3*(a*x+b)^2)_
@@ -1165,10 +1123,9 @@ bb:=-1/(2*b*x^2*(a*x+b)^2)_
 --R       2 5 4       6 3     7 2
 --R     2a b x  + 4a b x  + 2b x
 --R                                                     Type: Expression Integer
---E 83
-@
-<<*>>=
---S 84
+--E
+
+--S 87
 cc:=aa-bb
 --R
 --R            2                 2           2    a x + b
@@ -1178,35 +1135,33 @@ cc:=aa-bb
 --R                                5
 --R                               b
 --R                                                     Type: Expression Integer
---E 84
-@
+--E
 
-<<*>>=
---S 85
+--S 88
 divlog:=rule(log(a/b) == log(a) - log(b))
 --R
 --R            a
 --R   (4)  log(-) == - log(b) + log(a)
 --R            b
 --R                        Type: RewriteRule(Integer,Integer,Expression Integer)
---E 85
-@
+--E
 
-<<*>>=
---S 86
-divlog cc
+--S 89     14:79 Schaums and Axiom agree
+dd:=divlog cc
 --R
 --R   (5)  0
 --R                                                     Type: Expression Integer
---E 86
+--E
 @
 
-\section{\cite{1}:14.80~~~~~$\displaystyle\int{(ax+b)^n~dx}$}
-$$\int{(ax+b)^n~dx}=
-\frac{(ax+b)^{n+1}}{(n+1)a}{\rm\ provided\ }n \ne -1$$
+\section{\cite{1}:14.80~~~~~$\displaystyle
+\int{(ax+b)^n~dx}$}
+$$\int{(ax+b)^n}=
+\frac{(ax+b)^{n+1}}{(n+1)a}{\rm\ provided\ }n \ne -1
+$$
 <<*>>=
 )clear all
---S 87
+--S 90
 aa:=integrate((a*x+b)^n,x)
 --R
 --R                   n log(a x + b)
@@ -1214,44 +1169,208 @@ aa:=integrate((a*x+b)^n,x)
 --R   (1)  -------------------------
 --R                 a n + a
 --R                                          Type: Union(Expression Integer,...)
---E 87
-@
+--E
+
+--S 91
+bb:=(a*x+b)^(n+1)/((n+1)*a)
+--R
+--R                 n + 1
+--R        (a x + b)
+--R   (2)  --------------
+--R            a n + a
+--R                                                     Type: Expression Integer
+--E
 
+--S 92
+cc:=aa-bb
+--R
+--R                   n log(a x + b)            n + 1
+--R        (a x + b)%e               - (a x + b)
+--R   (3)  ------------------------------------------
+--R                          a n + a
+--R                                                     Type: Expression Integer
+--E
+@
+This messy formula can be simplified using the explog rule:
 <<*>>=
---S 88
+--S 93
 explog:=rule(%e^(n*log(x)) == x^n)
 --R
 --R          n log(x)     n
---R   (2)  %e         == x
+--R   (4)  %e         == x
 --R                        Type: RewriteRule(Integer,Integer,Expression Integer)
---E 88
-@
+--E
 
-<<*>>=
---S 89 
-explog aa
+--S 94     14:80 Schaums and Axiom agree
+dd:=explog cc
 --R
---R                          n
---R        (a x + b)(a x + b)
---R   (3)  -------------------
---R              a n + a
+--R                   n + 1                     n
+--R        - (a x + b)      + (a x + b)(a x + b)
+--R   (5)  --------------------------------------
+--R                        a n + a
 --R                                                     Type: Expression Integer
---E 89
+--E
 @
+The numerator is clearly zero but I cannot get Axiom to simplify it.
 
-\section{\cite{1}:14.81~~~~~$\displaystyle\int{x(ax+b)^n~dx}$}
-$$\int{x(ax+b)^n~dx}=
+\section{\cite{1}:14.81~~~~~$\displaystyle
+\int{x(ax+b)^n~dx}$}
+$$\int{x(ax+b)^n}=
 \frac{(ax+b)^{n+2}}{(n+2)a^2}-\frac{b(ax+b)^{n+1}}{(n+1)a^2}
-{\rm\ provided\ }n \ne -1,-2$$
+{\rm\ provided\ }n \ne -1,-2
+$$
+<<*>>=
+)clear all
+--S 95
+aa:=integrate(x*(a*x+b)^n,x)
+--R
+--R           2     2  2              2   n log(a x + b)
+--R        ((a n + a )x  + a b n x - b )%e
+--R   (1)  ---------------------------------------------
+--R                       2 2     2      2
+--R                      a n  + 3a n + 2a
+--R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 96
+bb:=((a*x+b)^(n+2))/((n+2)*a^2)-(b*(a*x+b)^(n+1))/((n+1)*a^2)
+--R
+--R                        n + 2                        n + 1
+--R        (n + 1)(a x + b)      + (- b n - 2b)(a x + b)
+--R   (2)  --------------------------------------------------
+--R                          2 2     2      2
+--R                         a n  + 3a n + 2a
+--R                                                     Type: Expression Integer
+--E
 
-\section{\cite{1}:14.82~~~~~$\displaystyle\int{x^2(ax+b)^n~dx}$}
-$$\int{x^2(ax+b)^n~dx}=
+--S 97
+cc:=aa-bb
+--R
+--R   (3)
+--R          2     2  2              2   n log(a x + b)                     n + 2
+--R       ((a n + a )x  + a b n x - b )%e               + (- n - 1)(a x + b)
+--R     + 
+--R                          n + 1
+--R       (b n + 2b)(a x + b)
+--R  /
+--R      2 2     2      2
+--R     a n  + 3a n + 2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 98
+explog:=rule(%e^(n*log(x)) == x^n)
+--R
+--R          n log(x)     n
+--R   (4)  %e         == x
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 99     14:81 Schaums and Axiom agreement cannot be determined
+dd:=explog cc
+--R
+--R   (5)
+--R                         n + 2                      n + 1
+--R       (- n - 1)(a x + b)      + (b n + 2b)(a x + b)
+--R     + 
+--R          2     2  2              2          n
+--R       ((a n + a )x  + a b n x - b )(a x + b)
+--R  /
+--R      2 2     2      2
+--R     a n  + 3a n + 2a
+--R                                                     Type: Expression Integer
+--E
+@
+\section{\cite{1}:14.82~~~~~$\displaystyle
+\int{x^2(ax+b)^n~dx}$}
+$$\int{x^2(ax+b)^n}=
 \frac{(ax+b)^{n+2}}{(n+3)a^3}-
 \frac{2b(ax+b)^{n+2}}{(n+2)a^3}+
 \frac{b^2(ax+b)^{n+1}}{(n+1)a^3}
-{\rm\ provided\ }n \ne -1,-2,-3$$
+{\rm\ provided\ }n \ne -1,-2,-3
+$$
 
 <<*>>=
+)clear all
+--S 100
+aa:=integrate(x^2*(a*x+b)^n,x)
+--R
+--R   (1)
+--R      3 2     3      3  3     2   2    2     2       2        3   n log(a x + b)
+--R   ((a n  + 3a n + 2a )x  + (a b n  + a b n)x  - 2a b n x + 2b )%e
+--R   -----------------------------------------------------------------------------
+--R                              3 3     3 2      3      3
+--R                             a n  + 6a n  + 11a n + 6a
+--R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 101
+bb:=(a*x+b)^(n+3)/((n+3)*a^3)-(2*b*(a*x+b)^(n+2))/((n+2)*a^3)+(b^2*(a*x+b)^(n+1))/((n+1)*a^3)
+--R
+--R   (2)
+--R         2                   n + 3          2                      n + 2
+--R       (n  + 3n + 2)(a x + b)      + (- 2b n  - 8b n - 6b)(a x + b)
+--R     + 
+--R         2 2     2      2          n + 1
+--R       (b n  + 5b n + 6b )(a x + b)
+--R  /
+--R      3 3     3 2      3      3
+--R     a n  + 6a n  + 11a n + 6a
+--R                                                     Type: Expression Integer
+--E
+
+--S 102    14:82 Schaums and Axiom agreement cannot be determined
+cc:=aa-bb
+--R
+--R   (3)
+--R            3 2     3      3  3     2   2    2     2       2        3
+--R         ((a n  + 3a n + 2a )x  + (a b n  + a b n)x  - 2a b n x + 2b )
+--R      *
+--R           n log(a x + b)
+--R         %e
+--R     + 
+--R           2                   n + 3        2                      n + 2
+--R       (- n  - 3n - 2)(a x + b)      + (2b n  + 8b n + 6b)(a x + b)
+--R     + 
+--R           2 2     2      2          n + 1
+--R       (- b n  - 5b n - 6b )(a x + b)
+--R  /
+--R      3 3     3 2      3      3
+--R     a n  + 6a n  + 11a n + 6a
+--R                                                     Type: Expression Integer
+--E
+@
+\section{\cite{1}:14.83~~~~~$\displaystyle
+\int{x^m(ax+b)^n}~dx$}
+$$\int{x^m(ax+b)^n}
+\left\{
+\begin{array}{l}
+\displaystyle
+\frac{x^{m+1}(ax+b)^n}{m+n+1}
++\frac{nb}{m+n+1}\int{x^m(ax+b)^{n-1}}\\
+\\
+\displaystyle
+\frac{x^{m+1}(ax+b)^{n+1}}{(m+n+1)a}
+-\frac{mb}{(m+n+1)a}\int{x^{m-1}(ax+b)^n}\\
+\\
+\displaystyle
+\frac{-x^{m+1}(ax+b)^{n+1}}{(n+1)b}
++\frac{m+n+2}{(n+1)b}\int{x^m(ax+b)^{n+1}}\\
+\end{array}
+\right.
+$$
+
+<<*>>=
+--S 103    14:83 Axiom cannot do this integration
+aa:=integrate(x^m*(a*x+b)^n,x)
+--R
+--R           x
+--R         ++    m          n
+--I   (1)   |   %U (b + %U a) d%U
+--R        ++
+--R                                          Type: Union(Expression Integer,...)
+--E
+
 )spool
 )lisp (bye)
 @



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Item   14:150 Schaums and Axiom DISAGREE BY A NON-CONSTANT
in schaum7.input.pamphlet is particularly interesting because
it appears that the derivative of Axiom's answer is the original
integrand but the derivative of Schaum's answer is not, implying
that Schaum's has a mistake. This will be verified using other 
systems later.

Axiom is weak in handling certain simplifications. Future work is
planned to correct this.

Richard Fateman has given me permission to use his TILU pattern
integration database in Axiom. This should give us much broader
integration results. TILU has not been tested against Schaums
but this testing will occur during the merge.

schaum2.input.pamphet
  14:84 Schaums and Axiom agree
  14:85 Schaums and Axiom agree
  14:86 Schaums and Axiom agree
  14:87a Schaums and Axiom differ by a constant
  14:87b Schaums and Axiom differ by a constant
  14:88 Schaums and Axiom differ by a constant
  14:89 Schaums and Axiom differ by a constant
  14:90 Axiom cannot simplify this expression
  14:91 Axiom cannot simplify this expression
  14:92 Axiom cannot simplify this expression
  14:93 Schaums and Axiom agree
  14:94 Axiom cannot do this integral
  14:95 Axiom cannot do this integral
  14:96 Axiom cannot do this integral
  14:97 Axiom cannot do this integral
  14:98 Axiom cannot do this integral
  14:99 Axiom cannot simplify this expression
  14:100 Axiom cannot simplify this expression
  14:101 Axiom cannot simplify this expression
  14:102 Axiom cannot do this integral
  14:103 Axiom cannot do this integral
  14:104 Axiom cannot do this integral

schaum3.input.pamphlet
  14:105 Schaums and Axiom agree
  14:106 Schaums and Axiom agree
  14:107 Schaums and Axiom agree
  14:108 Schaums and Axiom agree
  14:109 Schaums and Axiom agree
  14:110 Axiom cannot do this integral
  14:111 Schaums and Axiom agree
  14:112 Axiom cannot do this integral

schaum4.input.pamphlet
  14:113 Schaums and Axiom agree
  14:114 Axiom cannot simplify these answers
  14:115 Axiom cannot simplify these answers
  14:116 Axiom cannot compute this integral
  14:117 Axiom cannot compute this integral
  14:118 Axiom cannot compute this integral
  14:119 Axiom cannot compute this integral

schaum5.input.pamphlet
  14:120 Axiom cannot simplify these answers
  14:121 Axiom cannot simplify this answer
  14:122 Axiom cannot simplify this answer
  14:123 Axiom cannot simplify these results
  14:124 Axiom cannot simplify this result

schaum6.input.pamphlet
  14:125 Schaums and Axiom agree
  14:126 Schaums and Axiom agree
  14:127 Schaums and Axiom agree
  14:128 Schaums and Axiom agree
  14:129 Schaums and Axiom agree
  14:130 Schaums and Axiom agree
  14:131 Schaums and Axiom agree
  14:132 Schaums and Axiom agree
  14:133 Schaums and Axiom agree
  14:134 Schaums and Axiom differ by a constant
  14:135 Schaums and Axiom agree
  14:136 Schaums and Axiom agree
  14:137 Schaums and Axiom agree
  14:138 Schaums and Axiom agree
  14:139 Axiom cannot do this integral
  14:140 Schaums and Axiom cannot simplify this expression
  14:141 Axiom cannot do this integral
  14:142 Axiom cannot do this integral
  14:143 Axiom cannot do this integral

schaum7.input.pamphlet
  14:144 Schaums and Axiom agree
  14:145 Schaums and Axiom agree
  14:146 Schaums and Axiom agree
  14:147 Schaums and Axiom agree
  14:148 Schaums and Axiom agree
  14:149 Schaums and Axiom agree
  14:150 Schaums and Axiom DISAGREE BY A NON-CONSTANT
  14:151 Schaums and Axiom agree
  14:152 Schaums and Axiom agree
  14:153 Schaums and Axiom agree
  14:154 Schaums and Axiom agree
  14:155 Schaums and Axiom agree
  14:156 Schaums and Axiom agree
  14:157 Schaums and Axiom agree
  14:158 Axiom cannot do this integral
  14:159 Axiom cannot simplify this expression
  14:160 Axiom cannot compute this integral
  14:161 Axiom cannot compute this integral
  14:162 Axiom cannot compute this integral

======================================================================
diff --git a/changelog b/changelog
index 346e9f2..eda7bfd 100644
--- a/changelog
+++ b/changelog
@@ -1,3 +1,9 @@
+20080416 tpd src/input/schaum7.input show Schaums-Axiom equivalence
+20080416 tpd src/input/schaum6.input show Schaums-Axiom equivalence
+20080416 tpd src/input/schaum5.input show Schaums-Axiom equivalence
+20080416 tpd src/input/schaum4.input show Schaums-Axiom equivalence
+20080416 tpd src/input/schaum3.input show Schaums-Axiom equivalence
+20080416 tpd src/input/schaum2.input show Schaums-Axiom equivalence
 20080415 tpd src/input/schaum1.input show Schaums-Axiom equivalence
 20080414 tpd src/input/Makefile add integration regression testing	
 20080414 tpd src/input/schaum34.input integrals of csch(ax)
diff --git a/src/input/schaum2.input.pamphlet b/src/input/schaum2.input.pamphlet
index ba16925..184122e 100644
--- a/src/input/schaum2.input.pamphlet
+++ b/src/input/schaum2.input.pamphlet
@@ -7,15 +7,18 @@
 \eject
 \tableofcontents
 \eject
-\section{\cite{1}:14.84~~~~~$\displaystyle\int{\frac{dx}{\sqrt{ax+b}}}$}
-$$\int{\frac{1}{\sqrt{ax+b}}}=\frac{2\sqrt{ax+b}}{a}$$
+\section{\cite{1}:14.84~~~~~$\displaystyle
+\int{\frac{dx}{\sqrt{ax+b}}}$}
+$$\int{\frac{1}{\sqrt{ax+b}}}=
+\frac{2\sqrt{ax+b}}{a}
+$$
 <<*>>=
 )spool schaum2.output
 )set message test on
 )set message auto off
 )clear all
 
---S 1 of 92
+--S 1
 aa:=integrate(1/sqrt(a*x+b),x)
 --R 
 --R
@@ -25,9 +28,8 @@ aa:=integrate(1/sqrt(a*x+b),x)
 --R             a
 --R                                          Type: Union(Expression Integer,...)
 --E 
-@
-<<*>>=
---S 2 of 92
+
+--S 2
 bb:=(2*sqrt(a*x+b))/a
 --R 
 --R
@@ -37,9 +39,8 @@ bb:=(2*sqrt(a*x+b))/a
 --R             a
 --R                                                     Type: Expression Integer
 --E
-@
-<<*>>=
---S 3 of 92
+
+--S 3      14:84 Schaums and Axiom agree
 cc:=aa-bb
 --R 
 --R
@@ -48,12 +49,15 @@ cc:=aa-bb
 --E
 @
 
-\section{\cite{1}:14.85~~~~~$\displaystyle\int{\frac{x~dx}{\sqrt{ax+b}}}$}
-$$\int{\frac{x}{\sqrt{ax+b}}}=\frac{2(ax-2b)}{3a^2}\sqrt{ax+b}$$
+\section{\cite{1}:14.85~~~~~$\displaystyle
+\int{\frac{x~dx}{\sqrt{ax+b}}}$}
+$$\int{\frac{x}{\sqrt{ax+b}}}=
+\frac{2(ax-2b)}{3a^2}\sqrt{ax+b}
+$$
 <<*>>=
 )clear all
 
---S 4 of 92
+--S 4
 aa:=integrate(x/sqrt(a*x+b),x)
 --R 
 --R
@@ -64,9 +68,8 @@ aa:=integrate(x/sqrt(a*x+b),x)
 --R                 3a
 --R                                          Type: Union(Expression Integer,...)
 --E 
-@
-<<*>>=
---S 5 of 92
+
+--S 5
 bb:=(2*(a*x-2*b))/(3*a^2)*sqrt(a*x+b)
 --R 
 --R
@@ -77,9 +80,8 @@ bb:=(2*(a*x-2*b))/(3*a^2)*sqrt(a*x+b)
 --R                 3a
 --R                                                     Type: Expression Integer
 --E
-@
-<<*>>=
---S 6 of 92
+
+--S 6      14:85 Schaums and Axiom agree
 cc:=aa-bb
 --R 
 --R
@@ -88,13 +90,15 @@ cc:=aa-bb
 --E
 @
 
-\section{\cite{1}:14.86~~~~~$\displaystyle\int{\frac{x^2~dx}{\sqrt{ax+b}}}$}
+\section{\cite{1}:14.86~~~~~$\displaystyle
+\int{\frac{x^2~dx}{\sqrt{ax+b}}}$}
 $$\int{\frac{x}{\sqrt{ax+b}}}=
-\frac{2(3a^2x^2-4abx+8b^2)}{15a^2}\sqrt{ax+b}$$
+\frac{2(3a^2x^2-4abx+8b^2)}{15a^2}\sqrt{ax+b}
+$$
 <<*>>=
 )clear all
 
---S 7 of 92
+--S 7
 aa:=integrate(x^2/sqrt(a*x+b),x)
 --R 
 --R
@@ -105,9 +109,8 @@ aa:=integrate(x^2/sqrt(a*x+b),x)
 --R                       15a
 --R                                          Type: Union(Expression Integer,...)
 --E 
-@
-<<*>>=
---S 8 of 92
+
+--S 8
 bb:=(2*(3*a^2*x^2-4*a*b*x+8*b^2))/(15*a^3)*sqrt(a*x+b)
 --R 
 --R
@@ -118,9 +121,8 @@ bb:=(2*(3*a^2*x^2-4*a*b*x+8*b^2))/(15*a^3)*sqrt(a*x+b)
 --R                       15a
 --R                                                     Type: Expression Integer
 --E
-@
-<<*>>=
---S 9 of 92
+
+--S 9      14:86 Schaums and Axiom agree
 cc:=aa-bb
 --R 
 --R
@@ -129,7 +131,8 @@ cc:=aa-bb
 --E
 @
 
-\section{\cite{1}:14.87~~~~~$\displaystyle\int{\frac{dx}{x\sqrt{ax+b}}}$}
+\section{\cite{1}:14.87~~~~~$\displaystyle
+\int{\frac{dx}{x\sqrt{ax+b}}}$}
 $$\int{\frac{1}{x\sqrt{ax+b}}}=
 \left\{
 \begin{array}{l}
@@ -139,13 +142,14 @@ $$\int{\frac{1}{x\sqrt{ax+b}}}=
 \displaystyle
 \frac{2}{\sqrt{-b}}~\tan^{-1}\sqrt{\frac{ax+b}{-b}}
 \end{array}
-\right.$$
+\right.
+$$
 
 Note: the first answer assumes $b > 0$ and the second assumes $b < 0$.
 <<*>>=
 )clear all
 
---S 10 of 92
+--S 10
 aa:=integrate(1/(x*sqrt(a*x+b)),x)
 --R 
 --R
@@ -161,7 +165,7 @@ aa:=integrate(1/(x*sqrt(a*x+b)),x)
 @
 Cleary Spiegel's first answer assumes $b > 0$:
 <<*>>=
---S 11 of 92
+--S 11
 bb1:=1/sqrt(b)*log((sqrt(a*x+b)-sqrt(b))/(sqrt(a*x+b)+sqrt(b)))
 --R 
 --R
@@ -178,7 +182,7 @@ bb1:=1/sqrt(b)*log((sqrt(a*x+b)-sqrt(b))/(sqrt(a*x+b)+sqrt(b)))
 @
 So we try the difference of the two results
 <<*>>=
---S 12 of 92
+--S 12
 cc11:=aa.1-bb1
 --R
 --R               +-------+    +-+             +-------+              +-+
@@ -197,7 +201,7 @@ But the results don't simplify to 0. So we try some other tricks.
 Since both functions are of the form log(f(x))/sqrt(b) we extract
 the f(x) from each. First we get the function from Axiom's first answer:
 <<*>>=
---S 13 of 92
+--S 13
 ff:=exp(aa.1*sqrt(b))
 --R
 --R             +-------+              +-+
@@ -209,7 +213,7 @@ ff:=exp(aa.1*sqrt(b))
 @
 and we get the same form from Spiegel's answer
 <<*>>=
---S 14 of 92
+--S 14
 gg:=exp(bb1*sqrt(b))
 --R
 --R         +-------+    +-+
@@ -226,7 +230,7 @@ denominator by $1 == (sqrt(a*x+b) - sqrt(b))/(sqrt(a*x+b) - sqrt(b))$.
 
 First we multiply the numerator by $(sqrt(a*x+b) - sqrt(b))$
 <<*>>=
---S 15 of 92
+--S 15
 gg1:=gg*(sqrt(a*x+b) - sqrt(b))
 --R
 --R            +-+ +-------+
@@ -239,7 +243,7 @@ gg1:=gg*(sqrt(a*x+b) - sqrt(b))
 @
 Now we multiply the denominator by $(sqrt(a*x+b) - sqrt(b))$
 <<*>>=
---S 16 of 92
+--S 16
 gg2:=gg1/(sqrt(a*x+b) - sqrt(b))
 --R
 --R            +-+ +-------+
@@ -251,7 +255,7 @@ gg2:=gg1/(sqrt(a*x+b) - sqrt(b))
 @
 and now we multiply by the integration constant $a*sqrt(b)$
 <<*>>=
---S 17 of 92
+--S 17
 gg3:=gg2*(a*sqrt(b))
 --R
 --R             +-------+              +-+
@@ -263,7 +267,7 @@ gg3:=gg2*(a*sqrt(b))
 @
 and when we difference this with ff, the Axiom answer we get:
 <<*>>=
---S 18 of 92
+--S 18     14:87a Schaums and Axiom differ by a constant
 ff-gg3
 --R
 --R   (9)  0
@@ -275,7 +279,7 @@ So the constant of integration difference is $a*sqrt(b)$
 Now we look at the second equations. We difference Axiom's second answer
 from Spiegel's answer:
 <<*>>=
---S 19 of 92
+--S 19
 t1:=aa.2-bb1
 --R
 --R                      +-------+    +-+               +---+ +-------+
@@ -292,7 +296,7 @@ t1:=aa.2-bb1
 and again they do not simplify to zero. But we can show that both answers
 differ by a constant because the derivative is zero:
 <<*>>=
---S 20 of 92
+--S 20
 D(t1,x)
 --R
 --R   (11)  0
@@ -303,7 +307,7 @@ D(t1,x)
 Rather than find the constant this time we will differentiate both
 answers and compare them with the original equation.
 <<*>>=
---S 21 of 92
+--S 21
 target:=1/(x*sqrt(a*x+b))
 --R
 --R              1
@@ -315,7 +319,7 @@ target:=1/(x*sqrt(a*x+b))
 @
 and we select the second Axiom solution
 <<*>>=
---S 22 of 92
+--S 22
 aa2:=aa.2
 --R
 --R                  +---+ +-------+
@@ -330,7 +334,7 @@ aa2:=aa.2
 @
 take its derivative
 <<*>>=
---S 23 of 92
+--S 23
 ad2:=D(aa2,x)
 --R
 --R              1
@@ -343,7 +347,7 @@ ad2:=D(aa2,x)
 When we take the difference of Axiom's input and the derivative of the
 output we see:
 <<*>>=
---S 24 of 92
+--S 24
 ad2-target
 --R
 --R   (15)  0
@@ -355,7 +359,7 @@ Thus the original equation and Axiom's derivative of the integral are equal.
 Now we do the same with Spiegel's answer. We take the derivative of his
 answer.
 <<*>>=
---S 25 of 92
+--S 25
 ab1:=D(bb1,x)
 --R
 --R                +-------+    +-+
@@ -368,7 +372,7 @@ ab1:=D(bb1,x)
 @
 and we difference it from the original equation
 <<*>>=
---S 26 of 92
+--S 26     14:87b Schaums and Axiom differ by a constant
 ab1-target
 --R
 --R   (17)  0
@@ -380,13 +384,15 @@ Thus the original equation and Spiegel's derivative of the integral are equal.
 So we can conclude that both second answers are correct although they differ
 by a constant of integration.
 
-\section{\cite{1}:14.88~~~~~$\displaystyle\int{\frac{dx}{x^2\sqrt{ax+b}}}$}
+\section{\cite{1}:14.88~~~~~$\displaystyle
+\int{\frac{dx}{x^2\sqrt{ax+b}}}$}
 $$\int{\frac{1}{x^2\sqrt{ax+b}}}=
--\frac{\sqrt{ax+b}}{bx}-\frac{a}{2b}~\int{\frac{1}{x\sqrt{ax+b}}}$$
+-\frac{\sqrt{ax+b}}{bx}-\frac{a}{2b}~\int{\frac{1}{x\sqrt{ax+b}}}
+$$
 <<*>>=
 )clear all
 
---S 27 of 92
+--S 27
 aa:=integrate(1/(x^2*sqrt(a*x+b)),x)
 --R 
 --R
@@ -412,7 +418,7 @@ aa:=integrate(1/(x^2*sqrt(a*x+b)),x)
 In order to write down the book answer we need to first take the
 integral which has two results
 <<*>>=
---S 28 of 92
+--S 28
 dd:=integrate(1/(x*sqrt(a*x+b)),x)
 --R 
 --R
@@ -429,7 +435,7 @@ dd:=integrate(1/(x*sqrt(a*x+b)),x)
 and derive two results for the book answer. The first result assumes
 $b > 0$
 <<*>>=
---S 29 of 92
+--S 29
 bb1:=-sqrt(a*x+b)/(b*x)-a/(2*b)*dd.1
 --R 
 --R
@@ -445,7 +451,7 @@ bb1:=-sqrt(a*x+b)/(b*x)-a/(2*b)*dd.1
 @
 and the second result assumes $b < 0$.
 <<*>>=
---S 30 of 92
+--S 30
 bb2:=-sqrt(a*x+b)/(b*x)-a/(2*b)*dd.2
 --R 
 --R
@@ -463,7 +469,7 @@ bb2:=-sqrt(a*x+b)/(b*x)-a/(2*b)*dd.2
 So we compute the difference of Axiom's first result with Spiegel's
 first result
 <<*>>=
---S 31 of 92
+--S 31
 cc11:=bb1-aa.1
 --R
 --R   (5)
@@ -484,7 +490,7 @@ cc11:=bb1-aa.1
 @
 we compute its derivative
 <<*>>=
---S 32 of 92
+--S 32
 D(cc11,x)
 --R
 --R   (6)  0
@@ -495,7 +501,7 @@ and we can see that the answers differ by a constant, the constant of
 integration. So Axiom's first answer should differentiate back to the target
 equation.
 <<*>>=
---S 33 of 92
+--S 33
 target:=1/(x^2*sqrt(a*x+b))
 --R
 --R              1
@@ -507,7 +513,7 @@ target:=1/(x^2*sqrt(a*x+b))
 @
 We differentiate Axiom's first answer
 <<*>>=
---S 34 of 92
+--S 34
 ad1:=D(aa.1,x)
 --R
 --R                             +-+ +-------+              2
@@ -520,7 +526,7 @@ ad1:=D(aa.1,x)
 @
 and subtract it from the target equation
 <<*>>=
---S 35 of 92
+--S 35
 ad1-target
 --R
 --R   (9)  0
@@ -529,7 +535,7 @@ ad1-target
 @
 and now we do the same with first Spiegel's answer:
 <<*>>=
---S 36 of 92
+--S 36
 bd1:=D(bb1,x)
 --R
 --R                                +-+ +-------+              2
@@ -542,7 +548,7 @@ bd1:=D(bb1,x)
 @
 and we subtract it from the target
 <<*>>=
---S 37 of 92
+--S 37     
 bd1-target
 --R
 --R   (11)  0
@@ -555,7 +561,7 @@ integrals differ by a constant.
 Now we look at the second answers. We difference the answers and can
 see immediately that they are equal.
 <<*>>=
---S 38 of 92
+--S 38     14:88 Schaums and Axiom differ by a constant
 cc22:=bb2-aa.2
 --R 
 --R
@@ -564,13 +570,15 @@ cc22:=bb2-aa.2
 --E
 @
 
-\section{\cite{1}:14.89~~~~~$\displaystyle\int{\sqrt{ax+b}~dx}$}
+\section{\cite{1}:14.89~~~~~$\displaystyle
+\int{\sqrt{ax+b}~dx}$}
 $$\int{\sqrt{ax+b}}=
-\frac{2\sqrt{(ax+b)^3}}{3a}$$
+\frac{2\sqrt{(ax+b)^3}}{3a}
+$$
 <<*>>=
 )clear all
 
---S 39 of 92
+--S 39
 aa:=integrate(sqrt(a*x+b),x)
 --R 
 --R
@@ -582,7 +590,7 @@ aa:=integrate(sqrt(a*x+b),x)
 --E 
 @
 <<*>>=
---S 40 of 92
+--S 40
 bb:=(2*sqrt((a*x+b)^3))/(3*a)
 --R 
 --R
@@ -595,7 +603,7 @@ bb:=(2*sqrt((a*x+b)^3))/(3*a)
 --E
 @
 <<*>>=
---S 41 of 92
+--S 41
 cc:=aa-bb
 --R
 --R            +----------------------------+
@@ -608,7 +616,7 @@ cc:=aa-bb
 @
 Since this didn't simplify we could check each answer using the derivative
 <<*>>=
---S 42 of 92
+--S 42
 target:=sqrt(a*x+b)
 --R
 --R         +-------+
@@ -618,7 +626,7 @@ target:=sqrt(a*x+b)
 @
 We take the derivative of Axiom's answer
 <<*>>=
---S 43 of 92
+--S 43
 t1:=D(aa,x)
 --R
 --R          a x + b
@@ -630,7 +638,7 @@ t1:=D(aa,x)
 @
 And we subtract the target from the derivative of Axiom's answer
 <<*>>=
---S 44 of 92
+--S 44
 t1-target
 --R
 --R   (6)  0
@@ -639,7 +647,7 @@ t1-target
 @
 So they are equal. Now we do the same with Spiegel's answer
 <<*>>=
---S 45 of 92
+--S 45
 t2:=D(bb,x)
 --R
 --R                2 2             2
@@ -653,7 +661,7 @@ t2:=D(bb,x)
 @
 The numerator is
 <<*>>=
---S 46 of 92
+--S 46
 nn:=(a*x+b)^2
 --R
 --R         2 2             2
@@ -662,7 +670,7 @@ nn:=(a*x+b)^2
 --E
 @
 <<*>>=
---S 47 of 92
+--S 47
 mm:=(a*x+b)^3
 --R
 --R         3 3     2   2       2     3
@@ -672,7 +680,7 @@ mm:=(a*x+b)^3
 @
 which expands to Spiegel's version.
 <<*>>=
---S 48 of 92
+--S 48     14:89 Schaums and Axiom differ by a constant
 result=nn/sqrt(mm)
 --R
 --R                         2 2             2
@@ -686,13 +694,15 @@ result=nn/sqrt(mm)
 @
 and this reduces to $\sqrt{ax+b}$
 
-\section{\cite{1}:14.90~~~~~$\displaystyle\int{x\sqrt{ax+b}~dx}$}
+\section{\cite{1}:14.90~~~~~$\displaystyle
+\int{x\sqrt{ax+b}~dx}$}
 $$\int{x\sqrt{ax+b}}=
-\frac{2(3ax-2b)}{15a^2}~\sqrt{(ax+b)^3}$$
+\frac{2(3ax-2b)}{15a^2}~\sqrt{(ax+b)^3}
+$$
 <<*>>=
 )clear all
 
---S 49 of 92
+--S 49
 aa:=integrate(x*sqrt(a*x+b),x)
 --R 
 --R
@@ -703,9 +713,8 @@ aa:=integrate(x*sqrt(a*x+b),x)
 --R                      15a
 --R                                          Type: Union(Expression Integer,...)
 --E 
-@
-<<*>>=
---S 50 of 92
+
+--S 50
 bb:=(2*(3*a*x-2*b))/(15*a^2)*sqrt((a*x+b)^3)
 --R 
 --R
@@ -717,9 +726,8 @@ bb:=(2*(3*a*x-2*b))/(15*a^2)*sqrt((a*x+b)^3)
 --R                           15a
 --R                                                     Type: Expression Integer
 --E
-@
-<<*>>=
---S 51 of 92
+
+--S 51
 cc:=aa-bb
 --R
 --R   (3)
@@ -737,15 +745,14 @@ cc:=aa-bb
 @
 If we had the terms
 <<*>>=
---S 52 of 92
+--S 52
 t1:=(3*a*x-2*b)
 --R
 --R   (4)  3a x - 2b
 --R                                                     Type: Polynomial Integer
 --E
-@
-<<*>>=
---S 53 of 92
+
+--S 53
 t2:=(a*x+b)
 --R
 --R   (5)  a x + b
@@ -754,7 +761,7 @@ t2:=(a*x+b)
 @
 We can construct the Axiom result 
 <<*>>=
---S 54 of 92
+--S 54
 2*t1*t2*sqrt(t2)/(15*a^2)
 --R
 --R           2 2              2  +-------+
@@ -767,7 +774,7 @@ We can construct the Axiom result
 @
 and we can construct the Spiegel result
 <<*>>=
---S 55 of 92
+--S 55
 2*t1*sqrt(t2^3)/(15*a^2)
 --R
 --R                    +----------------------------+
@@ -781,7 +788,7 @@ and we can construct the Spiegel result
 @
 the difference of these two depends on
 <<*>>=
---S 56 of 92
+--S 56     14:90 Axiom cannot simplify this expression
 t2*sqrt(t2)-sqrt(t2^3)
 --R
 --R           +----------------------------+
@@ -791,14 +798,16 @@ t2*sqrt(t2)-sqrt(t2^3)
 --E
 @
 
-\section{\cite{1}:14.91~~~~~$\displaystyle\int{x^2\sqrt{ax+b}~dx}$}
+\section{\cite{1}:14.91~~~~~$\displaystyle
+\int{x^2\sqrt{ax+b}~dx}$}
 $$\int{x^2\sqrt{ax+b}}=
-\frac{2(15a^2x^2-12abx+8b^2)}{105a^2}~\sqrt{(a+bx)^3}$$
+\frac{2(15a^2x^2-12abx+8b^2)}{105a^2}~\sqrt{(a+bx)^3}
+$$
 Note: the sqrt term is almost certainly $\sqrt{(ax+b)}$
 <<*>>=
 )clear all
 
---S 57 of 92
+--S 57
 aa:=integrate(x^2*sqrt(a*x+b),x)
 --R 
 --R
@@ -809,9 +818,8 @@ aa:=integrate(x^2*sqrt(a*x+b),x)
 --R                            105a
 --R                                          Type: Union(Expression Integer,...)
 --E 
-@
-<<*>>=
---S 58 of 92
+
+--S 58
 bb:=(2*(15*a^2*x^2-12*a*b*x+8*b^2))/(105*a^2)*sqrt((a*x+b)^3)
 --R 
 --R
@@ -823,9 +831,8 @@ bb:=(2*(15*a^2*x^2-12*a*b*x+8*b^2))/(105*a^2)*sqrt((a*x+b)^3)
 --R                                  105a
 --R                                                     Type: Expression Integer
 --E
-@
-<<*>>=
---S 59 of 92
+
+--S 59     14:91 Axiom cannot simplify this expression
 cc:=aa-bb
 --R 
 --R
@@ -843,13 +850,15 @@ cc:=aa-bb
 --E
 @
 
-\section{\cite{1}:14.92~~~~~$\displaystyle\int{\frac{\sqrt{ax+b}}{x}~dx}$}
+\section{\cite{1}:14.92~~~~~$\displaystyle
+\int{\frac{\sqrt{ax+b}}{x}~dx}$}
 $$\int{\frac{\sqrt{ax+b}}{x}}=
-2\sqrt{ax+b}+b~\int{\frac{1}{x\sqrt{ax+b}}}$$
+2\sqrt{ax+b}+b~\int{\frac{1}{x\sqrt{ax+b}}}
+$$
 <<*>>=
 )clear all
 
---S 60 of 92
+--S 60
 aa:=integrate(sqrt(a*x+b)/x,x)
 --R 
 --R
@@ -865,9 +874,8 @@ aa:=integrate(sqrt(a*x+b)/x,x)
 --R                    \|- b
 --R                                     Type: Union(List Expression Integer,...)
 --E 
-@
-<<*>>=
---S 61 of 92
+
+--S 61
 dd:=integrate(1/(x*sqrt(a*x+b)),x)
 --R 
 --R
@@ -880,9 +888,8 @@ dd:=integrate(1/(x*sqrt(a*x+b)),x)
 --R                         \|b                             \|- b
 --R                                     Type: Union(List Expression Integer,...)
 --E
-@
-<<*>>=
---S 62 of 92
+
+--S 62
 bb1:=2*sqrt(a*x+b)+b*dd.1
 --R 
 --R
@@ -895,9 +902,8 @@ bb1:=2*sqrt(a*x+b)+b*dd.1
 --R                                  \|b
 --R                                                     Type: Expression Integer
 --E
-@
-<<*>>=
---S 63 of 92
+
+--S 63
 bb2:=2*sqrt(a*x+b)+b*dd.2
 --R 
 --R
@@ -910,9 +916,8 @@ bb2:=2*sqrt(a*x+b)+b*dd.2
 --R                             \|- b
 --R                                                     Type: Expression Integer
 --E
-@
-<<*>>=
---S 64 of 92
+
+--S 64
 cc11:=bb1-aa.1
 --R 
 --R
@@ -926,9 +931,8 @@ cc11:=bb1-aa.1
 --R                                       \|b
 --R                                                     Type: Expression Integer
 --E
-@
-<<*>>=
---S 65 of 92
+
+--S 65
 cc12:=bb1-aa.2
 --R 
 --R
@@ -942,9 +946,8 @@ cc12:=bb1-aa.2
 --R                                        \|b
 --R                                                     Type: Expression Integer
 --E
-@
-<<*>>=
---S 66 of 92
+
+--S 66
 cc21:=bb2-aa.1
 --R 
 --R
@@ -958,9 +961,8 @@ cc21:=bb2-aa.1
 --R                                     \|- b
 --R                                                     Type: Expression Integer
 --E
-@
-<<*>>=
---S 67 of 92
+
+--S 67     14:92 Axiom cannot simplify this expression
 cc22:=bb2-aa.2
 --R 
 --R
@@ -976,13 +978,15 @@ cc22:=bb2-aa.2
 --E
 @
 
-\section{\cite{1}:14.93~~~~~$\displaystyle\int{\frac{\sqrt{ax+b}}{x^2}~dx}$}
+\section{\cite{1}:14.93~~~~~$\displaystyle
+\int{\frac{\sqrt{ax+b}}{x^2}~dx}$}
 $$\int{\frac{\sqrt{ax+b}}{x^2}}=
--\frac{\sqrt{ax+b}}{x}+\frac{a}{2}~\int{\frac{1}{x\sqrt{ax+b}}}$$
+-\frac{\sqrt{ax+b}}{x}+\frac{a}{2}~\int{\frac{1}{x\sqrt{ax+b}}}
+$$
 <<*>>=
 )clear all
 
---S 68 of 92
+--S 68
 aa:=integrate(sqrt(a*x+b)/x^2,x)
 --R 
 --R
@@ -1003,9 +1007,8 @@ aa:=integrate(sqrt(a*x+b)/x^2,x)
 --R                        x\|- b
 --R                                     Type: Union(List Expression Integer,...)
 --E 
-@
-<<*>>=
---S 69 of 92
+
+--S 69
 dd:=integrate(1/(x*sqrt(a*x+b)),x)
 --R 
 --R
@@ -1018,9 +1021,8 @@ dd:=integrate(1/(x*sqrt(a*x+b)),x)
 --R                         \|b                             \|- b
 --R                                     Type: Union(List Expression Integer,...)
 --E
-@
-<<*>>=
---S 70 of 92
+
+--S 70
 bb1:=-sqrt(a*x+b)/x+a/2*dd.1
 --R 
 --R
@@ -1033,9 +1035,8 @@ bb1:=-sqrt(a*x+b)/x+a/2*dd.1
 --R                                  2x\|b
 --R                                                     Type: Expression Integer
 --E
-@
-<<*>>=
---S 71 of 92
+
+--S 71
 bb2:=-sqrt(a*x+b)/x+a/2*dd.2
 --R 
 --R
@@ -1048,18 +1049,16 @@ bb2:=-sqrt(a*x+b)/x+a/2*dd.2
 --R                            x\|- b
 --R                                                     Type: Expression Integer
 --E
-@
-<<*>>=
---S 72 of 92
+
+--S 72
 cc11:=bb1-aa.1
 --R 
 --R
 --R   (5)  0
 --R                                                     Type: Expression Integer
 --E
-@
-<<*>>=
---S 73 of 92
+
+--S 73
 cc21:=bb-aa.1
 --R 
 --R
@@ -1073,9 +1072,8 @@ cc21:=bb-aa.1
 --R                                    2x\|b
 --R                                                     Type: Expression Integer
 --E
-@
-<<*>>=
---S 74 of 92
+
+--S 74
 cc12:=bb1-aa.2
 --R 
 --R
@@ -1089,9 +1087,8 @@ cc12:=bb1-aa.2
 --R                                   2\|- b \|b
 --R                                                     Type: Expression Integer
 --E
-@
-<<*>>=
---S 75 of 92
+
+--S 75     14:93 Schaums and Axiom agree
 cc22:=bb2-aa.2
 --R 
 --R
@@ -1100,14 +1097,16 @@ cc22:=bb2-aa.2
 --E
 @
 
-\section{\cite{1}:14.94~~~~~$\displaystyle\int{\frac{x^m}{\sqrt{ax+b}}~dx}$}
+\section{\cite{1}:14.94~~~~~$\displaystyle
+\int{\frac{x^m}{\sqrt{ax+b}}~dx}$}
 $$\int{\frac{x^m}{\sqrt{ax+b}}}=
 \frac{2x^m\sqrt{ax+b}}{(2m+1)a}-\frac{2mb}{(2m+1)a}
-~\int{\frac{x^{m-1}}{\sqrt{ax+b}}}$$
+~\int{\frac{x^{m-1}}{\sqrt{ax+b}}}
+$$
 <<*>>=
 )clear all
 
---S 76 of 92
+--S 76     14:94 Axiom cannot do this integral
 aa:=integrate(x^m/sqrt(a*x+b),x)
 --R 
 --R
@@ -1120,14 +1119,16 @@ aa:=integrate(x^m/sqrt(a*x+b),x)
 --E 
 @
 
-\section{\cite{1}:14.95~~~~~$\displaystyle\int{\frac{dx}{x^m\sqrt{ax+b}}}$}
+\section{\cite{1}:14.95~~~~~$\displaystyle
+\int{\frac{dx}{x^m\sqrt{ax+b}}}$}
 $$\int{\frac{1}{x^m\sqrt{ax+b}}}=
 -\frac{\sqrt{ax+b}}{(m-1)bx^{m-1}}-\frac{(2m-3)a}{(2m-2)b}
-~\int{\frac{1}{x^{m-1}\sqrt{ax+b}}}$$
+~\int{\frac{1}{x^{m-1}\sqrt{ax+b}}}
+$$
 <<*>>=
 )clear all
 
---S 77 of 92
+--S 77     14:95 Axiom cannot do this integral
 aa:=integrate(1/(x^m*sqrt(a*x+b)),x)
 --R 
 --R
@@ -1140,14 +1141,16 @@ aa:=integrate(1/(x^m*sqrt(a*x+b)),x)
 --E 
 @
 
-\section{\cite{1}:14.96~~~~~$\displaystyle\int{x^m\sqrt{ax+b}~dx}$}
+\section{\cite{1}:14.96~~~~~$\displaystyle
+\int{x^m\sqrt{ax+b}~dx}$}
 $$\int{x^m\sqrt{ax+b}}=
 \frac{2x^m}{(2m+3)a}(ax+b)^{3/2}
--\frac{2mb}{(2m+3)a}~\int{x^{m-1}\sqrt{ax+b}}$$
+-\frac{2mb}{(2m+3)a}~\int{x^{m-1}\sqrt{ax+b}}
+$$
 <<*>>=
 )clear all
 
---S 78 of 92
+--S 78     14:96 Axiom cannot do this integral
 aa:=integrate(x^m*sqrt(a*x+b),x)
 --R 
 --R
@@ -1159,14 +1162,16 @@ aa:=integrate(x^m*sqrt(a*x+b),x)
 --E 
 @
 
-\section{\cite{1}:14.97~~~~~$\displaystyle\int{\frac{\sqrt{ax+b}}{x^m}~dx}$}
+\section{\cite{1}:14.97~~~~~$\displaystyle
+\int{\frac{\sqrt{ax+b}}{x^m}~dx}$}
 $$\int{\frac{\sqrt{ax+b}}{x^m}}=
 -\frac{\sqrt{ax+b}}{(m-1)x^{m-1}}
-+\frac{a}{2(m-1)}~\int{\frac{1}{x^{m-1}\sqrt{ax+b}}}$$
++\frac{a}{2(m-1)}~\int{\frac{1}{x^{m-1}\sqrt{ax+b}}}
+$$
 <<*>>=
 )clear all
 
---S 79 of 92
+--S 79     14:97 Axiom cannot do this integral
 aa:=integrate(sqrt(a*x+b)/x^m,x)
 --R 
 --R
@@ -1179,15 +1184,17 @@ aa:=integrate(sqrt(a*x+b)/x^m,x)
 --E 
 @
 
-\section{\cite{1}:14.98~~~~~$\displaystyle\int{\frac{\sqrt{ax+b}}{x^m}~dx}$}
+\section{\cite{1}:14.98~~~~~$\displaystyle
+\int{\frac{\sqrt{ax+b}}{x^m}~dx}$}
 $$\int{\frac{\sqrt{ax+b}}{x^m}}=
 \frac{-(ax+b)^{3/2}}{(m-1)bx^{m-1}}
--\frac{(2m-5)a}{(2m-2)b}~\int{\frac{\sqrt{ax+b}}{x^{m-1}}}$$
+-\frac{(2m-5)a}{(2m-2)b}~\int{\frac{\sqrt{ax+b}}{x^{m-1}}}
+$$
 Note: 14.98 is the same as 14.97
 <<*>>=
 )clear all
 
---S 80 of 92
+--S 80     14:98 Axiom cannot do this integral
 aa:=integrate(sqrt(a*x+b)/x^m,x)
 --R 
 --R
@@ -1200,13 +1207,15 @@ aa:=integrate(sqrt(a*x+b)/x^m,x)
 --E 
 @
 
-\section{\cite{1}:14.99~~~~~$\displaystyle\int{(ax+b)^{m/2}~dx}$}
+\section{\cite{1}:14.99~~~~~$\displaystyle
+\int{(ax+b)^{m/2}~dx}$}
 $$\int{(ax+b)^{m/2}}=
-\frac{2(ax+b)^{(m+2)/2}}{a(m+2)}$$
+\frac{2(ax+b)^{(m+2)/2}}{a(m+2)}
+$$
 <<*>>=
 )clear all
 
---S 81 of 92
+--S 81
 aa:=integrate((a*x+b)^(m/2),x)
 --R 
 --R
@@ -1218,9 +1227,8 @@ aa:=integrate((a*x+b)^(m/2),x)
 --R                  a m + 2a
 --R                                          Type: Union(Expression Integer,...)
 --E 
-@
-<<*>>=
---S 82 of 92
+
+--S 82
 bb:=(2*(a*x+b)^((m+2)/2))/(a*(m+2))
 --R 
 --R
@@ -1232,9 +1240,8 @@ bb:=(2*(a*x+b)^((m+2)/2))/(a*(m+2))
 --R            a m + 2a
 --R                                                     Type: Expression Integer
 --E
-@
-<<*>>=
---S 83 of 92
+
+--S 83     14:99 Axiom cannot simplify this expression
 cc:=aa-bb
 --R 
 --R
@@ -1248,14 +1255,16 @@ cc:=aa-bb
 --E
 @
 
-\section{\cite{1}:14.100~~~~~$\displaystyle\int{x(ax+b)^{m/2}~dx}$}
+\section{\cite{1}:14.100~~~~~$\displaystyle
+\int{x(ax+b)^{m/2}~dx}$}
 $$\int{x(ax+b)^{m/2}}=
 \frac{2(ax+b)^{(m+4)/2}}{a^2(m+4)}
--\frac{2b(ax+b)^{(m+2)/2}}{a^2(m+2)}$$
+-\frac{2b(ax+b)^{(m+2)/2}}{a^2(m+2)}
+$$
 <<*>>=
 )clear all
 
---S 84 of 92
+--S 84
 aa:=integrate(x*(a*x+b)^(m/2),x)
 --R 
 --R
@@ -1268,9 +1277,8 @@ aa:=integrate(x*(a*x+b)^(m/2),x)
 --R                        a m  + 6a m + 8a
 --R                                          Type: Union(Expression Integer,...)
 --E 
-@
-<<*>>=
---S 85 of 92
+
+--S 85
 bb:=(2*(a*x+b)^((m+4)/2))/(a^2*(m+4))-(2*b*(a*x+b)^((m+2)/2))/(a^2*(m+2))
 --R 
 --R
@@ -1283,9 +1291,8 @@ bb:=(2*(a*x+b)^((m+4)/2))/(a^2*(m+4))-(2*b*(a*x+b)^((m+2)/2))/(a^2*(m+2))
 --R                          a m  + 6a m + 8a
 --R                                                     Type: Expression Integer
 --E
-@
-<<*>>=
---S 86 of 92
+
+--S 86     14:100 Axiom cannot simplify this expression
 cc:=aa-bb
 --R 
 --R
@@ -1306,15 +1313,17 @@ cc:=aa-bb
 --E
 @
 
-\section{\cite{1}:14.101~~~~~$\displaystyle\int{x^2(ax+b)^{m/2}~dx}$}
+\section{\cite{1}:14.101~~~~~$\displaystyle
+\int{x^2(ax+b)^{m/2}~dx}$}
 $$\int{x^2(ax+b)^{m/2}}=
 \frac{2(ax+b)^{(m+6)/2}}{a^3(m+6)}
 -\frac{4b(ax+b)^{(m+4)/2}}{a^3(m+4)}
-+\frac{2b^2(ax+b)^{(m+2)/2}}{a^3(m+2)}$$
++\frac{2b^2(ax+b)^{(m+2)/2}}{a^3(m+2)}
+$$
 <<*>>=
 )clear all
 
---S 87 of 92
+--S 87
 aa:=integrate(x^2*(a*x+b)^(m/2),x)
 --R 
 --R
@@ -1331,9 +1340,8 @@ aa:=integrate(x^2*(a*x+b)^(m/2),x)
 --R     a m  + 12a m  + 44a m + 48a
 --R                                          Type: Union(Expression Integer,...)
 --E 
-@
-<<*>>=
---S 88 of 92
+
+--S 88
 bb:=(2*(a*x+b)^((m+6)/2))/(a^3*(m+6))-_
       (4*b*(a*x+b)^((m+4)/2))/(a^3*(m+4))+_
         (2*b^2*(a*x+b)^((m+2)/2))/(a^3*(m+2))
@@ -1354,9 +1362,8 @@ bb:=(2*(a*x+b)^((m+6)/2))/(a^3*(m+6))-_
 --R     a m  + 12a m  + 44a m + 48a
 --R                                                     Type: Expression Integer
 --E
-@
-<<*>>=
---S 89 of 92
+
+--S 89     14:101 Axiom cannot simplify this expression
 cc:=aa-bb
 --R 
 --R
@@ -1385,14 +1392,16 @@ cc:=aa-bb
 --E
 @
 
-\section{\cite{1}:14.102~~~~~$\displaystyle\int{\frac{(ax+b)^{m/2}}{x}~dx}$}
+\section{\cite{1}:14.102~~~~~$\displaystyle
+\int{\frac{(ax+b)^{m/2}}{x}~dx}$}
 $$\int{\frac{(ax+b)^{m/2}}{x}}=
 \frac{2(ax+b)^{m/2}}{m}
-+b~\int{\frac{(ax+b)^{(m-2)/2}}{x}}$$
++b~\int{\frac{(ax+b)^{(m-2)/2}}{x}}
+$$
 <<*>>=
 )clear all
 
---S 90 of 92
+--S 90     14:102 Axiom cannot do this integral
 aa:=integrate((a*x+b)^(m/2)/x,x)
 --R 
 --R
@@ -1409,11 +1418,12 @@ aa:=integrate((a*x+b)^(m/2)/x,x)
 \int{\frac{(ax+b)^{m/2}}{x^2}~dx}$}
 $$\int{\frac{(ax+b)^{m/2}}{x^2}}=
 -\frac{(ax+b)^{(m+2)/2}}{bx}
-+\frac{ma}{2b}~\int{\frac{(ax+b)^{m/2}}{x}}$$
++\frac{ma}{2b}~\int{\frac{(ax+b)^{m/2}}{x}}
+$$
 <<*>>=
 )clear all
 
---S 91 of 92
+--S 91     14:103 Axiom cannot do this integral
 aa:=integrate((a*x+b)^(m/2)/x^2,x)
 --R 
 --R
@@ -1431,11 +1441,12 @@ aa:=integrate((a*x+b)^(m/2)/x^2,x)
 \int{\frac{dx}{x(ax+b)^{m/2}}}$}
 $$\int{\frac{1}{x(ax+b)^{m/2}}}=
 \frac{2}{(m-2)b(ax+b)^{(m-2)/2}}
-+\frac{1}{b}~\int{\frac{1}{x(ax+b)^{(m-2)/2}}}$$
++\frac{1}{b}~\int{\frac{1}{x(ax+b)^{(m-2)/2}}}
+$$
 <<*>>=
 )clear all
 
---S 92 of 92
+--S 92     14:104 Axiom cannot do this integral
 aa:=integrate(1/(x*(a*x+b)^(m/2)),x)
 --R 
 --R
@@ -1448,9 +1459,7 @@ aa:=integrate(1/(x*(a*x+b)^(m/2)),x)
 --I             %L (b + %L a)
 --R                                          Type: Union(Expression Integer,...)
 --E 
-@
 
-<<*>>=
 )spool
 )lisp (bye)
 @
diff --git a/src/input/schaum3.input.pamphlet b/src/input/schaum3.input.pamphlet
index e1e030d..bed98c8 100644
--- a/src/input/schaum3.input.pamphlet
+++ b/src/input/schaum3.input.pamphlet
@@ -16,7 +16,7 @@ $$\int{\frac{1}{(ax+b)(px+q)}}=
 )set message auto off
 )clear all
 
---S 1 of 11
+--S 1
 aa:=integrate(1/((a*x+b)*(p*x+q)),x)
 --R 
 --R
@@ -25,9 +25,8 @@ aa:=integrate(1/((a*x+b)*(p*x+q)),x)
 --R                  a q - b p
 --R                                          Type: Union(Expression Integer,...)
 --E 
-@
-<<*>>=
---S 2 of 11
+
+--S 2
 bb:=1/(b*p-a*q)*log((p*x+q)/(a*x+b))
 --R 
 --R
@@ -38,9 +37,8 @@ bb:=1/(b*p-a*q)*log((p*x+q)/(a*x+b))
 --R            a q - b p
 --R                                                     Type: Expression Integer
 --E
-@
-<<*>>=
---S 3 of 11
+
+--S 3
 cc:=aa-bb
 --R 
 --R
@@ -51,6 +49,41 @@ cc:=aa-bb
 --R                          a q - b p
 --R                                                     Type: Expression Integer
 --E
+
+--S 4
+logdiv:=rule(log(a)-log(b) == log(a/b))
+--R
+--R                                      a
+--I   (4)  - log(b) + log(a) + %I == log(-) + %I
+--R                                      b
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 5
+dd:=logdiv cc
+--R
+--R                              1
+--R        log(a x + b) + log(-------)
+--R                           a x + b
+--R   (5)  ---------------------------
+--R                 a q - b p
+--R                                                     Type: Expression Integer
+--E
+
+--S 6
+logmul:=rule(log(a)+log(b) == log(a*b))
+--R
+--I   (6)  log(b) + log(a) + %J == log(a b) + %J
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 7      14:105 Schaums and Axiom agree
+ee:=logmul dd
+--R
+--R   (7)  0
+--R                                                     Type: Expression Integer
+--E
+
 @
 
 \section{\cite{1}:14.106~~~~~$\displaystyle\int{\frac{x~dx}{(ax+b)(px+q)}}$}
@@ -59,7 +92,7 @@ $$\int{\frac{x}{(ax+b)(px+q)}}=
 <<*>>=
 )clear all
 
---S 4 of 11
+--S 8
 aa:=integrate(x/((a*x+b)*(p*x+q)),x)
 --R 
 --R
@@ -69,9 +102,8 @@ aa:=integrate(x/((a*x+b)*(p*x+q)),x)
 --R                   a p q - a b p
 --R                                          Type: Union(Expression Integer,...)
 --E 
-@
-<<*>>=
---S 5 of 11
+
+--S 9
 bb:=1/(b*p-a*q)*(b/a*log(a*x+b)-q/p*log(p*x+q))
 --R 
 --R
@@ -81,9 +113,8 @@ bb:=1/(b*p-a*q)*(b/a*log(a*x+b)-q/p*log(p*x+q))
 --R                   a p q - a b p
 --R                                                     Type: Expression Integer
 --E
-@
-<<*>>=
---S 6 of 11
+
+--S 10     14:106 Schaums and Axiom agree
 cc:=aa-bb
 --R 
 --R
@@ -100,7 +131,7 @@ $$\int{\frac{1}{(ax+b)^2(px+q)}}=
 <<*>>=
 )clear all
 
---S 7 of 11
+--S 11
 aa:=integrate(1/((a*x+b)^2*(p*x+q)),x)
 --R 
 --R
@@ -110,9 +141,8 @@ aa:=integrate(1/((a*x+b)^2*(p*x+q)),x)
 --R               (a q  - 2a b p q + a b p )x + a b q  - 2a b p q + b p
 --R                                          Type: Union(Expression Integer,...)
 --E 
-@
-<<*>>=
---S 8 of 11
+
+--S 12
 bb:=1/(b*p-a*q)*(1/(a*x+b)+p/(b*p-a*q)*log((p*x+q)/(a*x+b)))
 --R 
 --R
@@ -124,9 +154,8 @@ bb:=1/(b*p-a*q)*(1/(a*x+b)+p/(b*p-a*q)*log((p*x+q)/(a*x+b)))
 --R        (a q  - 2a b p q + a b p )x + a b q  - 2a b p q + b p
 --R                                                     Type: Expression Integer
 --E
-@
-<<*>>=
---S 9 of 11
+
+--S 13
 cc:=aa-bb
 --R 
 --R
@@ -138,6 +167,23 @@ cc:=aa-bb
 --R                     a q  - 2a b p q + b p
 --R                                                     Type: Expression Integer
 --E
+
+--S 14
+divlog:=rule(log(a/b) == log(a) - log(b))
+--R
+--R            a
+--R   (4)  log(-) == - log(b) + log(a)
+--R            b
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 15     14:107 Schaums and Axiom agree
+dd:=divlog cc
+--R
+--R   (5)  0
+--R                                                     Type: Expression Integer
+--E
+
 @
 
 \section{\cite{1}:14.108~~~~~$\displaystyle\int{\frac{x~dx}{(ax+b)^2(px+q)}}$}
@@ -149,7 +195,7 @@ $$\int{\frac{x}{(ax+b)^2(px+q)}}=
 <<*>>=
 )clear all
 
---S 10 of 11
+--S 16
 aa:=integrate(x/((a*x+b)^2*(p*x+q)),x)
 --R 
 --R
@@ -161,9 +207,8 @@ aa:=integrate(x/((a*x+b)^2*(p*x+q)),x)
 --R            (a q  - 2a b p q + a b p )x + a b q  - 2a b p q + a b p
 --R                                          Type: Union(Expression Integer,...)
 --E 
-@
-<<*>>=
---S 11 of 11
+
+--S 17
 bb:=1/(b*p-a*q)*(q/(b*p-a*q)*log((a*x+b)/(p*x+q))-b/(a*(a*x+b)))
 --R 
 --R
@@ -175,8 +220,8 @@ bb:=1/(b*p-a*q)*(q/(b*p-a*q)*log((a*x+b)/(p*x+q))-b/(a*(a*x+b)))
 --R        (a q  - 2a b p q + a b p )x + a b q  - 2a b p q + a b p
 --R                                                     Type: Expression Integer
 --E
-@
-<<*>>=
+
+--S 18
 cc:=aa-bb
 --R 
 --R
@@ -188,6 +233,22 @@ cc:=aa-bb
 --R                      a q  - 2a b p q + b p
 --R                                                     Type: Expression Integer
 --E
+
+--S 19
+divlog:=rule(log(a/b) == log(a) - log(b))
+--R
+--R            a
+--R   (4)  log(-) == - log(b) + log(a)
+--R            b
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 20     14:108 Schaums and Axiom agree
+dd:=divlog cc
+--R
+--R   (5)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.109~~~~~$\displaystyle
@@ -198,7 +259,7 @@ $$\frac{b^2}{(bp-aq)a^2(ax+b)}+\frac{1}{(bp-aq)^2}
 <<*>>=
 )clear all
 
---S 
+--S 21
 aa:=integrate(x^2/((a*x+b)^2*(p*x+q)),x)
 --R 
 --R
@@ -213,9 +274,8 @@ aa:=integrate(x^2/((a*x+b)^2*(p*x+q)),x)
 --R     (a p q  - 2a b p q + a b p )x + a b p q  - 2a b p q + a b p
 --R                                          Type: Union(Expression Integer,...)
 --E 
-@
-<<*>>=
---S 
+
+--S 22
 bb:=b^2/((b*p-a*q)*a^2*(a*x+b))+_
      1/(b*p-a*q)^2*(q^2/p*log(p*x+q)+((b*(b*p-2*a*q))/a^2)*log(a*x+b))
 --R 
@@ -231,9 +291,8 @@ bb:=b^2/((b*p-a*q)*a^2*(a*x+b))+_
 --R     (a p q  - 2a b p q + a b p )x + a b p q  - 2a b p q + a b p
 --R                                                     Type: Expression Integer
 --E
-@
-<<*>>=
---S 
+
+--S 23     14:109 Schaums and Axiom agree
 cc:=aa-bb
 --R 
 --R
@@ -250,7 +309,7 @@ a(m+n-2)~\int{\frac{1}{(ax+b)^m(px+q)^{n-1}}}\right\}$$
 <<*>>=
 )clear all
 
---S 
+--S 24     14:110 Axiom cannot do this integral
 aa:=integrate(1/((a*x+b)^m*(p*x+q)^n),x)
 --R 
 --R
@@ -261,81 +320,14 @@ aa:=integrate(1/((a*x+b)^m*(p*x+q)^n),x)
 --I             (b + %L a) (q + %L p)
 --R                                          Type: Union(Expression Integer,...)
 --E 
-@
-<<*>>=
---S 
-dd:=integrate(1/((a*x+b)^m*(p*x+q)^(n-1)),x)
---R 
---R
---R           x
---R         ++               1
---I   (2)   |   -------------------------- d%L
---R        ++             m          n - 1
---I             (b + %L a) (q + %L p)
---R                                          Type: Union(Expression Integer,...)
---E
-@
 
-<<*>>=
---S 
-bb:=-1/((n-1)*(b*p-a*q))*(1/((a*x+b)^(m-1)*(p*x+q)^(n-1))+a*(m+n-2)*dd)
---R 
---R
---R   (3)
---R                                  m - 1         n - 1
---R         (a n + a m - 2a)(a x + b)     (p x + q)
---R      *
---R            x
---R          ++               1
---I          |   -------------------------- d%L
---R         ++             m          n - 1
---I              (b + %L a) (q + %L p)
---R     + 
---R       1
---R  /
---R                                         m - 1         n - 1
---R     ((a n - a)q + (- b n + b)p)(a x + b)     (p x + q)
---R                                                     Type: Expression Integer
---E
 @
-<<*>>=
---S 
-cc:=aa-bb
---R 
---R
---R   (4)
---R                                    m - 1         n - 1
---R         (- a n - a m + 2a)(a x + b)     (p x + q)
---R      *
---R            x
---R          ++               1
---I          |   -------------------------- d%L
---R         ++             m          n - 1
---I              (b + %L a) (q + %L p)
---R     + 
---R                                             m - 1         n - 1
---R         ((a n - a)q + (- b n + b)p)(a x + b)     (p x + q)
---R      *
---R            x
---R          ++             1
---I          |   ---------------------- d%L
---R         ++             m          n
---I              (b + %L a) (q + %L p)
---R     + 
---R       - 1
---R  /
---R                                         m - 1         n - 1
---R     ((a n - a)q + (- b n + b)p)(a x + b)     (p x + q)
---R                                                     Type: Expression Integer
---E
-@
-
 \section{\cite{1}:14.111~~~~~$\displaystyle\int{\frac{ax+b}{px+q}~dx}$}
 $$\int{\frac{ax+b}{px+q}}=\frac{ax}{p}+\frac{bp-aq}{p^2}~\ln(px+q)$$
 <<*>>=
 )clear all
 
---S 
+--S 25
 aa:=integrate((a*x+b)/(p*x+q),x)
 --R 
 --R
@@ -345,9 +337,8 @@ aa:=integrate((a*x+b)/(p*x+q),x)
 --R                        p
 --R                                          Type: Union(Expression Integer,...)
 --E 
-@
-<<*>>=
---S 
+
+--S 26
 bb:=(a*x)/p+(b*p-a*q)/p^2*log(p*x+q)
 --R 
 --R
@@ -357,9 +348,8 @@ bb:=(a*x)/p+(b*p-a*q)/p^2*log(p*x+q)
 --R                        p
 --R                                                     Type: Expression Integer
 --E
-@
-<<*>>=
---S 
+
+--S 27     14:111 Schaums and Axiom agree
 cc:=aa-bb
 --R 
 --R
@@ -383,7 +373,7 @@ $$\int{\frac{(ax+b)^m}{(px+q)^n}}=\left\{
 <<*>>=
 )clear all
 
---S 
+--S 28     14:112 Axiom cannot do this integral
 aa:=integrate((a*x+b)^m/(p*x+q)^n,x)
 --R 
 --R
@@ -393,7 +383,6 @@ aa:=integrate((a*x+b)^m/(p*x+q)^n,x)
 --R        ++             n
 --I             (q + %L p)
 --R                                          Type: Union(Expression Integer,...)
---R
 --E
 <<*>>=
 )spool
diff --git a/src/input/schaum4.input.pamphlet b/src/input/schaum4.input.pamphlet
index efd9edc..0edbbf9 100644
--- a/src/input/schaum4.input.pamphlet
+++ b/src/input/schaum4.input.pamphlet
@@ -16,7 +16,7 @@ $$\int{\frac{px+q}{\sqrt{ax+b}}}=
 )set message auto off
 )clear all
 
---S 1 of 7
+--S 1
 aa:=integrate((p*x+q)/sqrt(a*x+b),x)
 --R 
 --R
@@ -27,6 +27,24 @@ aa:=integrate((p*x+q)/sqrt(a*x+b),x)
 --R                       3a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 2
+bb:=(2*(a*p*x+3*a*q-2*b*p))/(3*a^2)*sqrt(a*x+b)
+--R
+--R                               +-------+
+--R        (2a p x + 6a q - 4b p)\|a x + b
+--R   (2)  --------------------------------
+--R                         2
+--R                       3a
+--R                                                     Type: Expression Integer
+--E
+
+--S 3      14:113 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.114~~~~~$\displaystyle
@@ -43,7 +61,7 @@ $$
 <<*>>=
 )clear all
 
---S 2 of 7
+--S 4
 aa:=integrate(1/((p*x+q)*sqrt(a*x+b)),x)
 --R 
 --R
@@ -68,6 +86,157 @@ aa:=integrate(1/((p*x+q)*sqrt(a*x+b)),x)
 --R             \|a p q - b p
 --R                                     Type: Union(List Expression Integer,...)
 --E 
+
+--S 5
+aa1:=aa.1
+--R
+--R   (2)
+--R                                                         +--------------+
+--R                     2  +-------+                        |             2
+--R       (2a p q - 2b p )\|a x + b  + (a p x - a q + 2b p)\|- a p q + b p
+--R   log(------------------------------------------------------------------)
+--R                                     p x + q
+--R   -----------------------------------------------------------------------
+--R                               +--------------+
+--R                               |             2
+--R                              \|- a p q + b p
+--R                                                     Type: Expression Integer
+--E
+
+--S 6
+aa2:=aa.2
+--R
+--R               +------------+
+--R               |           2  +-------+
+--R              \|a p q - b p  \|a x + b
+--R        2atan(-------------------------)
+--R                      a q - b p
+--R   (3)  --------------------------------
+--R                  +------------+
+--R                  |           2
+--R                 \|a p q - b p
+--R                                                     Type: Expression Integer
+--E
+
+--S 7
+bb1:=1/sqrt(b*p-a*q)*log((sqrt(p*(a*x+b))-sqrt(b*p-a*q))/(sqrt(p*(a*x+b))+sqrt(b*p-a*q)))
+--R
+--R             +-----------+    +-----------+
+--R            \|a p x + b p  - \|- a q + b p
+--R        log(-------------------------------)
+--R             +-----------+    +-----------+
+--R            \|a p x + b p  + \|- a q + b p
+--R   (4)  ------------------------------------
+--R                    +-----------+
+--R                   \|- a q + b p
+--R                                                     Type: Expression Integer
+--E
+
+--S 8
+bb2:=2/(sqrt(a*q-b*p)*sqrt(p))*atan(sqrt((p*(a*x+b))/(a*q-b*p)))
+--R
+--R               +-----------+
+--R               |a p x + b p
+--R        2atan( |----------- )
+--R              \| a q - b p
+--R   (5)  ---------------------
+--R            +-+ +---------+
+--R           \|p \|a q - b p
+--R                                                     Type: Expression Integer
+--E
+
+--S 9
+cc1:=aa1-bb1
+--R
+--R   (6)
+--R          +-----------+
+--R         \|- a q + b p
+--R      *
+--R                                                             +--------------+
+--R                         2  +-------+                        |             2
+--R           (2a p q - 2b p )\|a x + b  + (a p x - a q + 2b p)\|- a p q + b p
+--R       log(------------------------------------------------------------------)
+--R                                         p x + q
+--R     + 
+--R          +--------------+     +-----------+    +-----------+
+--R          |             2     \|a p x + b p  - \|- a q + b p
+--R       - \|- a p q + b p  log(-------------------------------)
+--R                               +-----------+    +-----------+
+--R                              \|a p x + b p  + \|- a q + b p
+--R  /
+--R      +--------------+
+--R      |             2  +-----------+
+--R     \|- a p q + b p  \|- a q + b p
+--R                                                     Type: Expression Integer
+--E
+
+--S 10
+cc2:=aa1-bb2
+--R
+--R   (7)
+--R          +-+ +---------+
+--R         \|p \|a q - b p
+--R      *
+--R                                                             +--------------+
+--R                         2  +-------+                        |             2
+--R           (2a p q - 2b p )\|a x + b  + (a p x - a q + 2b p)\|- a p q + b p
+--R       log(------------------------------------------------------------------)
+--R                                         p x + q
+--R     + 
+--R           +--------------+      +-----------+
+--R           |             2       |a p x + b p
+--R       - 2\|- a p q + b p  atan( |----------- )
+--R                                \| a q - b p
+--R  /
+--R      +--------------+
+--R      |             2  +-+ +---------+
+--R     \|- a p q + b p  \|p \|a q - b p
+--R                                                     Type: Expression Integer
+--E
+
+--S 11
+cc3:=aa2-bb1
+--R
+--R   (8)
+--R          +------------+     +-----------+    +-----------+
+--R          |           2     \|a p x + b p  - \|- a q + b p
+--R       - \|a p q - b p  log(-------------------------------)
+--R                             +-----------+    +-----------+
+--R                            \|a p x + b p  + \|- a q + b p
+--R     + 
+--R                            +------------+
+--R                            |           2  +-------+
+--R         +-----------+     \|a p q - b p  \|a x + b
+--R       2\|- a q + b p atan(-------------------------)
+--R                                   a q - b p
+--R  /
+--R                    +------------+
+--R      +-----------+ |           2
+--R     \|- a q + b p \|a p q - b p
+--R                                                     Type: Expression Integer
+--E
+
+--S 12     14:114 Axiom cannot simplify these answers
+cc4:=aa2-bb2
+--R
+--R   (9)
+--R                              +------------+
+--R                              |           2  +-------+
+--R         +-+ +---------+     \|a p q - b p  \|a x + b
+--R       2\|p \|a q - b p atan(-------------------------)
+--R                                     a q - b p
+--R     + 
+--R           +------------+      +-----------+
+--R           |           2       |a p x + b p
+--R       - 2\|a p q - b p  atan( |----------- )
+--R                              \| a q - b p
+--R  /
+--R                      +------------+
+--R      +-+ +---------+ |           2
+--R     \|p \|a q - b p \|a p q - b p
+--R                                                     Type: Expression Integer
+--E
+
 @
 
 \section{\cite{1}:14.115~~~~~$\displaystyle\int{\frac{\sqrt{ax+b}}{px+q}}~dx$}
@@ -83,7 +252,7 @@ $$\int{\frac{\sqrt{ax+b}}{px+q}}=
 <<*>>=
 )clear all
 
---S 3 of 7
+--S 13
 aa:=integrate(sqrt(a*x+b)/(p*x+q),x)
 --R 
 --R
@@ -112,6 +281,150 @@ aa:=integrate(sqrt(a*x+b)/(p*x+q),x)
 --R                           p
 --R                                     Type: Union(List Expression Integer,...)
 --E 
+
+--S 14
+aa1:=aa.1
+--R
+--R   (2)
+--R                              +-----------+
+--R                              |- a q + b p  +-------+
+--R        +-----------+    - 2p |----------- \|a x + b  + a p x - a q + 2b p
+--R        |- a q + b p         \|     p
+--R        |----------- log(-------------------------------------------------)
+--R       \|     p                               p x + q
+--R     + 
+--R         +-------+
+--R       2\|a x + b
+--R  /
+--R     p
+--R                                                     Type: Expression Integer
+--E
+
+--S 15
+aa2:=aa.2
+--R
+--R             +---------+       +-------+
+--R             |a q - b p       \|a x + b       +-------+
+--R        - 2  |--------- atan(------------ + 2\|a x + b
+--R            \|    p           +---------+
+--R                              |a q - b p
+--R                              |---------
+--R                             \|    p
+--R   (3)  -----------------------------------------------
+--R                               p
+--R                                                     Type: Expression Integer
+--E
+
+--S 16
+bb1:=(2*sqrt(a*x+b))/p+sqrt(b*p-a*q)/(p*sqrt(p))*log((sqrt(p*(a*x+b))-sqrt(b*p-a*q))/(sqrt(p*(a*x+b))+sqrt(b*p-a*q)))
+--R
+--R                           +-----------+    +-----------+
+--R         +-----------+    \|a p x + b p  - \|- a q + b p       +-+ +-------+
+--R        \|- a q + b p log(-------------------------------) + 2\|p \|a x + b
+--R                           +-----------+    +-----------+
+--R                          \|a p x + b p  + \|- a q + b p
+--R   (4)  --------------------------------------------------------------------
+--R                                          +-+
+--R                                        p\|p
+--R                                                     Type: Expression Integer
+--E
+
+--S 17
+bb2:=(2*sqrt(a*x+b))/p-(2*sqrt(a*q-b*p))/(p*sqrt(p))*atan(sqrt((p*(a*x+b))/(a*q-b*p)))
+--R
+--R                             +-----------+
+--R            +---------+      |a p x + b p       +-+ +-------+
+--R        - 2\|a q - b p atan( |----------- ) + 2\|p \|a x + b
+--R                            \| a q - b p
+--R   (5)  -----------------------------------------------------
+--R                                  +-+
+--R                                p\|p
+--R                                                     Type: Expression Integer
+--E
+
+--S 18
+cc1:=aa1-bb1
+--R
+--R   (6)
+--R                            +-----------+    +-----------+
+--R          +-----------+    \|a p x + b p  - \|- a q + b p
+--R       - \|- a q + b p log(-------------------------------)
+--R                            +-----------+    +-----------+
+--R                           \|a p x + b p  + \|- a q + b p
+--R     + 
+--R                                  +-----------+
+--R                                  |- a q + b p  +-------+
+--R        +-----------+        - 2p |----------- \|a x + b  + a p x - a q + 2b p
+--R        |- a q + b p  +-+        \|     p
+--R        |----------- \|p log(-------------------------------------------------)
+--R       \|     p                                   p x + q
+--R  /
+--R       +-+
+--R     p\|p
+--R                                                     Type: Expression Integer
+--E
+
+--S 19
+cc2:=aa1-bb2
+--R
+--R   (7)
+--R                                  +-----------+
+--R                                  |- a q + b p  +-------+
+--R        +-----------+        - 2p |----------- \|a x + b  + a p x - a q + 2b p
+--R        |- a q + b p  +-+        \|     p
+--R        |----------- \|p log(-------------------------------------------------)
+--R       \|     p                                   p x + q
+--R     + 
+--R                          +-----------+
+--R         +---------+      |a p x + b p
+--R       2\|a q - b p atan( |----------- )
+--R                         \| a q - b p
+--R  /
+--R       +-+
+--R     p\|p
+--R                                                     Type: Expression Integer
+--E
+
+--S 20
+cc3:=aa2-bb1
+--R
+--R   (8)
+--R                            +-----------+    +-----------+
+--R          +-----------+    \|a p x + b p  - \|- a q + b p
+--R       - \|- a q + b p log(-------------------------------)
+--R                            +-----------+    +-----------+
+--R                           \|a p x + b p  + \|- a q + b p
+--R     + 
+--R               +---------+       +-------+
+--R           +-+ |a q - b p       \|a x + b
+--R       - 2\|p  |--------- atan(------------)
+--R              \|    p           +---------+
+--R                                |a q - b p
+--R                                |---------
+--R                               \|    p
+--R  /
+--R       +-+
+--R     p\|p
+--R                                                     Type: Expression Integer
+--E
+
+--S 21     14:115 Axiom cannot simplify these answers
+cc4:=aa2-bb2
+--R
+--R   (9)
+--R           +---------+       +-------+                        +-----------+
+--R       +-+ |a q - b p       \|a x + b        +---------+      |a p x + b p
+--R   - 2\|p  |--------- atan(------------) + 2\|a q - b p atan( |----------- )
+--R          \|    p           +---------+                      \| a q - b p
+--R                            |a q - b p
+--R                            |---------
+--R                           \|    p
+--R   -------------------------------------------------------------------------
+--R                                       +-+
+--R                                     p\|p
+--R                                                     Type: Expression Integer
+--E
+
 @
 
 \section{\cite{1}:14.116~~~~~$\displaystyle\int{(px+b)^n\sqrt{ax+b}}~dx$}
@@ -122,7 +435,7 @@ $$\int{(px+b)^n\sqrt{ax+b}}=
 <<*>>=
 )clear all
 
---S 4 of 7
+--S 22     14:116 Axiom cannot compute this integral
 aa:=integrate((p*x+q)^n*sqrt(a*x+b),x)
 --R 
 --R
@@ -144,7 +457,7 @@ $$\int{\frac{1}{(px+b)^n\sqrt{ax+b}}}=
 <<*>>=
 )clear all
 
---S 5 of 7
+--S 23     14:117 Axiom cannot compute this integral
 aa:=integrate(1/((p*x+q)^n*sqrt(a*x+b)),x)
 --R 
 --R
@@ -166,7 +479,7 @@ $$\int{\frac{(px+q)^n}{\sqrt{ax+b}}}=
 <<*>>=
 )clear all
 
---S 6 of 7
+--S 24     14:118 Axiom cannot compute this integral
 aa:=integrate((p*x+q)^n/sqrt(a*x+b),x)
 --R 
 --R
@@ -187,7 +500,7 @@ $$\int{\frac{\sqrt{ax+b}}{(px+q)^n}}=
 <<*>>=
 )clear all
 
---S 7 of 7
+--S 25     14:119 Axiom cannot compute this integral
 aa:=integrate(sqrt(a*x+b)/(p*x+q)^n,x)
 --R 
 --R
diff --git a/src/input/schaum5.input.pamphlet b/src/input/schaum5.input.pamphlet
index f8bccc8..50ea618 100644
--- a/src/input/schaum5.input.pamphlet
+++ b/src/input/schaum5.input.pamphlet
@@ -22,7 +22,7 @@ $$\int{\frac{1}{\sqrt{(ax+b)(px+q)}}}=
 )set message auto off
 )clear all
 
---S 1 of 5
+--S 1
 aa:=integrate(1/sqrt((a*x+b)*(p*x+q)),x)
 --R 
 --R
@@ -53,6 +53,157 @@ aa:=integrate(1/sqrt((a*x+b)*(p*x+q)),x)
 --R                               \|- a p
 --R                                     Type: Union(List Expression Integer,...)
 --E 
+
+--S 2
+aa1:=aa.1
+--R
+--R   (2)
+--R     log
+--R                                     +---------------------------+
+--R               +---+ +---+           |     2
+--R            (2\|a p \|b q  - 2a p x)\|a p x  + (a q + b p)x + b q
+--R          + 
+--R                   +---+            2                          +---+
+--R            2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
+--R       /
+--R                  +---------------------------+
+--R            +---+ |     2
+--R          2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
+--R  /
+--R      +---+
+--R     \|a p
+--R                                                     Type: Expression Integer
+--E
+
+--S 3
+aa2:=aa.2
+--R
+--R                       +---------------------------+
+--R               +-----+ |     2                          +-----+ +---+
+--R              \|- a p \|a p x  + (a q + b p)x + b q  - \|- a p \|b q
+--R        2atan(-------------------------------------------------------)
+--R                                       a p x
+--R   (3)  --------------------------------------------------------------
+--R                                    +-----+
+--R                                   \|- a p
+--R                                                     Type: Expression Integer
+--E
+
+--S 4
+bb1:=2/sqrt(a*p)*log(sqrt(a*(p*x+q))+sqrt(p*(a*x+b)))
+--R
+--R              +-----------+    +-----------+
+--R        2log(\|a p x + a q  + \|a p x + b p )
+--R   (4)  -------------------------------------
+--R                         +---+
+--R                        \|a p
+--R                                                     Type: Expression Integer
+--E
+
+--S 5
+bb2:=2/sqrt(-a*p)*atan(sqrt((-p*(a*x+b))/(a*(p*x+q))))
+--R
+--R               +-------------+
+--R               |- a p x - b p
+--R        2atan( |------------- )
+--R              \| a p x + a q
+--R   (5)  -----------------------
+--R                 +-----+
+--R                \|- a p
+--R                                                     Type: Expression Integer
+--E
+
+--S 6
+cc1:=aa1-bb1
+--R
+--R   (6)
+--R               +-----------+    +-----------+
+--R       - 2log(\|a p x + a q  + \|a p x + b p )
+--R     + 
+--R       log
+--R                                       +---------------------------+
+--R                 +---+ +---+           |     2
+--R              (2\|a p \|b q  - 2a p x)\|a p x  + (a q + b p)x + b q
+--R            + 
+--R                     +---+            2                          +---+
+--R              2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
+--R         /
+--R                    +---------------------------+
+--R              +---+ |     2
+--R            2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
+--R  /
+--R      +---+
+--R     \|a p
+--R                                                     Type: Expression Integer
+--E
+
+--S 7
+cc2:=aa1-bb2
+--R
+--R   (7)
+--R          +-----+
+--R         \|- a p
+--R      *
+--R         log
+--R                                         +---------------------------+
+--R                   +---+ +---+           |     2
+--R                (2\|a p \|b q  - 2a p x)\|a p x  + (a q + b p)x + b q
+--R              + 
+--R                       +---+            2                          +---+
+--R                2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
+--R           /
+--R                      +---------------------------+
+--R                +---+ |     2
+--R              2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
+--R     + 
+--R                      +-------------+
+--R           +---+      |- a p x - b p
+--R       - 2\|a p atan( |------------- )
+--R                     \| a p x + a q
+--R  /
+--R      +-----+ +---+
+--R     \|- a p \|a p
+--R                                                     Type: Expression Integer
+--E
+
+--S 8
+cc3:=aa2-bb1
+--R
+--R   (8)
+--R           +-----+     +-----------+    +-----------+
+--R       - 2\|- a p log(\|a p x + a q  + \|a p x + b p )
+--R     + 
+--R                            +---------------------------+
+--R                    +-----+ |     2                          +-----+ +---+
+--R         +---+     \|- a p \|a p x  + (a q + b p)x + b q  - \|- a p \|b q
+--R       2\|a p atan(-------------------------------------------------------)
+--R                                            a p x
+--R  /
+--R      +-----+ +---+
+--R     \|- a p \|a p
+--R                                                     Type: Expression Integer
+--E
+
+--S 9      14:120 Axiom cannot simplify these answers
+cc4:=aa2-bb2
+--R
+--R   (9)
+--R                      +---------------------------+
+--R              +-----+ |     2                          +-----+ +---+
+--R             \|- a p \|a p x  + (a q + b p)x + b q  - \|- a p \|b q
+--R       2atan(-------------------------------------------------------)
+--R                                      a p x
+--R     + 
+--R                +-------------+
+--R                |- a p x - b p
+--R       - 2atan( |------------- )
+--R               \| a p x + a q
+--R  /
+--R      +-----+
+--R     \|- a p
+--R                                                     Type: Expression Integer
+--E
+
 @
 
 \section{\cite{1}:14.121~~~~~$\displaystyle
@@ -64,7 +215,7 @@ $$
 <<*>>=
 )clear all
 
---S 2 of 5
+--S 10
 aa:=integrate(x/sqrt((a*x+b)*(p*x+q)),x)
 --R 
 --R
@@ -133,6 +284,187 @@ aa:=integrate(x/sqrt((a*x+b)*(p*x+q)),x)
 --R     ]
 --R                                     Type: Union(List Expression Integer,...)
 --E 
+
+--S 11
+bb1:=integrate(1/(sqrt(a*x+b)*(p*x+q)),x)
+--R
+--R   (2)
+--R                                                          +--------------+
+--R                      2  +-------+                        |             2
+--R        (2a p q - 2b p )\|a x + b  + (a p x - a q + 2b p)\|- a p q + b p
+--R    log(------------------------------------------------------------------)
+--R                                      p x + q
+--R   [-----------------------------------------------------------------------,
+--R                                +--------------+
+--R                                |             2
+--R                               \|- a p q + b p
+--R           +------------+
+--R           |           2  +-------+
+--R          \|a p q - b p  \|a x + b
+--R    2atan(-------------------------)
+--R                  a q - b p
+--R    --------------------------------]
+--R              +------------+
+--R              |           2
+--R             \|a p q - b p
+--R                                     Type: Union(List Expression Integer,...)
+--E
+
+--S 12
+bb2:=sqrt((a*x+b)*(p*x+q))/(a*p)-(b*p+a*q)/(2*a*p)
+--R
+--R          +---------------------------+
+--R          |     2
+--R        2\|a p x  + (a q + b p)x + b q  - a q - b p
+--R   (3)  -------------------------------------------
+--R                            2a p
+--R                                                     Type: Expression Integer
+--E
+
+--S 13
+bb:=bb2*bb1
+--R
+--R   (4)
+--R   [
+--R            +---------------------------+
+--R            |     2
+--R         (2\|a p x  + (a q + b p)x + b q  - a q - b p)
+--R      *
+--R                                                             +--------------+
+--R                         2  +-------+                        |             2
+--R           (2a p q - 2b p )\|a x + b  + (a p x - a q + 2b p)\|- a p q + b p
+--R       log(------------------------------------------------------------------)
+--R                                         p x + q
+--R    /
+--R            +--------------+
+--R            |             2
+--R       2a p\|- a p q + b p
+--R     ,
+--R                                                       +------------+
+--R       +---------------------------+                   |           2  +-------+
+--R       |     2                                        \|a p q - b p  \|a x + b
+--R    (2\|a p x  + (a q + b p)x + b q  - a q - b p)atan(-------------------------)
+--R                                                              a q - b p
+--R    ----------------------------------------------------------------------------
+--R                                     +------------+
+--R                                     |           2
+--R                                 a p\|a p q - b p
+--R     ]
+--R                                              Type: Vector Expression Integer
+--E
+
+--S 14     14:121 Axiom cannot simplify this answer
+cc:=aa-bb
+--R
+--R   (5)
+--R   [
+--R                              +---+ +---+                           +---+
+--R               ((2a q + 2b p)\|a p \|b q  + ((2a q + 2b p)x + 4b q)\|a p )
+--R            *
+--R                +---------------------------+
+--R                |     2
+--R               \|a p x  + (a q + b p)x + b q
+--R           + 
+--R                      2                            +---+ +---+
+--R             (- 4a p x  + (- 4a q - 4b p)x - 4b q)\|a p \|b q
+--R           + 
+--R                  2 2               2 2           2     2     +---+
+--R             ((- a q  - 2a b p q - b p )x - 2a b q  - 2b p q)\|a p
+--R        *
+--R                                                               +--------------+
+--R                           2  +-------+                        |             2
+--R             (2a p q - 2b p )\|a x + b  + (a p x - a q + 2b p)\|- a p q + b p
+--R         log(------------------------------------------------------------------)
+--R                                           p x + q
+--R       + 
+--R                           +--------------+       +---------------------------+
+--R                           |             2  +---+ |     2
+--R             (2a q + 2b p)\|- a p q + b p  \|b q \|a p x  + (a q + b p)x + b q
+--R           + 
+--R                                                              +--------------+
+--R                  2 2               2 2           2     2     |             2
+--R             ((- a q  - 2a b p q - b p )x - 2a b q  - 2b p q)\|- a p q + b p
+--R        *
+--R           log
+--R                                           +---------------------------+
+--R                     +---+ +---+           |     2
+--R                  (2\|a p \|b q  + 2a p x)\|a p x  + (a q + b p)x + b q
+--R                + 
+--R                           +---+            2                          +---+
+--R                  - 2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
+--R             /
+--R                        +---------------------------+
+--R                  +---+ |     2
+--R                2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
+--R       + 
+--R                          +--------------+       +---------------------------+
+--R                          |             2  +---+ |     2
+--R         (- 2a q - 2b p)x\|- a p q + b p  \|a p \|a p x  + (a q + b p)x + b q
+--R       + 
+--R                                    +--------------+
+--R                2                   |             2  +---+ +---+
+--R         (4a p x  + (2a q + 2b p)x)\|- a p q + b p  \|a p \|b q
+--R    /
+--R              +--------------+             +---------------------------+
+--R              |             2  +---+ +---+ |     2
+--R         4a p\|- a p q + b p  \|a p \|b q \|a p x  + (a q + b p)x + b q
+--R       + 
+--R                                            +--------------+
+--R               2            2               |             2  +---+
+--R         ((- 2a p q - 2a b p )x - 4a b p q)\|- a p q + b p  \|a p
+--R     ,
+--R
+--R                                   +------------+ +---------------------------+
+--R                             +---+ |           2  |     2
+--R             (- 2a q - 2b p)\|b q \|a p q - b p  \|a p x  + (a q + b p)x + b q
+--R           + 
+--R                                                            +------------+
+--R                2 2               2 2           2     2     |           2
+--R             ((a q  + 2a b p q + b p )x + 2a b q  + 2b p q)\|a p q - b p
+--R        *
+--R                         +---------------------------+
+--R                 +-----+ |     2                          +-----+ +---+
+--R                \|- a p \|a p x  + (a q + b p)x + b q  - \|- a p \|b q
+--R           atan(-------------------------------------------------------)
+--R                                         a p x
+--R       + 
+--R                              +-----+ +---+                           +-----+
+--R               ((2a q + 2b p)\|- a p \|b q  + ((2a q + 2b p)x + 4b q)\|- a p )
+--R            *
+--R                +---------------------------+
+--R                |     2
+--R               \|a p x  + (a q + b p)x + b q
+--R           + 
+--R                      2                            +-----+ +---+
+--R             (- 4a p x  + (- 4a q - 4b p)x - 4b q)\|- a p \|b q
+--R           + 
+--R                  2 2               2 2           2     2     +-----+
+--R             ((- a q  - 2a b p q - b p )x - 2a b q  - 2b p q)\|- a p
+--R        *
+--R                 +------------+
+--R                 |           2  +-------+
+--R                \|a p q - b p  \|a x + b
+--R           atan(-------------------------)
+--R                        a q - b p
+--R       + 
+--R                                +------------+ +---------------------------+
+--R                        +-----+ |           2  |     2
+--R         (- a q - b p)x\|- a p \|a p q - b p  \|a p x  + (a q + b p)x + b q
+--R       + 
+--R                                                +------------+
+--R                2                 +-----+ +---+ |           2
+--R         (2a p x  + (a q + b p)x)\|- a p \|b q \|a p q - b p
+--R    /
+--R                            +------------+ +---------------------------+
+--R              +-----+ +---+ |           2  |     2
+--R         2a p\|- a p \|b q \|a p q - b p  \|a p x  + (a q + b p)x + b q
+--R       + 
+--R                                                  +------------+
+--R              2           2               +-----+ |           2
+--R         ((- a p q - a b p )x - 2a b p q)\|- a p \|a p q - b p
+--R     ]
+--R                                              Type: Vector Expression Integer
+--E
 @
 
 \section{\cite{1}:14.122~~~~~$\displaystyle\int{\sqrt{(ax+b)(px+q)}}~dx$}
@@ -143,7 +475,7 @@ $$
 <<*>>=
 )clear all
 
---S 3 of 5
+--S 15
 aa:=integrate(sqrt((a*x+b)*(p*x+q)),x)
 --R 
 --R
@@ -289,7 +621,639 @@ aa:=integrate(sqrt((a*x+b)*(p*x+q)),x)
 --R           \|- a p
 --R     ]
 --R                                     Type: Union(List Expression Integer,...)
---E 
+--E
+@
+Since there are two parts to the aa variable we split them: 
+<<*>>=
+--S 16
+aa1:=aa.1
+--R
+--R   (2)
+--R                  3 3     2     2       2 2      3 3       2   3        2   2
+--R               (4a q  - 4a b p q  - 4a b p q + 4b p )x + 8a b q  - 16a b p q
+--R             + 
+--R                 3 2
+--R               8b p q
+--R          *
+--R                    +---------------------------+
+--R              +---+ |     2
+--R             \|b q \|a p x  + (a q + b p)x + b q
+--R         + 
+--R               4 4     3     3      2 2 2 2       3 3     4 4  2
+--R           (- a q  - 4a b p q  + 10a b p q  - 4a b p q - b p )x
+--R         + 
+--R                3   4     2 2   3       3 2 2     4 3        2 2 4        3   3
+--R           (- 8a b q  + 8a b p q  + 8a b p q  - 8b p q)x - 8a b q  + 16a b p q
+--R         + 
+--R               4 2 2
+--R           - 8b p q
+--R      *
+--R         log
+--R                                         +---------------------------+
+--R                   +---+ +---+           |     2
+--R                (2\|a p \|b q  + 2a p x)\|a p x  + (a q + b p)x + b q
+--R              + 
+--R                         +---+            2                          +---+
+--R                - 2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
+--R           /
+--R                      +---------------------------+
+--R                +---+ |     2
+--R              2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
+--R     + 
+--R                3   2      2   2        2 3  3
+--R           (- 4a p q  - 24a b p q - 4a b p )x
+--R         + 
+--R                3 3      2     2        2 2      3 3  2
+--R           (- 2a q  - 46a b p q  - 46a b p q - 2b p )x
+--R         + 
+--R                2   3        2   2     3 2
+--R           (- 8a b q  - 48a b p q  - 8b p q)x
+--R      *
+--R                +---------------------------+
+--R          +---+ |     2
+--R         \|a p \|a p x  + (a q + b p)x + b q
+--R     + 
+--R               3 2       2   3  4       3   2      2   2         2 3  3
+--R           (16a p q + 16a b p )x  + (24a p q  + 80a b p q + 24a b p )x
+--R         + 
+--R              3 3      2     2        2 2      3 3  2
+--R           (6a q  + 74a b p q  + 74a b p q + 6b p )x
+--R         + 
+--R              2   3        2   2     3 2
+--R           (8a b q  + 48a b p q  + 8b p q)x
+--R      *
+--R          +---+ +---+
+--R         \|a p \|b q
+--R  /
+--R              2             2                +---+ +---+
+--R         ((32a p q + 32a b p )x + 64a b p q)\|a p \|b q
+--R      *
+--R          +---------------------------+
+--R          |     2
+--R         \|a p x  + (a q + b p)x + b q
+--R     + 
+--R                3   2      2   2        2 3  2         2     2        2 2
+--R           (- 8a p q  - 48a b p q - 8a b p )x  + (- 64a b p q  - 64a b p q)x
+--R         + 
+--R                  2   2
+--R           - 64a b p q
+--R      *
+--R          +---+
+--R         \|a p
+--R                                                     Type: Expression Integer
+--E
+
+--S 17
+aa2:=aa.2
+--R
+--R   (3)
+--R                    3 3     2     2       2 2      3 3       2   3        2   2
+--R               (- 4a q  + 4a b p q  + 4a b p q - 4b p )x - 8a b q  + 16a b p q
+--R             + 
+--R                   3 2
+--R               - 8b p q
+--R          *
+--R                    +---------------------------+
+--R              +---+ |     2
+--R             \|b q \|a p x  + (a q + b p)x + b q
+--R         + 
+--R             4 4     3     3      2 2 2 2       3 3     4 4  2
+--R           (a q  + 4a b p q  - 10a b p q  + 4a b p q + b p )x
+--R         + 
+--R              3   4     2 2   3       3 2 2     4 3        2 2 4        3   3
+--R           (8a b q  - 8a b p q  - 8a b p q  + 8b p q)x + 8a b q  - 16a b p q
+--R         + 
+--R             4 2 2
+--R           8b p q
+--R      *
+--R                       +---------------------------+
+--R               +-----+ |     2                          +-----+ +---+
+--R              \|- a p \|a p x  + (a q + b p)x + b q  - \|- a p \|b q
+--R         atan(-------------------------------------------------------)
+--R                                       a p x
+--R     + 
+--R                3   2      2   2        2 3  3
+--R           (- 2a p q  - 12a b p q - 2a b p )x
+--R         + 
+--R               3 3      2     2        2 2     3 3  2
+--R           (- a q  - 23a b p q  - 23a b p q - b p )x
+--R         + 
+--R                2   3        2   2     3 2
+--R           (- 4a b q  - 24a b p q  - 4b p q)x
+--R      *
+--R                  +---------------------------+
+--R          +-----+ |     2
+--R         \|- a p \|a p x  + (a q + b p)x + b q
+--R     + 
+--R              3 2      2   3  4       3   2      2   2         2 3  3
+--R           (8a p q + 8a b p )x  + (12a p q  + 40a b p q + 12a b p )x
+--R         + 
+--R              3 3      2     2        2 2      3 3  2
+--R           (3a q  + 37a b p q  + 37a b p q + 3b p )x
+--R         + 
+--R              2   3        2   2     3 2
+--R           (4a b q  + 24a b p q  + 4b p q)x
+--R      *
+--R          +-----+ +---+
+--R         \|- a p \|b q
+--R  /
+--R              2             2                +-----+ +---+
+--R         ((16a p q + 16a b p )x + 32a b p q)\|- a p \|b q
+--R      *
+--R          +---------------------------+
+--R          |     2
+--R         \|a p x  + (a q + b p)x + b q
+--R     + 
+--R                3   2      2   2        2 3  2         2     2        2 2
+--R           (- 4a p q  - 24a b p q - 4a b p )x  + (- 32a b p q  - 32a b p q)x
+--R         + 
+--R                  2   2
+--R           - 32a b p q
+--R      *
+--R          +-----+
+--R         \|- a p
+--R                                                     Type: Expression Integer
+--E
+@
+We break the books answer into 3 parts, the first term, the coefficient
+of the second term, and the integral.
+<<*>>=
+--S 18
+bba:=((2*a*p*x+b*p+a*q)/(4*a*p))*sqrt((a*x+b)*(p*x+q))
+--R
+--R                             +---------------------------+
+--R                             |     2
+--R        (2a p x + a q + b p)\|a p x  + (a q + b p)x + b q
+--R   (4)  --------------------------------------------------
+--R                               4a p
+--R                                                     Type: Expression Integer
+--E
+
+--S 19
+bbb:=-(b*p-a*q)^2/(8*a*p)
+--R
+--R           2 2               2 2
+--R        - a q  + 2a b p q - b p
+--R   (5)  ------------------------
+--R                  8a p
+--R                                            Type: Fraction Polynomial Integer
+--E
+
+--S 20
+bbc:=integrate(1/sqrt((a*x+b)*(p*x+q)),x)
+--R
+--R   (6)
+--R   [
+--R       log
+--R                                       +---------------------------+
+--R                 +---+ +---+           |     2
+--R              (2\|a p \|b q  - 2a p x)\|a p x  + (a q + b p)x + b q
+--R            + 
+--R                     +---+            2                          +---+
+--R              2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
+--R         /
+--R                    +---------------------------+
+--R              +---+ |     2
+--R            2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
+--R    /
+--R        +---+
+--R       \|a p
+--R     ,
+--R                   +---------------------------+
+--R           +-----+ |     2                          +-----+ +---+
+--R          \|- a p \|a p x  + (a q + b p)x + b q  - \|- a p \|b q
+--R    2atan(-------------------------------------------------------)
+--R                                   a p x
+--R    --------------------------------------------------------------]
+--R                                +-----+
+--R                               \|- a p
+--R                                     Type: Union(List Expression Integer,...)
+--E
+@
+Since the integral has two parts, we break them apart
+<<*>>=
+--S 21
+bbc1:=bbc.1
+--R
+--R   (7)
+--R     log
+--R                                     +---------------------------+
+--R               +---+ +---+           |     2
+--R            (2\|a p \|b q  - 2a p x)\|a p x  + (a q + b p)x + b q
+--R          + 
+--R                   +---+            2                          +---+
+--R            2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
+--R       /
+--R                  +---------------------------+
+--R            +---+ |     2
+--R          2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
+--R  /
+--R      +---+
+--R     \|a p
+--R                                                     Type: Expression Integer
+--E
+
+--S 22
+bbc2:=bbc.2
+--R
+--R                       +---------------------------+
+--R               +-----+ |     2                          +-----+ +---+
+--R              \|- a p \|a p x  + (a q + b p)x + b q  - \|- a p \|b q
+--R        2atan(-------------------------------------------------------)
+--R                                       a p x
+--R   (8)  --------------------------------------------------------------
+--R                                    +-----+
+--R                                   \|- a p
+--R                                                     Type: Expression Integer
+--E
+@ 
+And now we construct the two bb answers based on the integral parts
+<<*>>=
+--S 23
+bb1:=bba+bbb*bbc1
+--R
+--R   (9)
+--R             2 2               2 2
+--R         (- a q  + 2a b p q - b p )
+--R      *
+--R         log
+--R                                         +---------------------------+
+--R                   +---+ +---+           |     2
+--R                (2\|a p \|b q  - 2a p x)\|a p x  + (a q + b p)x + b q
+--R              + 
+--R                       +---+            2                          +---+
+--R                2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
+--R           /
+--R                      +---------------------------+
+--R                +---+ |     2
+--R              2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
+--R     + 
+--R                                    +---------------------------+
+--R                              +---+ |     2
+--R       (4a p x + 2a q + 2b p)\|a p \|a p x  + (a q + b p)x + b q
+--R  /
+--R          +---+
+--R     8a p\|a p
+--R                                                     Type: Expression Integer
+--E
+
+--S 24
+bb2:=bba+bbb*bbc2
+--R
+--R   (10)
+--R             2 2               2 2
+--R         (- a q  + 2a b p q - b p )
+--R      *
+--R                       +---------------------------+
+--R               +-----+ |     2                          +-----+ +---+
+--R              \|- a p \|a p x  + (a q + b p)x + b q  - \|- a p \|b q
+--R         atan(-------------------------------------------------------)
+--R                                       a p x
+--R     + 
+--R                                    +---------------------------+
+--R                            +-----+ |     2
+--R       (2a p x + a q + b p)\|- a p \|a p x  + (a q + b p)x + b q
+--R  /
+--R          +-----+
+--R     4a p\|- a p
+--R                                                     Type: Expression Integer
+--E
+@
+So there are 4 possible combinations that might yield an answer.
+We construct all four.
+<<*>>=
+--S 25
+cc1:=aa1-bb1
+--R
+--R   (11)
+--R                  3 3     2     2       2 2      3 3       2   3        2   2
+--R               (4a q  - 4a b p q  - 4a b p q + 4b p )x + 8a b q  - 16a b p q
+--R             + 
+--R                 3 2
+--R               8b p q
+--R          *
+--R                    +---------------------------+
+--R              +---+ |     2
+--R             \|b q \|a p x  + (a q + b p)x + b q
+--R         + 
+--R               4 4     3     3      2 2 2 2       3 3     4 4  2
+--R           (- a q  - 4a b p q  + 10a b p q  - 4a b p q - b p )x
+--R         + 
+--R                3   4     2 2   3       3 2 2     4 3        2 2 4        3   3
+--R           (- 8a b q  + 8a b p q  + 8a b p q  - 8b p q)x - 8a b q  + 16a b p q
+--R         + 
+--R               4 2 2
+--R           - 8b p q
+--R      *
+--R         log
+--R                                         +---------------------------+
+--R                   +---+ +---+           |     2
+--R                (2\|a p \|b q  + 2a p x)\|a p x  + (a q + b p)x + b q
+--R              + 
+--R                         +---+            2                          +---+
+--R                - 2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
+--R           /
+--R                      +---------------------------+
+--R                +---+ |     2
+--R              2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
+--R     + 
+--R                  3 3     2     2       2 2      3 3       2   3        2   2
+--R               (4a q  - 4a b p q  - 4a b p q + 4b p )x + 8a b q  - 16a b p q
+--R             + 
+--R                 3 2
+--R               8b p q
+--R          *
+--R                    +---------------------------+
+--R              +---+ |     2
+--R             \|b q \|a p x  + (a q + b p)x + b q
+--R         + 
+--R               4 4     3     3      2 2 2 2       3 3     4 4  2
+--R           (- a q  - 4a b p q  + 10a b p q  - 4a b p q - b p )x
+--R         + 
+--R                3   4     2 2   3       3 2 2     4 3        2 2 4        3   3
+--R           (- 8a b q  + 8a b p q  + 8a b p q  - 8b p q)x - 8a b q  + 16a b p q
+--R         + 
+--R               4 2 2
+--R           - 8b p q
+--R      *
+--R         log
+--R                                         +---------------------------+
+--R                   +---+ +---+           |     2
+--R                (2\|a p \|b q  - 2a p x)\|a p x  + (a q + b p)x + b q
+--R              + 
+--R                       +---+            2                          +---+
+--R                2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
+--R           /
+--R                      +---------------------------+
+--R                +---+ |     2
+--R              2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
+--R     + 
+--R             2   3        2   2     3 2           2 3      3   2  +---+
+--R         ((8a b q  + 16a b p q  + 8b p q)x + 16a b q  + 16b p q )\|a p
+--R      *
+--R          +---------------------------+
+--R          |     2
+--R         \|a p x  + (a q + b p)x + b q
+--R     + 
+--R                3 3      2     2        2 2      3 3  2
+--R           (- 2a q  - 14a b p q  - 14a b p q - 2b p )x
+--R         + 
+--R                 2   3        2   2      3 2           2 3      3   2
+--R           (- 16a b q  - 32a b p q  - 16b p q)x - 16a b q  - 16b p q
+--R      *
+--R          +---+ +---+
+--R         \|a p \|b q
+--R  /
+--R              2             2                +---+ +---+
+--R         ((32a p q + 32a b p )x + 64a b p q)\|a p \|b q
+--R      *
+--R          +---------------------------+
+--R          |     2
+--R         \|a p x  + (a q + b p)x + b q
+--R     + 
+--R                3   2      2   2        2 3  2         2     2        2 2
+--R           (- 8a p q  - 48a b p q - 8a b p )x  + (- 64a b p q  - 64a b p q)x
+--R         + 
+--R                  2   2
+--R           - 64a b p q
+--R      *
+--R          +---+
+--R         \|a p
+--R                                                     Type: Expression Integer
+--E
+
+--S 26
+cc2:=aa1-bb2
+--R
+--R   (12)
+--R                  3 3     2     2       2 2      3 3       2   3        2   2
+--R               (4a q  - 4a b p q  - 4a b p q + 4b p )x + 8a b q  - 16a b p q
+--R             + 
+--R                 3 2
+--R               8b p q
+--R          *
+--R                            +---------------------------+
+--R              +-----+ +---+ |     2
+--R             \|- a p \|b q \|a p x  + (a q + b p)x + b q
+--R         + 
+--R                   4 4     3     3      2 2 2 2       3 3     4 4  2
+--R               (- a q  - 4a b p q  + 10a b p q  - 4a b p q - b p )x
+--R             + 
+--R                    3   4     2 2   3       3 2 2     4 3        2 2 4
+--R               (- 8a b q  + 8a b p q  + 8a b p q  - 8b p q)x - 8a b q
+--R             + 
+--R                    3   3     4 2 2
+--R               16a b p q  - 8b p q
+--R          *
+--R              +-----+
+--R             \|- a p
+--R      *
+--R         log
+--R                                         +---------------------------+
+--R                   +---+ +---+           |     2
+--R                (2\|a p \|b q  + 2a p x)\|a p x  + (a q + b p)x + b q
+--R              + 
+--R                         +---+            2                          +---+
+--R                - 2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
+--R           /
+--R                      +---------------------------+
+--R                +---+ |     2
+--R              2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
+--R     + 
+--R                  3 3     2     2       2 2      3 3        2   3        2   2
+--R               (8a q  - 8a b p q  - 8a b p q + 8b p )x + 16a b q  - 32a b p q
+--R             + 
+--R                  3 2
+--R               16b p q
+--R          *
+--R                          +---------------------------+
+--R              +---+ +---+ |     2
+--R             \|a p \|b q \|a p x  + (a q + b p)x + b q
+--R         + 
+--R                    4 4     3     3      2 2 2 2       3 3      4 4  2
+--R               (- 2a q  - 8a b p q  + 20a b p q  - 8a b p q - 2b p )x
+--R             + 
+--R                     3   4      2 2   3        3 2 2      4 3         2 2 4
+--R               (- 16a b q  + 16a b p q  + 16a b p q  - 16b p q)x - 16a b q
+--R             + 
+--R                    3   3      4 2 2
+--R               32a b p q  - 16b p q
+--R          *
+--R              +---+
+--R             \|a p
+--R      *
+--R                       +---------------------------+
+--R               +-----+ |     2                          +-----+ +---+
+--R              \|- a p \|a p x  + (a q + b p)x + b q  - \|- a p \|b q
+--R         atan(-------------------------------------------------------)
+--R                                       a p x
+--R     + 
+--R             2   3        2   2     3 2           2 3      3   2  +-----+ +---+
+--R         ((8a b q  + 16a b p q  + 8b p q)x + 16a b q  + 16b p q )\|- a p \|a p
+--R      *
+--R          +---------------------------+
+--R          |     2
+--R         \|a p x  + (a q + b p)x + b q
+--R     + 
+--R                3 3      2     2        2 2      3 3  2
+--R           (- 2a q  - 14a b p q  - 14a b p q - 2b p )x
+--R         + 
+--R                 2   3        2   2      3 2           2 3      3   2
+--R           (- 16a b q  - 32a b p q  - 16b p q)x - 16a b q  - 16b p q
+--R      *
+--R          +-----+ +---+ +---+
+--R         \|- a p \|a p \|b q
+--R  /
+--R              2             2                +-----+ +---+ +---+
+--R         ((32a p q + 32a b p )x + 64a b p q)\|- a p \|a p \|b q
+--R      *
+--R          +---------------------------+
+--R          |     2
+--R         \|a p x  + (a q + b p)x + b q
+--R     + 
+--R                3   2      2   2        2 3  2         2     2        2 2
+--R           (- 8a p q  - 48a b p q - 8a b p )x  + (- 64a b p q  - 64a b p q)x
+--R         + 
+--R                  2   2
+--R           - 64a b p q
+--R      *
+--R          +-----+ +---+
+--R         \|- a p \|a p
+--R                                                     Type: Expression Integer
+--E
+
+--S 27
+cc3:=aa1-bb1
+--R
+--R   (13)
+--R                  3 3     2     2       2 2      3 3       2   3        2   2
+--R               (4a q  - 4a b p q  - 4a b p q + 4b p )x + 8a b q  - 16a b p q
+--R             + 
+--R                 3 2
+--R               8b p q
+--R          *
+--R                    +---------------------------+
+--R              +---+ |     2
+--R             \|b q \|a p x  + (a q + b p)x + b q
+--R         + 
+--R               4 4     3     3      2 2 2 2       3 3     4 4  2
+--R           (- a q  - 4a b p q  + 10a b p q  - 4a b p q - b p )x
+--R         + 
+--R                3   4     2 2   3       3 2 2     4 3        2 2 4        3   3
+--R           (- 8a b q  + 8a b p q  + 8a b p q  - 8b p q)x - 8a b q  + 16a b p q
+--R         + 
+--R               4 2 2
+--R           - 8b p q
+--R      *
+--R         log
+--R                                         +---------------------------+
+--R                   +---+ +---+           |     2
+--R                (2\|a p \|b q  + 2a p x)\|a p x  + (a q + b p)x + b q
+--R              + 
+--R                         +---+            2                          +---+
+--R                - 2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
+--R           /
+--R                      +---------------------------+
+--R                +---+ |     2
+--R              2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
+--R     + 
+--R                  3 3     2     2       2 2      3 3       2   3        2   2
+--R               (4a q  - 4a b p q  - 4a b p q + 4b p )x + 8a b q  - 16a b p q
+--R             + 
+--R                 3 2
+--R               8b p q
+--R          *
+--R                    +---------------------------+
+--R              +---+ |     2
+--R             \|b q \|a p x  + (a q + b p)x + b q
+--R         + 
+--R               4 4     3     3      2 2 2 2       3 3     4 4  2
+--R           (- a q  - 4a b p q  + 10a b p q  - 4a b p q - b p )x
+--R         + 
+--R                3   4     2 2   3       3 2 2     4 3        2 2 4        3   3
+--R           (- 8a b q  + 8a b p q  + 8a b p q  - 8b p q)x - 8a b q  + 16a b p q
+--R         + 
+--R               4 2 2
+--R           - 8b p q
+--R      *
+--R         log
+--R                                         +---------------------------+
+--R                   +---+ +---+           |     2
+--R                (2\|a p \|b q  - 2a p x)\|a p x  + (a q + b p)x + b q
+--R              + 
+--R                       +---+            2                          +---+
+--R                2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
+--R           /
+--R                      +---------------------------+
+--R                +---+ |     2
+--R              2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
+--R     + 
+--R             2   3        2   2     3 2           2 3      3   2  +---+
+--R         ((8a b q  + 16a b p q  + 8b p q)x + 16a b q  + 16b p q )\|a p
+--R      *
+--R          +---------------------------+
+--R          |     2
+--R         \|a p x  + (a q + b p)x + b q
+--R     + 
+--R                3 3      2     2        2 2      3 3  2
+--R           (- 2a q  - 14a b p q  - 14a b p q - 2b p )x
+--R         + 
+--R                 2   3        2   2      3 2           2 3      3   2
+--R           (- 16a b q  - 32a b p q  - 16b p q)x - 16a b q  - 16b p q
+--R      *
+--R          +---+ +---+
+--R         \|a p \|b q
+--R  /
+--R              2             2                +---+ +---+
+--R         ((32a p q + 32a b p )x + 64a b p q)\|a p \|b q
+--R      *
+--R          +---------------------------+
+--R          |     2
+--R         \|a p x  + (a q + b p)x + b q
+--R     + 
+--R                3   2      2   2        2 3  2         2     2        2 2
+--R           (- 8a p q  - 48a b p q - 8a b p )x  + (- 64a b p q  - 64a b p q)x
+--R         + 
+--R                  2   2
+--R           - 64a b p q
+--R      *
+--R          +---+
+--R         \|a p
+--R                                                     Type: Expression Integer
+--E
+
+--S 28     14:122 Axiom cannot simplify this answer
+cc4:=aa2-bb2
+--R
+--R   (14)
+--R             2   3       2   2     3 2          2 3     3   2
+--R         ((4a b q  + 8a b p q  + 4b p q)x + 8a b q  + 8b p q )
+--R      *
+--R          +---------------------------+
+--R          |     2
+--R         \|a p x  + (a q + b p)x + b q
+--R     + 
+--R               3 3     2     2       2 2     3 3  2
+--R           (- a q  - 7a b p q  - 7a b p q - b p )x
+--R         + 
+--R                2   3        2   2     3 2          2 3     3   2
+--R           (- 8a b q  - 16a b p q  - 8b p q)x - 8a b q  - 8b p q
+--R      *
+--R          +---+
+--R         \|b q
+--R  /
+--R                                                 +---------------------------+
+--R            2             2                +---+ |     2
+--R       ((16a p q + 16a b p )x + 32a b p q)\|b q \|a p x  + (a q + b p)x + b q
+--R     + 
+--R            3   2      2   2        2 3  2         2     2        2 2
+--R       (- 4a p q  - 24a b p q - 4a b p )x  + (- 32a b p q  - 32a b p q)x
+--R     + 
+--R              2   2
+--R       - 32a b p q
+--R                                                     Type: Expression Integer
+--E
+
 @
 
 \section{\cite{1}:14.123~~~~~$\displaystyle\int{\sqrt{\frac{px+q}{ax+b}}}~dx$}
@@ -300,7 +1264,7 @@ $$
 <<*>>=
 )clear all
 
---S 4 of 5
+--S 29
 aa:=integrate(sqrt((p*x+q)/(a*x+b)),x)
 --R 
 --R
@@ -332,6 +1296,310 @@ aa:=integrate(sqrt((p*x+q)/(a*x+b)),x)
 --R                                a\|- a p
 --R                                     Type: Union(List Expression Integer,...)
 --E 
+
+--S 30
+aa1:=aa.1
+--R
+--R   (2)
+--R                                                                     +-------+
+--R                                           +---+      2              |p x + q
+--R       (a q - b p)log((2a p x + a q + b p)\|a p  + (2a p x + 2a b p) |------- )
+--R                                                                    \|a x + b
+--R     + 
+--R                   +-------+
+--R                   |p x + q  +---+
+--R       (2a x + 2b) |------- \|a p
+--R                  \|a x + b
+--R  /
+--R        +---+
+--R     2a\|a p
+--R                                                     Type: Expression Integer
+--E
+
+--S 31
+aa2:=aa.2
+--R
+--R                                 +-------+
+--R                         +-----+ |p x + q
+--R                        \|- a p  |-------                       +-------+
+--R                                \|a x + b               +-----+ |p x + q
+--R        (a q - b p)atan(------------------) + (a x + b)\|- a p  |-------
+--R                                 p                             \|a x + b
+--R   (3)  -----------------------------------------------------------------
+--R                                      +-----+
+--R                                    a\|- a p
+--R                                                     Type: Expression Integer
+--E
+
+--S 32
+bba:=sqrt((a*x+b)*(p*x+q))/a
+--R
+--R         +---------------------------+
+--R         |     2
+--R        \|a p x  + (a q + b p)x + b q
+--R   (4)  ------------------------------
+--R                       a
+--R                                                     Type: Expression Integer
+--E
+
+--S 33
+bbb:=(a*q-b*p)/(2*a)
+--R
+--R        a q - b p
+--R   (5)  ---------
+--R            2a
+--R                                            Type: Fraction Polynomial Integer
+--E
+
+--S 34
+bbc:=integrate(1/(sqrt((a*x+b)*(p*x+q))),x)
+--R
+--R   (6)
+--R   [
+--R       log
+--R                                       +---------------------------+
+--R                 +---+ +---+           |     2
+--R              (2\|a p \|b q  - 2a p x)\|a p x  + (a q + b p)x + b q
+--R            + 
+--R                     +---+            2                          +---+
+--R              2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
+--R         /
+--R                    +---------------------------+
+--R              +---+ |     2
+--R            2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
+--R    /
+--R        +---+
+--R       \|a p
+--R     ,
+--R                   +---------------------------+
+--R           +-----+ |     2                          +-----+ +---+
+--R          \|- a p \|a p x  + (a q + b p)x + b q  - \|- a p \|b q
+--R    2atan(-------------------------------------------------------)
+--R                                   a p x
+--R    --------------------------------------------------------------]
+--R                                +-----+
+--R                               \|- a p
+--R                                     Type: Union(List Expression Integer,...)
+--E
+
+--S 35
+bbc1:=bbc.1
+--R
+--R   (7)
+--R     log
+--R                                     +---------------------------+
+--R               +---+ +---+           |     2
+--R            (2\|a p \|b q  - 2a p x)\|a p x  + (a q + b p)x + b q
+--R          + 
+--R                   +---+            2                          +---+
+--R            2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
+--R       /
+--R                  +---------------------------+
+--R            +---+ |     2
+--R          2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
+--R  /
+--R      +---+
+--R     \|a p
+--R                                                     Type: Expression Integer
+--E
+
+--S 36
+bbc2:=bbc.2
+--R
+--R                       +---------------------------+
+--R               +-----+ |     2                          +-----+ +---+
+--R              \|- a p \|a p x  + (a q + b p)x + b q  - \|- a p \|b q
+--R        2atan(-------------------------------------------------------)
+--R                                       a p x
+--R   (8)  --------------------------------------------------------------
+--R                                    +-----+
+--R                                   \|- a p
+--R                                                     Type: Expression Integer
+--E
+
+--S 37
+bb1:=bba+bbb*bbc1
+--R
+--R   (9)
+--R         (a q - b p)
+--R      *
+--R         log
+--R                                         +---------------------------+
+--R                   +---+ +---+           |     2
+--R                (2\|a p \|b q  - 2a p x)\|a p x  + (a q + b p)x + b q
+--R              + 
+--R                       +---+            2                          +---+
+--R                2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
+--R           /
+--R                      +---------------------------+
+--R                +---+ |     2
+--R              2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
+--R     + 
+--R               +---------------------------+
+--R         +---+ |     2
+--R       2\|a p \|a p x  + (a q + b p)x + b q
+--R  /
+--R        +---+
+--R     2a\|a p
+--R                                                     Type: Expression Integer
+--E
+
+--S 38
+bb2:=bba+bbb*bbc2
+--R
+--R   (10)
+--R                                +---------------------------+
+--R                        +-----+ |     2                          +-----+ +---+
+--R                       \|- a p \|a p x  + (a q + b p)x + b q  - \|- a p \|b q
+--R       (a q - b p)atan(-------------------------------------------------------)
+--R                                                a p x
+--R     + 
+--R                +---------------------------+
+--R        +-----+ |     2
+--R       \|- a p \|a p x  + (a q + b p)x + b q
+--R  /
+--R       +-----+
+--R     a\|- a p
+--R                                                     Type: Expression Integer
+--E
+
+--S 39
+cc1:=aa1-bb1
+--R
+--R   (11)
+--R                                                                     +-------+
+--R                                           +---+      2              |p x + q
+--R       (a q - b p)log((2a p x + a q + b p)\|a p  + (2a p x + 2a b p) |------- )
+--R                                                                    \|a x + b
+--R     + 
+--R         (- a q + b p)
+--R      *
+--R         log
+--R                                         +---------------------------+
+--R                   +---+ +---+           |     2
+--R                (2\|a p \|b q  - 2a p x)\|a p x  + (a q + b p)x + b q
+--R              + 
+--R                       +---+            2                          +---+
+--R                2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
+--R           /
+--R                      +---------------------------+
+--R                +---+ |     2
+--R              2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
+--R     + 
+--R                 +---------------------------+               +-------+
+--R           +---+ |     2                                     |p x + q  +---+
+--R       - 2\|a p \|a p x  + (a q + b p)x + b q  + (2a x + 2b) |------- \|a p
+--R                                                            \|a x + b
+--R  /
+--R        +---+
+--R     2a\|a p
+--R                                                     Type: Expression Integer
+--E
+
+--S 40
+cc2:=aa1-bb2
+--R
+--R   (12)
+--R                     +-----+
+--R         (a q - b p)\|- a p
+--R      *
+--R                                                            +-------+
+--R                                  +---+      2              |p x + q
+--R         log((2a p x + a q + b p)\|a p  + (2a p x + 2a b p) |------- )
+--R                                                           \|a x + b
+--R     + 
+--R                         +---+
+--R         (- 2a q + 2b p)\|a p
+--R      *
+--R                       +---------------------------+
+--R               +-----+ |     2                          +-----+ +---+
+--R              \|- a p \|a p x  + (a q + b p)x + b q  - \|- a p \|b q
+--R         atan(-------------------------------------------------------)
+--R                                       a p x
+--R     + 
+--R                         +---------------------------+
+--R           +-----+ +---+ |     2
+--R       - 2\|- a p \|a p \|a p x  + (a q + b p)x + b q
+--R     + 
+--R                           +-------+
+--R                   +-----+ |p x + q  +---+
+--R       (2a x + 2b)\|- a p  |------- \|a p
+--R                          \|a x + b
+--R  /
+--R        +-----+ +---+
+--R     2a\|- a p \|a p
+--R                                                     Type: Expression Integer
+--E
+
+--S 41
+cc3:=aa2-bb1
+--R
+--R   (13)
+--R                       +-----+
+--R         (- a q + b p)\|- a p
+--R      *
+--R         log
+--R                                         +---------------------------+
+--R                   +---+ +---+           |     2
+--R                (2\|a p \|b q  - 2a p x)\|a p x  + (a q + b p)x + b q
+--R              + 
+--R                       +---+            2                          +---+
+--R                2a p x\|b q  + (- 2a p x  + (- a q - b p)x - 2b q)\|a p
+--R           /
+--R                      +---------------------------+
+--R                +---+ |     2
+--R              2\|b q \|a p x  + (a q + b p)x + b q  + (- a q - b p)x - 2b q
+--R     + 
+--R                                        +-------+
+--R                                +-----+ |p x + q
+--R                               \|- a p  |-------
+--R                     +---+             \|a x + b
+--R       (2a q - 2b p)\|a p atan(------------------)
+--R                                        p
+--R     + 
+--R                         +---------------------------+
+--R           +-----+ +---+ |     2
+--R       - 2\|- a p \|a p \|a p x  + (a q + b p)x + b q
+--R     + 
+--R                           +-------+
+--R                   +-----+ |p x + q  +---+
+--R       (2a x + 2b)\|- a p  |------- \|a p
+--R                          \|a x + b
+--R  /
+--R        +-----+ +---+
+--R     2a\|- a p \|a p
+--R                                                     Type: Expression Integer
+--E
+
+--S 42     14:88 Axiom cannot simplify these results
+cc4:=aa2-bb2
+--R
+--R   (14)
+--R         (- a q + b p)
+--R      *
+--R                       +---------------------------+
+--R               +-----+ |     2                          +-----+ +---+
+--R              \|- a p \|a p x  + (a q + b p)x + b q  - \|- a p \|b q
+--R         atan(-------------------------------------------------------)
+--R                                       a p x
+--R     + 
+--R                                +-------+
+--R                        +-----+ |p x + q
+--R                       \|- a p  |-------
+--R                               \|a x + b
+--R       (a q - b p)atan(------------------)
+--R                                p
+--R     + 
+--R                  +---------------------------+                     +-------+
+--R          +-----+ |     2                                   +-----+ |p x + q
+--R       - \|- a p \|a p x  + (a q + b p)x + b q  + (a x + b)\|- a p  |-------
+--R                                                                   \|a x + b
+--R  /
+--R       +-----+
+--R     a\|- a p
+--R                                                     Type: Expression Integer
+--E
+
 @
 
 \section{\cite{1}:14.124~~~~~$\displaystyle
@@ -342,7 +1610,7 @@ $$
 <<*>>=
 )clear all
 
---S 5 of 5
+--S 43
 aa:=integrate(1/((p*x+q)*sqrt((a*x+b)*(p*x+q))),x)
 --R 
 --R
@@ -354,6 +1622,38 @@ aa:=integrate(1/((p*x+q)*sqrt((a*x+b)*(p*x+q))),x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
 
+--S 44
+bb:=(2*sqrt(a*x+b))/((a*q-b*p)*sqrt(p*x+q))
+--R
+--R               +-------+
+--R             2\|a x + b
+--R   (2)  ---------------------
+--R                    +-------+
+--R        (a q - b p)\|p x + q
+--R                                                     Type: Expression Integer
+--E
+
+--S 45     14:124 Axiom cannot simplify this result
+cc:=aa-bb
+--R
+--R   (3)
+--R                      +---------------------------+
+--R            +-------+ |     2                                        +-------+
+--R       - 2q\|a x + b \|a p x  + (a q + b p)x + b q  + (2a q - 2b p)x\|p x + q
+--R     + 
+--R                   +---+ +-------+
+--R       (2p x + 2q)\|b q \|a x + b
+--R  /
+--R                                +---------------------------+
+--R           2          +-------+ |     2
+--R       (a q  - b p q)\|p x + q \|a p x  + (a q + b p)x + b q
+--R     + 
+--R                      2        2          +---+ +-------+
+--R       ((- a p q + b p )x - a q  + b p q)\|b q \|p x + q
+--R                                                     Type: Expression Integer
+--E
+
+
 )spool
 )lisp (bye)
 @
diff --git a/src/input/schaum6.input.pamphlet b/src/input/schaum6.input.pamphlet
index 9a08dc6..9b6f4f0 100644
--- a/src/input/schaum6.input.pamphlet
+++ b/src/input/schaum6.input.pamphlet
@@ -15,7 +15,7 @@ $$\int{\frac{1}{x^2+a^2}}=\frac{1}{a}\tan^{-1}\frac{x}{a}$$
 )set message auto off
 )clear all
 
---S 1 of 19
+--S 1
 aa:=integrate(1/(x^2+a^2),x)
 --R 
 --R
@@ -26,6 +26,25 @@ aa:=integrate(1/(x^2+a^2),x)
 --R           a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 2
+bb:=(1/a)*atan(x/a)
+--R
+--R             x
+--R        atan(-)
+--R             a
+--R   (2)  -------
+--R           a
+--R                                                     Type: Expression Integer
+--E
+
+--S 3      14:125 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
+
 @
 
 \section{\cite{1}:14.126~~~~~$\displaystyle\int{\frac{x~dx}{x^2+a^2}}$}
@@ -33,7 +52,7 @@ $$\int{\frac{x}{x^2+a^2}}=\frac{1}{2}\ln(x^2+a^2)$$
 <<*>>=
 )clear all
 
---S 2 of 19
+--S 4
 aa:=integrate(x/(x^2+a^2),x)
 --R 
 --R
@@ -43,6 +62,23 @@ aa:=integrate(x/(x^2+a^2),x)
 --R              2
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 5
+bb:=(1/2)*log(x^2+a^2)
+--R
+--R             2    2
+--R        log(x  + a )
+--R   (2)  ------------
+--R              2
+--R                                                     Type: Expression Integer
+--E
+
+--S 6      14:126 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E 
 @
 
 \section{\cite{1}:14.127~~~~~$\displaystyle\int{\frac{x^2~dx}{x^2+a^2}}$}
@@ -50,7 +86,7 @@ $$\int{\frac{x^2}{x^2+a^2}}=x-a\tan^{-1}\frac{x}{a}$$
 <<*>>=
 )clear all
 
---S 3 of 19
+--S 7
 aa:=integrate(x^2/(x^2+a^2),x)
 --R 
 --R
@@ -59,6 +95,23 @@ aa:=integrate(x^2/(x^2+a^2),x)
 --R                 a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 8
+bb:=x-a*atan(x/a)
+--R
+--R                 x
+--R   (2)  - a atan(-) + x
+--R                 a
+--R                                                     Type: Expression Integer
+--E
+
+--S 9      14:127 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
+
 @
 
 \section{\cite{1}:14.128~~~~~$\displaystyle\int{\frac{x^3~dx}{x^2+a^2}}$}
@@ -67,7 +120,7 @@ $$\int{\frac{x^3}{x^2+a^2}}=\frac{x^2}{2}-\frac{a^2}{2}\ln(x^2+a^2)$$
 <<*>>=
 )clear all
 
---S 4 of 19
+--S 10
 aa:=integrate(x^3/(x^2+a^2),x)
 --R 
 --R
@@ -77,6 +130,23 @@ aa:=integrate(x^3/(x^2+a^2),x)
 --R                  2
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 11
+bb:=x^2/2-a^2/2*log(x^2+a^2)
+--R
+--R           2     2    2     2
+--R        - a log(x  + a ) + x
+--R   (2)  ---------------------
+--R                  2
+--R                                                     Type: Expression Integer
+--E
+
+--S 12     14:128 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.129~~~~~$\displaystyle\int{\frac{dx}{x(x^2+a^2)}}$}
@@ -86,7 +156,7 @@ $$
 <<*>>=
 )clear all
 
---S 5 of 19
+--S 13
 aa:=integrate(1/(x*(x^2+a^2)),x)
 --R 
 --R
@@ -97,6 +167,70 @@ aa:=integrate(1/(x*(x^2+a^2)),x)
 --R                   2a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 14
+bb:=1/(2*a^2)*log(x^2/(x^2+a^2))
+--R
+--R                2
+--R               x
+--R        log(-------)
+--R             2    2
+--R            x  + a
+--R   (2)  ------------
+--R               2
+--R             2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 15
+cc:=aa-bb
+--R
+--R                                           2
+--R               2    2                     x
+--R        - log(x  + a ) + 2log(x) - log(-------)
+--R                                        2    2
+--R                                       x  + a
+--R   (3)  ---------------------------------------
+--R                            2
+--R                          2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 16
+divlog:=rule(log(a/b) == log(a) - log(b))
+--R
+--R            a
+--R   (4)  log(-) == - log(b) + log(a)
+--R            b
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 17
+dd:=divlog cc
+--R
+--R               2
+--R        - log(x ) + 2log(x)
+--R   (5)  -------------------
+--R                  2
+--R                2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 18
+logpow:=rule(log(a^n) == n*log(a))
+--R
+--R             n
+--R   (6)  log(a ) == n log(a)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 19     14:129 Schaums and Axiom agree
+ee:=logpow dd
+--R
+--R   (7)  0
+--R                                                     Type: Expression Integer
+--E
+
 @
 
 \section{\cite{1}:14.130~~~~~$\displaystyle\int{\frac{dx}{x^2(x^2+a^2)}}$}
@@ -106,7 +240,7 @@ $$
 <<*>>=
 )clear all
 
---S 6 of 19
+--S 20
 aa:=integrate(1/(x^2*(x^2+a^2)),x)
 --R 
 --R
@@ -118,6 +252,26 @@ aa:=integrate(1/(x^2*(x^2+a^2)),x)
 --R              a x
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 21
+bb:=-1/(a^2*x)-1/a^3*atan(x/a)
+--R
+--R                 x
+--R        - x atan(-) - a
+--R                 a
+--R   (2)  ---------------
+--R               3
+--R              a x
+--R                                                     Type: Expression Integer
+--E
+
+--S 22     14:130 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
+
 @
 
 \section{\cite{1}:14.131~~~~~$\displaystyle\int{\frac{dx}{x^3(x^2+a^2)}}$}
@@ -127,7 +281,7 @@ $$
 <<*>>=
 )clear all
 
---S 7 of 19
+--S 23
 aa:=integrate(1/(x^3*(x^2+a^2)),x)
 --R 
 --R
@@ -138,6 +292,70 @@ aa:=integrate(1/(x^3*(x^2+a^2)),x)
 --R                     2a x
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 24
+bb:=-1/(2*a^2*x^2)-1/(2*a^4)*log(x^2/(x^2+a^2))
+--R
+--R                    2
+--R           2       x        2
+--R        - x log(-------) - a
+--R                 2    2
+--R                x  + a
+--R   (2)  ---------------------
+--R                  4 2
+--R                2a x
+--R                                                     Type: Expression Integer
+--E
+
+--S 25
+cc:=aa-bb
+--R
+--R                                         2
+--R             2    2                     x
+--R        log(x  + a ) - 2log(x) + log(-------)
+--R                                      2    2
+--R                                     x  + a
+--R   (3)  -------------------------------------
+--R                           4
+--R                         2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 26
+divlog:=rule(log(a/b) == log(a) - log(b))
+--R
+--R            a
+--R   (4)  log(-) == - log(b) + log(a)
+--R            b
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 27
+dd:=divlog cc
+--R
+--R             2
+--R        log(x ) - 2log(x)
+--R   (5)  -----------------
+--R                 4
+--R               2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 28
+logpow:=rule(log(a^n) == n*log(a))
+--R
+--R             n
+--R   (6)  log(a ) == n log(a)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 29     14:131 Schaums and Axiom agree
+ee:=logpow dd
+--R
+--R   (7)  0
+--R                                                     Type: Expression Integer
+--E
+
 @
 
 \section{\cite{1}:14.132~~~~~$\displaystyle\int{\frac{dx}{(x^2+a^2)^2}}$}
@@ -147,7 +365,7 @@ $$
 <<*>>=
 )clear all
 
---S 8 of 19
+--S 30
 aa:=integrate(1/((x^2+a^2)^2),x)
 --R 
 --R
@@ -159,6 +377,26 @@ aa:=integrate(1/((x^2+a^2)^2),x)
 --R              2a x  + 2a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 31
+bb:=x/(2*a^2*(x^2+a^2))+1/(2*a^3)*atan(x/a)
+--R
+--R          2    2      x
+--R        (x  + a )atan(-) + a x
+--R                      a
+--R   (2)  ----------------------
+--R                3 2     5
+--R              2a x  + 2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 32     14:132 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
+
 @
 
 \section{\cite{1}:14.133~~~~~$\displaystyle\int{\frac{x~dx}{(x^2+a^2)^2}}$}
@@ -168,7 +406,7 @@ $$
 <<*>>=
 )clear all
 
---S 9 of 19
+--S 33
 aa:=integrate(x/((x^2+a^2)^2),x)
 --R 
 --R
@@ -178,6 +416,23 @@ aa:=integrate(x/((x^2+a^2)^2),x)
 --R          2x  + 2a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 34
+bb:=-1/(2*(x^2+a^2))
+--R
+--R              1
+--R   (2)  - ---------
+--R            2     2
+--R          2x  + 2a
+--R                                            Type: Fraction Polynomial Integer
+--E
+
+--S 35     14:133 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.134~~~~~$\displaystyle\int{\frac{x^2dx}{(x^2+a^2)^2}}$}
@@ -187,7 +442,7 @@ $$
 <<*>>=
 )clear all
 
---S 10 of 19
+--S 36
 aa:=integrate(x^2/((x^2+a^2)^2),x)
 --R 
 --R
@@ -199,6 +454,25 @@ aa:=integrate(x^2/((x^2+a^2)^2),x)
 --R              2a x  + 2a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 37
+bb:=-x/(2*(x^2+a^2))+1/(2*a)*atan(x/a)
+--R
+--R          2    2      x
+--R        (x  + a )atan(-) - a x
+--R                      a
+--R   (2)  ----------------------
+--R                  2     3
+--R              2a x  + 2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 38     14:134 Schaums and Axiom differ by a constant
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.135~~~~~$\displaystyle\int{\frac{x^3dx}{(x^2+a^2)^2}}$}
@@ -208,7 +482,7 @@ $$
 <<*>>=
 )clear all
 
---S 11 of 19
+--S 39
 aa:=integrate(x^3/((x^2+a^2)^2),x)
 --R 
 --R
@@ -219,6 +493,24 @@ aa:=integrate(x^3/((x^2+a^2)^2),x)
 --R                 2x  + 2a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 40
+bb:=a^2/(2*(x^2+a^2))+1/2*log(x^2+a^2)
+--R
+--R          2    2      2    2     2
+--R        (x  + a )log(x  + a ) + a
+--R   (2)  --------------------------
+--R                   2     2
+--R                 2x  + 2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 41     14:135 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.136~~~~~$\displaystyle\int{\frac{dx}{x(x^2+a^2)^2}}$}
@@ -228,7 +520,7 @@ $$
 <<*>>=
 )clear all
 
---S 12 of 19
+--S 42
 aa:=integrate(1/(x*(x^2+a^2)^2),x)
 --R 
 --R
@@ -239,6 +531,69 @@ aa:=integrate(1/(x*(x^2+a^2)^2),x)
 --R                           2a x  + 2a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 43
+bb:=1/(2*a^2*(x^2+a^2))+1/(2*a^4)*log(x^2/(x^2+a^2))
+--R
+--R                         2
+--R          2    2        x        2
+--R        (x  + a )log(-------) + a
+--R                      2    2
+--R                     x  + a
+--R   (2)  --------------------------
+--R                  4 2     6
+--R                2a x  + 2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 44
+cc:=aa-bb
+--R
+--R                                           2
+--R               2    2                     x
+--R        - log(x  + a ) + 2log(x) - log(-------)
+--R                                        2    2
+--R                                       x  + a
+--R   (3)  ---------------------------------------
+--R                            4
+--R                          2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 45
+divlog:=rule(log(a/b) == log(a) - log(b))
+--R
+--R            a
+--R   (4)  log(-) == - log(b) + log(a)
+--R            b
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 46
+dd:=divlog cc
+--R
+--R               2
+--R        - log(x ) + 2log(x)
+--R   (5)  -------------------
+--R                  4
+--R                2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 47
+logpow:=rule(log(a^n) == n*log(a))
+--R
+--R             n
+--R   (6)  log(a ) == n log(a)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 48     14:136 Schaums and Axiom agree
+ee:=logpow dd
+--R
+--R   (7)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.137~~~~~$\displaystyle\int{\frac{dx}{x^2(x^2+a^2)^2}}$}
@@ -248,18 +603,36 @@ $$
 <<*>>=
 )clear all
 
---S 13 of 19
-aa:=integrate(1/((x^2+a^2)^2),x)
---R 
+--S 49
+aa:=integrate(1/(x^2*(x^2+a^2)^2),x)
 --R
---R          2    2      x
---R        (x  + a )atan(-) + a x
---R                      a
---R   (1)  ----------------------
---R                3 2     5
---R              2a x  + 2a
+--R             3     2       x        2     3
+--R        (- 3x  - 3a x)atan(-) - 3a x  - 2a
+--R                           a
+--R   (1)  -----------------------------------
+--R                      5 3     7
+--R                    2a x  + 2a x
 --R                                          Type: Union(Expression Integer,...)
---E 
+--E
+
+--S 50
+bb:=-1/(a^4*x)-x/(2*a^4*(x^2+a^2))-3/(2*a^5)*atan(x/a)
+--R
+--R             3     2       x        2     3
+--R        (- 3x  - 3a x)atan(-) - 3a x  - 2a
+--R                           a
+--R   (2)  -----------------------------------
+--R                      5 3     7
+--R                    2a x  + 2a x
+--R                                                     Type: Expression Integer
+--E
+
+--S 51     14:137 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.138~~~~~$\displaystyle\int{\frac{dx}{x^3(x^2+a^2)^2}}$}
@@ -270,7 +643,7 @@ $$
 <<*>>=
 )clear all
 
---S 14 of 19
+--S 52
 aa:=integrate(1/(x^3*(x^2+a^2)^2),x)
 --R 
 --R
@@ -281,6 +654,70 @@ aa:=integrate(1/(x^3*(x^2+a^2)^2),x)
 --R                                 2a x  + 2a x
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 53
+bb:=-1/(2*a^4*x^2)-1/(2*a^4*(x^2+a^2))-1/a^6*log(x^2/(x^2+a^2))
+--R
+--R                               2
+--R             4     2 2        x         2 2    4
+--R        (- 2x  - 2a x )log(-------) - 2a x  - a
+--R                            2    2
+--R                           x  + a
+--R   (2)  ----------------------------------------
+--R                        6 4     8 2
+--R                      2a x  + 2a x
+--R                                                     Type: Expression Integer
+--E
+
+--S 54
+cc:=aa-bb
+--R
+--R                                         2
+--R             2    2                     x
+--R        log(x  + a ) - 2log(x) + log(-------)
+--R                                      2    2
+--R                                     x  + a
+--R   (3)  -------------------------------------
+--R                           6
+--R                          a
+--R                                                     Type: Expression Integer
+--E
+
+--S 55
+divlog:=rule(log(a/b) == log(a) - log(b))
+--R
+--R            a
+--R   (4)  log(-) == - log(b) + log(a)
+--R            b
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 56
+dd:=divlog cc
+--R
+--R             2
+--R        log(x ) - 2log(x)
+--R   (5)  -----------------
+--R                 6
+--R                a
+--R                                                     Type: Expression Integer
+--E
+
+--S 57
+logpow:=rule(log(a^n) == n*log(a))
+--R
+--R             n
+--R   (6)  log(a ) == n log(a)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 58     14:138 Schaums and Axiom agree
+ee:=logpow dd
+--R
+--R   (7)  0
+--R                                                     Type: Expression Integer
+--E
+
 @
 
 \section{\cite{1}:14.139~~~~~$\displaystyle\int{\frac{dx}{(x^2+a^2)^n}}$}
@@ -291,7 +728,7 @@ $$
 <<*>>=
 )clear all
 
---S 15 of 19
+--S 59     14:139 Axiom cannot do this integral
 aa:=integrate(1/((x^2+a^2)^n),x)
 --R 
 --R
@@ -311,7 +748,7 @@ $$
 <<*>>=
 )clear all
 
---S 16 of 19
+--S 60
 aa:=integrate(x/((x^2+a^2)^n),x)
 --R 
 --R
@@ -323,6 +760,48 @@ aa:=integrate(x/((x^2+a^2)^n),x)
 --R        (2n - 2)%e
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 61
+bb:=-1/(2*(n-1)*(x^2+a^2)^(n-1))
+--R
+--R                     1
+--R   (2)  - ----------------------
+--R                    2    2 n - 1
+--R          (2n - 2)(x  + a )
+--R                                                     Type: Expression Integer
+--E
+
+--S 62
+cc:=aa-bb
+--R
+--R                 2    2
+--R          n log(x  + a )       2    2   2    2 n - 1
+--R        %e               + (- x  - a )(x  + a )
+--R   (3)  --------------------------------------------
+--R                                          2    2
+--R                     2    2 n - 1  n log(x  + a )
+--R           (2n - 2)(x  + a )     %e
+--R                                                     Type: Expression Integer
+--E
+
+--S 63
+explog:=rule(%e^(n*log(x)) == x^n)
+--R
+--R          n log(x)     n
+--R   (4)  %e         == x
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 64     14:140 Schaums and Axiom cannot simplify this expression
+dd:=explog cc
+--R
+--R          2    2 n       2    2   2    2 n - 1
+--R        (x  + a )  + (- x  - a )(x  + a )
+--R   (5)  --------------------------------------
+--R                     2    2 n - 1  2    2 n
+--R           (2n - 2)(x  + a )     (x  + a )
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.141~~~~~$\displaystyle\int{\frac{dx}{x(x^2+a^2)^n}}$}
@@ -333,7 +812,7 @@ $$
 <<*>>=
 )clear all
 
---S 17 of 19
+--S 65     14:141 Axiom cannot do this integral
 aa:=integrate(1/(x*(x^2+a^2)^n),x)
 --R 
 --R
@@ -354,7 +833,7 @@ $$
 <<*>>=
 )clear all
 
---S 18 of 19
+--S 66     14:142 Axiom cannot do this integral
 aa:=integrate(x^m/((x^2+a^2)^n),x)
 --R 
 --R
@@ -375,7 +854,7 @@ $$
 <<*>>=
 )clear all
 
---S 19 of 19
+--S 67     14:143 Axiom cannot do this integral
 aa:=integrate(1/(x^m*(x^2+a^2)^n),x)
 --R 
 --R
diff --git a/src/input/schaum7.input.pamphlet b/src/input/schaum7.input.pamphlet
index 9226da0..3062d2e 100644
--- a/src/input/schaum7.input.pamphlet
+++ b/src/input/schaum7.input.pamphlet
@@ -16,7 +16,7 @@ $$\int{\frac{1}{x^2-a^2}}=-\frac{1}{a}\coth^{-1}\frac{x}{a}$$
 )set message auto off
 )clear all
 
---S 1 of 19
+--S 1
 aa:=integrate(1/(x^2-a^2),x)
 --R 
 --R
@@ -25,6 +25,45 @@ aa:=integrate(1/(x^2-a^2),x)
 --R                    2a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 2
+bb:=1/(2*a)*log((x-a)/(x+a))
+--R
+--R            x - a
+--R        log(-----)
+--R            x + a
+--R   (2)  ----------
+--R            2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 3
+cc:=aa-bb
+--R
+--R                                        x - a
+--R        - log(x + a) + log(x - a) - log(-----)
+--R                                        x + a
+--R   (3)  --------------------------------------
+--R                          2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 4
+divlog:=rule(log(a/b) == log(a) - log(b))
+--R
+--R            a
+--R   (4)  log(-) == - log(b) + log(a)
+--R            b
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 5      14:144 Schaums and Axiom agree
+dd:=divlog cc
+--R
+--R   (5)  0
+--R                                                     Type: Expression Integer
+--E
+
 @
 
 \section{\cite{1}:14.145~~~~~$\displaystyle\int{\frac{x~dx}{x^2-a^2}}$}
@@ -32,7 +71,7 @@ $$\int{\frac{x}{x^2-a^2}}=\frac{1}{2}\ln(x^2-a^2)$$
 <<*>>=
 )clear all
 
---S 2 of 19
+--S 6
 aa:=integrate(x/(x^2-a^2),x)
 --R 
 --R
@@ -42,6 +81,24 @@ aa:=integrate(x/(x^2-a^2),x)
 --R              2
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 7
+bb:=1/2*log(x^2-a^2)
+--R
+--R             2    2
+--R        log(x  - a )
+--R   (2)  ------------
+--R              2
+--R                                                     Type: Expression Integer
+--E
+
+--S 8      14:145 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
+
 @
 
 \section{\cite{1}:14.146~~~~~$\displaystyle\int{\frac{x^2~dx}{x^2-a^2}}$}
@@ -49,7 +106,7 @@ $$\int{\frac{x^2}{x^2-a^2}}=x+\frac{a}{2}\ln\left(\frac{x-a}{x+a}\right)$$
 <<*>>=
 )clear all
 
---S 3 of 19
+--S 9
 aa:=integrate(x^2/(x^2-a^2),x)
 --R 
 --R
@@ -58,6 +115,45 @@ aa:=integrate(x^2/(x^2-a^2),x)
 --R                         2
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 10
+bb:=x+a/2*log((x-a)/(x+a))
+--R
+--R              x - a
+--R        a log(-----) + 2x
+--R              x + a
+--R   (2)  -----------------
+--R                2
+--R                                                     Type: Expression Integer
+--E
+
+--S 11
+cc:=aa-bb
+--R
+--R                                              x - a
+--R        - a log(x + a) + a log(x - a) - a log(-----)
+--R                                              x + a
+--R   (3)  --------------------------------------------
+--R                              2
+--R                                                     Type: Expression Integer
+--E
+
+--S 12
+divlog:=rule(log(a/b) == log(a) - log(b))
+--R
+--R            a
+--R   (4)  log(-) == - log(b) + log(a)
+--R            b
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 13     14:146 Schaums and Axiom agree
+dd:=divlog cc
+--R
+--R   (5)  0
+--R                                                     Type: Expression Integer
+--E
+
 @
 
 \section{\cite{1}:14.147~~~~~$\displaystyle\int{\frac{x^3~dx}{x^2-a^2}}$}
@@ -66,7 +162,7 @@ $$\int{\frac{x^3}{x^2-a^2}}=\frac{x^2}{2}+\frac{a^2}{2}\ln(x^2-a^2)$$
 <<*>>=
 )clear all
 
---S 4 of 19
+--S 14
 aa:=integrate(x^3/(x^2-a^2),x)
 --R 
 --R
@@ -76,6 +172,24 @@ aa:=integrate(x^3/(x^2-a^2),x)
 --R                 2
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 15
+bb:=x^2/2+a^2/2*log(x^2-a^2)
+--R
+--R         2     2    2     2
+--R        a log(x  - a ) + x
+--R   (2)  -------------------
+--R                 2
+--R                                                     Type: Expression Integer
+--E
+
+--S 16     14:147 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
+
 @
 
 \section{\cite{1}:14.148~~~~~$\displaystyle\int{\frac{dx}{x(x^2-a^2)}}$}
@@ -85,7 +199,7 @@ $$
 <<*>>=
 )clear all
 
---S 5 of 19
+--S 17
 aa:=integrate(1/(x*(x^2-a^2)),x)
 --R 
 --R
@@ -96,6 +210,70 @@ aa:=integrate(1/(x*(x^2-a^2)),x)
 --R                  2a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 18
+bb:=1/(2*a^2)*log((x^2-a^2)/x^2)
+--R
+--R             2    2
+--R            x  - a
+--R        log(-------)
+--R                2
+--R               x
+--R   (2)  ------------
+--R               2
+--R             2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 19
+cc:=aa-bb
+--R
+--R                                      2    2
+--R             2    2                  x  - a
+--R        log(x  - a ) - 2log(x) - log(-------)
+--R                                         2
+--R                                        x
+--R   (3)  -------------------------------------
+--R                           2
+--R                         2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 20
+divlog:=rule(log(a/b) == log(a) - log(b))
+--R
+--R            a
+--R   (4)  log(-) == - log(b) + log(a)
+--R            b
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 21
+dd:=divlog cc
+--R
+--R             2
+--R        log(x ) - 2log(x)
+--R   (5)  -----------------
+--R                 2
+--R               2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 22
+logpow:=rule(log(a^n) == n*log(a))
+--R
+--R             n
+--R   (6)  log(a ) == n log(a)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 23     14:148 Schaums and Axiom agree
+ee:=logpow dd
+--R
+--R   (7)  0
+--R                                                     Type: Expression Integer
+--E
+
 @
 
 \section{\cite{1}:14.149~~~~~$\displaystyle\int{\frac{dx}{x^2(x^2-a^2)}}$}
@@ -105,7 +283,7 @@ $$
 <<*>>=
 )clear all
 
---S 6 of 19
+--S 24
 aa:=integrate(1/(x^2*(x^2-a^2)),x)
 --R 
 --R
@@ -115,6 +293,47 @@ aa:=integrate(1/(x^2*(x^2-a^2)),x)
 --R                       2a x
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 25
+bb:=1/(a^2*x)+1/(2*a^3)*log((x-a)/(x+a))
+--R
+--R              x - a
+--R        x log(-----) + 2a
+--R              x + a
+--R   (2)  -----------------
+--R                 3
+--R               2a x
+--R                                                     Type: Expression Integer
+--E
+
+--S 26
+cc:=aa-bb
+--R
+--R                                        x - a
+--R        - log(x + a) + log(x - a) - log(-----)
+--R                                        x + a
+--R   (3)  --------------------------------------
+--R                            3
+--R                          2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 27
+divlog:=rule(log(a/b) == log(a) - log(b))
+--R
+--R            a
+--R   (4)  log(-) == - log(b) + log(a)
+--R            b
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 28     14:149 Schaums and Axiom agree
+dd:=divlog cc
+--R
+--R   (5)  0
+--R                                                     Type: Expression Integer
+--E
+
 @
 
 \section{\cite{1}:14.150~~~~~$\displaystyle\int{\frac{dx}{x^3(x^2-a^2)}}$}
@@ -124,7 +343,7 @@ $$
 <<*>>=
 )clear all
 
---S 7 of 19
+--S 29
 aa:=integrate(1/(x^3*(x^2-a^2)),x)
 --R 
 --R
@@ -135,6 +354,73 @@ aa:=integrate(1/(x^3*(x^2-a^2)),x)
 --R                     2a x
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 30
+bb:=1/(2*a^2*x*2)-1/(2*a^4)*log(x^2/(x^2-a^2))
+--R
+--R                     2
+--R                    x        2
+--R        - 2x log(-------) + a
+--R                  2    2
+--R                 x  - a
+--R   (2)  ----------------------
+--R                   4
+--R                 4a x
+--R                                                     Type: Expression Integer
+--E
+
+--S 31
+cc:=aa-bb
+--R
+--R                                                 2
+--R          2     2    2      2           2       x        2      2
+--R        2x log(x  - a ) - 4x log(x) + 2x log(-------) - a x + 2a
+--R                                              2    2
+--R                                             x  - a
+--R   (3)  ---------------------------------------------------------
+--R                                    4 2
+--R                                  4a x
+--R                                                     Type: Expression Integer
+--E
+
+--S 32
+divlog:=rule(log(a/b) == log(a) - log(b))
+--R
+--R            a
+--R   (4)  log(-) == - log(b) + log(a)
+--R            b
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 33
+dd:=divlog cc
+--R
+--R          2     2      2          2      2
+--R        2x log(x ) - 4x log(x) - a x + 2a
+--R   (5)  ----------------------------------
+--R                         4 2
+--R                       4a x
+--R                                                     Type: Expression Integer
+--E
+
+--S 34
+logpow:=rule(log(a^n) == n*log(a))
+--R
+--R             n
+--R   (6)  log(a ) == n log(a)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 35     14:150 Schaums and Axiom DISAGREE BY A NON-CONSTANT
+ee:=logpow dd
+--R
+--R        - x + 2
+--R   (7)  -------
+--R           2 2
+--R         4a x
+--R                                                     Type: Expression Integer
+--E
+
 @
 
 \section{\cite{1}:14.151~~~~~$\displaystyle\int{\frac{dx}{(x^2-a^2)^2}}$}
@@ -144,7 +430,7 @@ $$
 <<*>>=
 )clear all
 
---S 8 of 19
+--S 36
 aa:=integrate(1/((x^2-a^2)^2),x)
 --R 
 --R
@@ -155,6 +441,47 @@ aa:=integrate(1/((x^2-a^2)^2),x)
 --R                            4a x  - 4a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 37
+bb:=-x/(2*a^2*(x^2-a^2))-1/(4*a^3)*log((x-a)/(x+a))
+--R
+--R            2    2     x - a
+--R        (- x  + a )log(-----) - 2a x
+--R                       x + a
+--R   (2)  ----------------------------
+--R                   3 2     5
+--R                 4a x  - 4a
+--R                                                     Type: Expression Integer
+--E
+
+--S 38
+cc:=aa-bb
+--R
+--R                                      x - a
+--R        log(x + a) - log(x - a) + log(-----)
+--R                                      x + a
+--R   (3)  ------------------------------------
+--R                           3
+--R                         4a
+--R                                                     Type: Expression Integer
+--E
+
+--S 39
+divlog:=rule(log(a/b) == log(a) - log(b))
+--R
+--R            a
+--R   (4)  log(-) == - log(b) + log(a)
+--R            b
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 40     14:151 Schaums and Axiom agree
+dd:=divlog cc
+--R
+--R   (5)  0
+--R                                                     Type: Expression Integer
+--E
+
 @
 
 \section{\cite{1}:14.152~~~~~$\displaystyle\int{\frac{x~dx}{(x^2-a^2)^2}}$}
@@ -164,7 +491,7 @@ $$
 <<*>>=
 )clear all
 
---S 9 of 19
+--S 41
 aa:=integrate(x/((x^2-a^2)^2),x)
 --R 
 --R
@@ -174,6 +501,24 @@ aa:=integrate(x/((x^2-a^2)^2),x)
 --R          2x  - 2a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 42
+bb:=-1/(2*(x^2-a^2))
+--R
+--R              1
+--R   (2)  - ---------
+--R            2     2
+--R          2x  - 2a
+--R                                            Type: Fraction Polynomial Integer
+--E
+
+--S 43     14:152 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
+
 @
 
 \section{\cite{1}:14.153~~~~~$\displaystyle\int{\frac{x^2dx}{(x^2-a^2)^2}}$}
@@ -183,7 +528,7 @@ $$
 <<*>>=
 )clear all
 
---S 10 of 19
+--S 44
 aa:=integrate(x^2/((x^2-a^2)^2),x)
 --R 
 --R
@@ -194,6 +539,46 @@ aa:=integrate(x^2/((x^2-a^2)^2),x)
 --R                            4a x  - 4a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 45
+bb:=-x/(2*(x^2-a^2))+1/(4*a)*log((x-a)/(x+a))
+--R
+--R          2    2     x - a
+--R        (x  - a )log(-----) - 2a x
+--R                     x + a
+--R   (2)  --------------------------
+--R                    2     3
+--R                4a x  - 4a
+--R                                                     Type: Expression Integer
+--E
+
+--S 46
+cc:=aa-bb
+--R
+--R                                        x - a
+--R        - log(x + a) + log(x - a) - log(-----)
+--R                                        x + a
+--R   (3)  --------------------------------------
+--R                          4a
+--R                                                     Type: Expression Integer
+--E
+
+--S 47
+divlog:=rule(log(a/b) == log(a) - log(b))
+--R
+--R            a
+--R   (4)  log(-) == - log(b) + log(a)
+--R            b
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 48     14:153 Schaums and Axiom agree
+dd:=divlog cc
+--R
+--R   (5)  0
+--R                                                     Type: Expression Integer
+--E
+
 @
 
 \section{\cite{1}:14.154~~~~~$\displaystyle\int{\frac{x^3dx}{(x^2-a^2)^2}}$}
@@ -203,7 +588,7 @@ $$
 <<*>>=
 )clear all
 
---S 11 of 19
+--S 49
 aa:=integrate(x^3/((x^2-a^2)^2),x)
 --R 
 --R
@@ -214,6 +599,25 @@ aa:=integrate(x^3/((x^2-a^2)^2),x)
 --R                 2x  - 2a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 50
+bb:=-a^2/(2*(x^2-a^2))+1/2*log(x^2-a^2)
+--R
+--R          2    2      2    2     2
+--R        (x  - a )log(x  - a ) - a
+--R   (2)  --------------------------
+--R                   2     2
+--R                 2x  - 2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 51     14:154 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
+
 @
 
 \section{\cite{1}:14.155~~~~~$\displaystyle\int{\frac{dx}{x(x^2-a^2)^2}}$}
@@ -223,7 +627,7 @@ $$
 <<*>>=
 )clear all
 
---S 12 of 19
+--S 52
 aa:=integrate(1/(x*(x^2-a^2)^2),x)
 --R 
 --R
@@ -234,6 +638,70 @@ aa:=integrate(1/(x*(x^2-a^2)^2),x)
 --R                           2a x  - 2a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 53
+bb:=-1/(2*a^2*(x^2-a^2))+1/(2*a^4)*log(x^2/(x^2-a^2))
+--R
+--R                         2
+--R          2    2        x        2
+--R        (x  - a )log(-------) - a
+--R                      2    2
+--R                     x  - a
+--R   (2)  --------------------------
+--R                  4 2     6
+--R                2a x  - 2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 54
+cc:=aa-bb
+--R
+--R                                           2
+--R               2    2                     x
+--R        - log(x  - a ) + 2log(x) - log(-------)
+--R                                        2    2
+--R                                       x  - a
+--R   (3)  ---------------------------------------
+--R                            4
+--R                          2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 55
+divlog:=rule(log(a/b) == log(a) - log(b))
+--R
+--R            a
+--R   (4)  log(-) == - log(b) + log(a)
+--R            b
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 56
+dd:=divlog cc
+--R
+--R               2
+--R        - log(x ) + 2log(x)
+--R   (5)  -------------------
+--R                  4
+--R                2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 57
+logpow:=rule(log(a^n) == n*log(a))
+--R
+--R             n
+--R   (6)  log(a ) == n log(a)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 58     14:155 Schaums and Axiom agree
+ee:=logpow dd
+--R
+--R   (7)  0
+--R                                                     Type: Expression Integer
+--E
+
 @
 
 \section{\cite{1}:14.156~~~~~$\displaystyle\int{\frac{dx}{x^2(x^2-a^2)^2}}$}
@@ -244,17 +712,57 @@ $$
 <<*>>=
 )clear all
 
---S 13 of 19
-aa:=integrate(1/((x^2-a^2)^2),x)
---R 
+--S 59
+aa:=integrate(1/(x^2*(x^2-a^2)^2),x)
 --R
---R          2    2                  2    2
---R        (x  - a )log(x + a) + (- x  + a )log(x - a) - 2a x
---R   (1)  --------------------------------------------------
---R                              3 2     5
---R                            4a x  - 4a
+--R           3     2                    3     2                   2     3
+--R        (3x  - 3a x)log(x + a) + (- 3x  + 3a x)log(x - a) - 6a x  + 4a
+--R   (1)  ---------------------------------------------------------------
+--R                                    5 3     7
+--R                                  4a x  - 4a x
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 60
+bb:=-1/(a^4*x)-x/(2*a^4*(x^2-a^2))-3/(4*a^5)*log((x-a)/(x+a))
+--R
+--R             3     2      x - a        2     3
+--R        (- 3x  + 3a x)log(-----) - 6a x  + 4a
+--R                          x + a
+--R   (2)  --------------------------------------
+--R                       5 3     7
+--R                     4a x  - 4a x
+--R                                                     Type: Expression Integer
+--E
+
+--S 61
+cc:=aa-bb
+--R
+--R                                         x - a
+--R        3log(x + a) - 3log(x - a) + 3log(-----)
+--R                                         x + a
+--R   (3)  ---------------------------------------
+--R                            5
+--R                          4a
+--R                                                     Type: Expression Integer
+--E
+
+--S 62
+divlog:=rule(log(a/b) == log(a) - log(b))
+--R
+--R            a
+--R   (4)  log(-) == - log(b) + log(a)
+--R            b
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 63     14:156 Schaums and Axiom agree
+dd:=divlog cc
+--R
+--R   (5)  0
+--R                                                     Type: Expression Integer
+--E
+
 @
 
 \section{\cite{1}:14.157~~~~~$\displaystyle\int{\frac{dx}{x^3(x^2-a^2)^2}}$}
@@ -265,7 +773,7 @@ $$
 <<*>>=
 )clear all
 
---S 14 of 19
+--S 64
 aa:=integrate(1/(x^3*(x^2-a^2)^2),x)
 --R 
 --R
@@ -276,6 +784,70 @@ aa:=integrate(1/(x^3*(x^2-a^2)^2),x)
 --R                                 2a x  - 2a x
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 65
+bb:=-1/(2*a^4*x^2)-1/(2*a^4*(x^2-a^2))+1/a^6*log(x^2/(x^2-a^2))
+--R
+--R                             2
+--R           4     2 2        x         2 2    4
+--R        (2x  - 2a x )log(-------) - 2a x  + a
+--R                          2    2
+--R                         x  - a
+--R   (2)  --------------------------------------
+--R                       6 4     8 2
+--R                     2a x  - 2a x
+--R                                                     Type: Expression Integer
+--E
+
+--S 66
+cc:=aa-bb
+--R
+--R                                           2
+--R               2    2                     x
+--R        - log(x  - a ) + 2log(x) - log(-------)
+--R                                        2    2
+--R                                       x  - a
+--R   (3)  ---------------------------------------
+--R                            6
+--R                           a
+--R                                                     Type: Expression Integer
+--E
+
+--S 67
+divlog:=rule(log(a/b) == log(a) - log(b))
+--R
+--R            a
+--R   (4)  log(-) == - log(b) + log(a)
+--R            b
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 68
+dd:=divlog cc
+--R
+--R               2
+--R        - log(x ) + 2log(x)
+--R   (5)  -------------------
+--R                  6
+--R                 a
+--R                                                     Type: Expression Integer
+--E
+
+--S 69
+logpow:=rule(log(a^n) == n*log(a))
+--R
+--R             n
+--R   (6)  log(a ) == n log(a)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 70     14:157 Schaums and Axiom agree
+ee:=logpow dd
+--R
+--R   (7)  0
+--R                                                     Type: Expression Integer
+--E
+
 @
 
 \section{\cite{1}:14.158~~~~~$\displaystyle\int{\frac{dx}{(x^2-a^2)^n}}$}
@@ -286,7 +858,7 @@ $$
 <<*>>=
 )clear all
 
---S 15 of 19
+--S 71     14:158 Axiom cannot do this integral
 aa:=integrate(1/((x^2-a^2)^n),x)
 --R 
 --R
@@ -306,7 +878,7 @@ $$
 <<*>>=
 )clear all
 
---S 16 of 19
+--S 72
 aa:=integrate(x/((x^2-a^2)^n),x)
 --R 
 --R
@@ -318,6 +890,49 @@ aa:=integrate(x/((x^2-a^2)^n),x)
 --R        (2n - 2)%e
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 73
+bb:=-1/(2*(n-1)*(x^2-a^2)^(n-1))
+--R
+--R                     1
+--R   (2)  - ----------------------
+--R                    2    2 n - 1
+--R          (2n - 2)(x  - a )
+--R                                                     Type: Expression Integer
+--E
+
+--S 74
+cc:=aa-bb
+--R
+--R                 2    2
+--R          n log(x  - a )       2    2   2    2 n - 1
+--R        %e               + (- x  + a )(x  - a )
+--R   (3)  --------------------------------------------
+--R                                          2    2
+--R                     2    2 n - 1  n log(x  - a )
+--R           (2n - 2)(x  - a )     %e
+--R                                                     Type: Expression Integer
+--E
+
+--S 75
+explog:=rule(%e^(n*log(x)) == x^n)
+--R
+--R          n log(x)     n
+--R   (4)  %e         == x
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 76     14:159 Axiom cannot simplify this expression
+dd:=explog cc
+--R
+--R          2    2 n       2    2   2    2 n - 1
+--R        (x  - a )  + (- x  + a )(x  - a )
+--R   (5)  --------------------------------------
+--R                     2    2 n - 1  2    2 n
+--R           (2n - 2)(x  - a )     (x  - a )
+--R                                                     Type: Expression Integer
+--E
+
 @
 
 \section{\cite{1}:14.160~~~~~$\displaystyle\int{\frac{dx}{x(x^2-a^2)^n}}$}
@@ -328,7 +943,7 @@ $$
 <<*>>=
 )clear all
 
---S 17 of 19
+--S 77     14:160 Axiom cannot compute this integral
 aa:=integrate(1/(x*(x^2-a^2)^n),x)
 --R 
 --R
@@ -349,7 +964,7 @@ $$
 <<*>>=
 )clear all
 
---S 18 of 19
+--S 78     14:161 Axiom cannot compute this integral
 aa:=integrate(x^m/((x^2-a^2)^n),x)
 --R 
 --R
@@ -370,7 +985,7 @@ $$
 <<*>>=
 )clear all
 
---S 19 of 19
+--S 79     14:162 Axiom cannot compute this integral
 aa:=integrate(1/(x^m*(x^2-a^2)^n),x)
 --R 
 --R




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To: daly@axiom-developer.org
Subject: Re: [Axiom-developer] 20080416.01.tpd.patch (CATS
	Schaums-Axiom	equivalence testing (2-7))
References: <200804170603.m3H63lR0009180@axiom-developer.org>
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daly@axiom-developer.org wrote:
> Item   14:150 Schaums and Axiom DISAGREE BY A NON-CONSTANT
> in schaum7.input.pamphlet is particularly interesting because
> it appears that the derivative of Axiom's answer is the original
> integrand but the derivative of Schaum's answer is not, implying
> that Schaum's has a mistake. This will be verified using other 
> systems later.
>
> Axiom is weak in handling certain simplifications. Future work is
> planned to correct this.
>
> Richard Fateman has given me permission to use his TILU pattern
> integration database in Axiom. This should give us much broader
> integration results. TILU has not been tested against Schaums
> but this testing will occur during the merge.
>
> schaum2.input.pamphet
>
>   14:150 Schaums and Axiom DISAGREE BY A NON-CONSTANT
>  
>  \section{\cite{1}:14.150~~~~~$\displaystyle\int{\frac{dx}{x^3(x^2-a^2)}}$}
> @@ -124,7 +343,7 @@ $$
>  <<*>>=
>  )clear all
>  
> ---S 7 of 19
> +--S 29
>  aa:=integrate(1/(x^3*(x^2-a^2)),x)
>  --R 
>  --R
> @@ -135,6 +354,73 @@ aa:=integrate(1/(x^3*(x^2-a^2)),x)
>  --R                     2a x
>  --R                                          Type: Union(Expression Integer,...)
>  --E 
> +
> +--S 30
> +bb:=1/(2*a^2*x*2)-1/(2*a^4)*log(x^2/(x^2-a^2))
> +--R
> +--R                     2
> +--R                    x        2
> +--R        - 2x log(-------) + a
> +--R                  2    2
> +--R                 x  - a
> +--R   (2)  ----------------------
> +--R                   4
> +--R                 4a x
> +--R                                                     Type: Expression Integer
> +--E
> +
> +--S 31
> +cc:=aa-bb
> +--R
> +--R                                                 2
> +--R          2     2    2      2           2       x        2      2
> +--R        2x log(x  - a ) - 4x log(x) + 2x log(-------) - a x + 2a
> +--R                                              2    2
> +--R                                             x  - a
> +--R   (3)  ---------------------------------------------------------
> +--R                                    4 2
> +--R                                  4a x
> +--R                                                     Type: Expression Integer
> +--E
> +
> +--S 32
> +divlog:=rule(log(a/b) == log(a) - log(b))
> +--R
> +--R            a
> +--R   (4)  log(-) == - log(b) + log(a)
> +--R            b
> +--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
> +--E
> +
> +--S 33
> +dd:=divlog cc
> +--R
> +--R          2     2      2          2      2
> +--R        2x log(x ) - 4x log(x) - a x + 2a
> +--R   (5)  ----------------------------------
> +--R                         4 2
> +--R                       4a x
> +--R                                                     Type: Expression Integer
> +--E
> +
> +--S 34
> +logpow:=rule(log(a^n) == n*log(a))
> +--R
> +--R             n
> +--R   (6)  log(a ) == n log(a)
> +--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
> +--E
> +
> +--S 35     14:150 Schaums and Axiom DISAGREE BY A NON-CONSTANT
> +ee:=logpow dd
> +--R
> +--R        - x + 2
> +--R   (7)  -------
> +--R           2 2
> +--R         4a x
> +--R                                                     Type: Expression Integer
> +--E
> +
>  @
>  
>   


I tried it on maximum and got:

(%i6) integrate(1/(x^3*(x^2-a^2)),x);
                             2      2
                      log(x  - a )            log(x)                    1
(%o6)                 ------------      -       ------              + 
-------
                                      4              4                  
      2  2
                                2 a                a                    
2 a  x

and this agrees with my schaums book;




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Subject: [Axiom-developer] 20080417.01.tpd.patch (fixed 14:150)
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Doug,

I fired up Maxima this morning and got the same answer.
I finally saw that the mistake is a typo in the answer I transcribed
from the Schaum's book. Specifically, the answer from the book is the
variable 'bb' which needed the following change:

-bb:=1/(2*a^2*x*2)-1/(2*a^4)*log(x^2/(x^2-a^2))
+bb:=1/(2*a^2*x^2)-1/(2*a^4)*log(x^2/(x^2-a^2))


So it is just a typo and thus the best of all possible worlds.
Schaums and Axiom now agree on 14:150.

Tim

=======================================================================
diff --git a/changelog b/changelog
index eda7bfd..456e2f9 100644
--- a/changelog
+++ b/changelog
@@ -1,3 +1,5 @@
+20080417 tpd src/input/schaum7.input fix typo in --S 30
+20080417 tpd src/input/schaum5.input fix typo 14:88 -> 14:123
 20080416 tpd src/input/schaum7.input show Schaums-Axiom equivalence
 20080416 tpd src/input/schaum6.input show Schaums-Axiom equivalence
 20080416 tpd src/input/schaum5.input show Schaums-Axiom equivalence
diff --git a/src/input/schaum5.input.pamphlet b/src/input/schaum5.input.pamphlet
index 50ea618..a5d3fc3 100644
--- a/src/input/schaum5.input.pamphlet
+++ b/src/input/schaum5.input.pamphlet
@@ -1571,7 +1571,7 @@ cc3:=aa2-bb1
 --R                                                     Type: Expression Integer
 --E
 
---S 42     14:88 Axiom cannot simplify these results
+--S 42     14:123 Axiom cannot simplify these results
 cc4:=aa2-bb2
 --R
 --R   (14)
diff --git a/src/input/schaum7.input.pamphlet b/src/input/schaum7.input.pamphlet
index 3062d2e..ce37f19 100644
--- a/src/input/schaum7.input.pamphlet
+++ b/src/input/schaum7.input.pamphlet
@@ -356,71 +356,64 @@ aa:=integrate(1/(x^3*(x^2-a^2)),x)
 --E 
 
 --S 30
-bb:=1/(2*a^2*x*2)-1/(2*a^4)*log(x^2/(x^2-a^2))
+bb:=1/(2*a^2*x^2)-1/(2*a^4)*log(x^2/(x^2-a^2))
 --R
---R                     2
---R                    x        2
---R        - 2x log(-------) + a
---R                  2    2
---R                 x  - a
---R   (2)  ----------------------
---R                   4
---R                 4a x
+--R                    2
+--R           2       x        2
+--R        - x log(-------) + a
+--R                 2    2
+--R                x  - a
+--R   (2)  ---------------------
+--R                  4 2
+--R                2a x
 --R                                                     Type: Expression Integer
 --E
 
 --S 31
-cc:=aa-bb
---R
---R                                                 2
---R          2     2    2      2           2       x        2      2
---R        2x log(x  - a ) - 4x log(x) + 2x log(-------) - a x + 2a
---R                                              2    2
---R                                             x  - a
---R   (3)  ---------------------------------------------------------
---R                                    4 2
---R                                  4a x
---R                                                     Type: Expression Integer
---E
-
---S 32
 divlog:=rule(log(a/b) == log(a) - log(b))
 --R
 --R            a
---R   (4)  log(-) == - log(b) + log(a)
+--R   (3)  log(-) == - log(b) + log(a)
 --R            b
 --R                        Type: RewriteRule(Integer,Integer,Expression Integer)
 --E
 
---S 33
-dd:=divlog cc
+--S 32
+t1:=divlog bb
 --R
---R          2     2      2          2      2
---R        2x log(x ) - 4x log(x) - a x + 2a
---R   (5)  ----------------------------------
---R                         4 2
---R                       4a x
+--R           2     2     2     2    2     2
+--R        - x log(x ) + x log(x  - a ) + a
+--R   (4)  ---------------------------------
+--R                        4 2
+--R                      2a x
 --R                                                     Type: Expression Integer
 --E
 
---S 34
+--S 33
 logpow:=rule(log(a^n) == n*log(a))
 --R
 --R             n
---R   (6)  log(a ) == n log(a)
+--R   (5)  log(a ) == n log(a)
 --R                        Type: RewriteRule(Integer,Integer,Expression Integer)
 --E
 
---S 35     14:150 Schaums and Axiom DISAGREE BY A NON-CONSTANT
-ee:=logpow dd
+--S 34
+t2:=logpow t1
 --R
---R        - x + 2
---R   (7)  -------
---R           2 2
---R         4a x
+--R         2     2    2      2          2
+--R        x log(x  - a ) - 2x log(x) + a
+--R   (6)  -------------------------------
+--R                       4 2
+--R                     2a x
 --R                                                     Type: Expression Integer
 --E
 
+--S 35     14:150 Schaums and Axiom agree
+cc:=aa-t2
+
+   (7)  0
+                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.151~~~~~$\displaystyle\int{\frac{dx}{(x^2-a^2)^2}}$}



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From: "William Sit" <wyscc@sci.ccny.cuny.edu>
Subject: Re: [Axiom-developer] 20080416.01.tpd.patch (CATS
	Schaums-Axiom	equivalence testing (2-7))
To: Doug Stewart <dastew@sympatico.ca>,daly@axiom-developer.org
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Tim:

You have a typo at bb:
bb:=1/(2*a^2*x*2)-1/(2*a^4)*log(x^2/(x^2-a^2))

x*2 should have been x^2; so this should be:

bb:=1/(2*a^2*x^2)-1/(2*a^4)*log(x^2/(x^2-a^2))

William


On Thu, 17 Apr 2008 06:26:26 -0400
  Doug Stewart <dastew@sympatico.ca> wrote:
>daly@axiom-developer.org wrote:
>>Item   14:150 Schaums and Axiom DISAGREE BY A 
>>NON-CONSTANT
>>in schaum7.input.pamphlet is particularly interesting 
>>because
>>it appears that the derivative of Axiom's answer is the 
>>original
>>integrand but the derivative of Schaum's answer is not, 
>>implying
>>that Schaum's has a mistake. This will be verified using 
>>other 
>>systems later.
>>
>>Axiom is weak in handling certain simplifications. Future 
>>work is
>>planned to correct this.
>>
>>Richard Fateman has given me permission to use his TILU 
>>pattern
>>integration database in Axiom. This should give us much 
>>broader
>>integration results. TILU has not been tested against 
>>Schaums
>>but this testing will occur during the merge.
>>
>>schaum2.input.pamphet
>>
>>  14:150 Schaums and Axiom DISAGREE BY A NON-CONSTANT
>> 
>> \section{\cite{1}:14.150~~~~~$\displaystyle\int{\frac{dx}{x^3(x^2-a^2)}}$}
>>@@ -124,7 +343,7 @@ $$
>> <<*>>=
>> )clear all
>> 
>>---S 7 of 19
>>+--S 29
>> aa:=integrate(1/(x^3*(x^2-a^2)),x)
>> --R 
>> --R
>>@@ -135,6 +354,73 @@ aa:=integrate(1/(x^3*(x^2-a^2)),x)
>> --R                     2a x
>> --R                                          Type: 
>>Union(Expression Integer,...)
>> --E 
>>+
>>+--S 30
>>+bb:=1/(2*a^2*x*2)-1/(2*a^4)*log(x^2/(x^2-a^2))
>>+--R
>>+--R                     2
>>+--R                    x        2
>>+--R        - 2x log(-------) + a
>>+--R                  2    2
>>+--R                 x  - a
>>+--R   (2)  ----------------------
>>+--R                   4
>>+--R                 4a x
>>+--R 
>>                                                    Type: 
>>Expression Integer
>>+--E
>>+
>>+--S 31
>>+cc:=aa-bb
>>+--R
>>+--R                                                 2
>>+--R          2     2    2      2           2       x 
>>       2      2
>>+--R        2x log(x  - a ) - 4x log(x) + 2x log(-------) 
>>- a x + 2a
>>+--R                                              2    2
>>+--R                                             x  - a
>>+--R   (3) 
>> ---------------------------------------------------------
>>+--R                                    4 2
>>+--R                                  4a x
>>+--R 
>>                                                    Type: 
>>Expression Integer
>>+--E
>>+
>>+--S 32
>>+divlog:=rule(log(a/b) == log(a) - log(b))
>>+--R
>>+--R            a
>>+--R   (4)  log(-) == - log(b) + log(a)
>>+--R            b
>>+--R                        Type: 
>>RewriteRule(Integer,Integer,Expression Integer)
>>+--E
>>+
>>+--S 33
>>+dd:=divlog cc
>>+--R
>>+--R          2     2      2          2      2
>>+--R        2x log(x ) - 4x log(x) - a x + 2a
>>+--R   (5)  ----------------------------------
>>+--R                         4 2
>>+--R                       4a x
>>+--R 
>>                                                    Type: 
>>Expression Integer
>>+--E
>>+
>>+--S 34
>>+logpow:=rule(log(a^n) == n*log(a))
>>+--R
>>+--R             n
>>+--R   (6)  log(a ) == n log(a)
>>+--R                        Type: 
>>RewriteRule(Integer,Integer,Expression Integer)
>>+--E
>>+
>>+--S 35     14:150 Schaums and Axiom DISAGREE BY A 
>>NON-CONSTANT
>>+ee:=logpow dd
>>+--R
>>+--R        - x + 2
>>+--R   (7)  -------
>>+--R           2 2
>>+--R         4a x
>>+--R 
>>                                                    Type: 
>>Expression Integer
>>+--E
>>+
>> @
>> 
>>  
>
>
>I tried it on maximum and got:
>
>(%i6) integrate(1/(x^3*(x^2-a^2)),x);
>                             2      2
>                      log(x  - a )            log(x) 
>                   1
>(%o6)                 ------------      -       ------ 
>             + -------
>                                      4              4 
>                 
>      2  2
>                                2 a                a 
>                   
>2a  x
>
>and this agrees with my schaums book;
>
>
>
>_______________________________________________
>Axiom-developer mailing list
>Axiom-developer@nongnu.org
>http://lists.nongnu.org/mailman/listinfo/axiom-developer

William Sit, 
Professor of Mathematics, City College of New York 
                 
Office: R6/202C Tel: 212-650-5179, Fax: 212-862-0004
Home Page: http://scisun.sci.ccny.cuny.edu/~wyscc/



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Subject: Re: [Axiom-developer] 20080416.01.tpd.patch (CATS
	Schaums-Axiom	equivalence testing (2-7))
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William,

Yes, thanks. I found that problem this morning when I was more awake.

It would be useful if you (or anyone) could look at some of the 
problems where I could not find a simplification and post a way
to reduce the problem to zero (or a constant). I have found that
using pattern matching rules I can "help" the simplifications along.

Any rules you find would be useful. I'm accumulating the rules I
used as I go along. They will become part of a set of optional
"simplification" routines.

Tim



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Subject: [Axiom-developer] 20080417.02.tpd.patch (CATS Schaums-Axiom
	equivalence testing (8-10))
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schaum8.input.pamphlet
  14:163 Schaums and Axiom differ by a constant
  14:164 Schaums and Axiom differ by a constant
  14:165 Schaums and Axiom differ by a constant
  14:166 Schaums and Axiom differ by a constant
  14:167 Schaums and Axiom differ by a constant
  14:168 Schaums and Axiom differ by a constant
  14:169 Schaums and Axiom differ by a constant
  14:170 Schaums and Axiom differ by a constant
  14:171 Schaums and Axiom agree
  14:172 Schaums and Axiom differ by a constant
  14:173 Schaums and Axiom differ by a constant
  14:174 Schaums and Axiom differ by a constant
  14:175 Schaums and Axiom differ by a constant
  14:176 Schaums and Axiom differ by a constant
  14:177 Axiom cannot do this integration
  14:178 Axiom cannot simplify this expression
  14:179 Axiom cannot integrate this expression
  14:180 Axiom cannot integrate this expression
  14:181 Axiom cannot integrate this expression

schaum9.input.pamphlet
  14:182 Axiom cannot simplify this expression
  14:183 Schaums and Axiom agree
  14:184 Schaums and Axiom differ by a constant
  14:185 Schaums and Axiom agree
  14:186 Axiom cannot simplify this expression
  14:187 Schaums and Axiom differ by a constant
  14:188 Axiom cannot simplify this expression
  14:189 Axiom cannot simplify this expression
  14:190 Schaums and Axiom agree
  14:191 Axiom cannot simplify this expression
  14:192 Schaums and Axiom agree
  14:193 Axiom cannot simplify this expression
  14:194 Axiom cannot simplify this expression
  14:195 Axiom cannot simplify this expression
  14:196 Schaums and Axiom differ by a constant
  14:197 Schaums and Axiom agree
  14:198 Axiom cannot simplify this expression
  14:199 Schaums and Axiom agree
  14:200 Axiom cannot simplify this expression
  14:201 Schaums and Axiom differ by a constant
  14:202 Axiom cannot simplify this expression
  14:203 Axiom cannot simplify this expression
  14:204 Schaums and Axiom agree
  14:205 Axiom cannot simplify this expression
  14:206 Schaums and Axiom agree
  14:207 Axiom cannot simplify this expression
  14:208 Axiom cannot simplify this expression
  14:209 Axiom cannot simplify this expression
  
schaum10.input.pamphlet
  14:210 Schaums and Axiom differ by a constant
  14:xxx Schaums and Axiom agree
  14:211 Axiom cannot simplify this expression
  14:212 Schaums and Axiom agree
  14:213 Axiom cannot simplify this expression
  14:214 Schaums and Axiom differ by a constant
  14:215 Axiom cannot simplify this expression
  14:216 Axiom cannot simplify this expression
  14:217 Schaums and Axiom agree
  14:218 Axiom cannot simplify this expression
  14:219 Schaums and Axiom agree
  14:220 Axiom cannot simplify this expression
  14:221 Axiom cannot simplify this expression
  14:222 Axiom cannot simplify this expression
  14:223 Schaums and Axiom differ by a constant
  14:224 Schaums and Axiom agree
  14:225 Axiom cannot simplify this expression
  14:226 Schaums and Axiom agree
  14:227 Axiom cannot simplify this expression
  14:228 Schaums and Axiom differ by a constant
  14:229 Axiom cannot simplify this expression
  14:230 Axiom cannot simplify this expression
  14:231 Schaums and Axiom agree
  14:232 Axiom cannot simplify this expression
  14:233 Schaums and Axiom agree
  14:234 Axiom cannot simplify this expression
  14:235 Axiom cannot simplify this expression
  14:236 Axiom cannot simplify this expression

========================================================================
diff --git a/changelog b/changelog
index 456e2f9..502aa1e 100644
--- a/changelog
+++ b/changelog
@@ -1,3 +1,6 @@
+20080417 tpd src/input/schaum10.input show Schaums-Axiom equivalence
+20080417 tpd src/input/schaum9.input show Schaums-Axiom equivalence
+20080417 tpd src/input/schaum8.input show Schaums-Axiom equivalence
 20080417 tpd src/input/schaum7.input fix typo in --S 30
 20080417 tpd src/input/schaum5.input fix typo 14:88 -> 14:123
 20080416 tpd src/input/schaum7.input show Schaums-Axiom equivalence
diff --git a/src/input/schaum10.input.pamphlet b/src/input/schaum10.input.pamphlet
index 8582086..d0ba7d9 100644
--- a/src/input/schaum10.input.pamphlet
+++ b/src/input/schaum10.input.pamphlet
@@ -15,7 +15,7 @@ $$\int{\frac{1}{\sqrt{x^2-a^2}}}=\ln\left(x+\sqrt{x^2-a^2}\right)$$
 )set message auto off
 )clear all
 
---S 1 of 28
+--S 1
 aa:=integrate(1/(sqrt(x^2-a^2)),x)
 --R 
 --R
@@ -24,6 +24,39 @@ aa:=integrate(1/(sqrt(x^2-a^2)),x)
 --R   (1)  - log(\|x  - a   - x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 2
+bb:=log(x+sqrt(x^2-a^2))
+--R
+--R             +-------+
+--R             | 2    2
+--R   (2)  log(\|x  - a   + x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 3
+cc:=aa-bb
+--R
+--R               +-------+             +-------+
+--R               | 2    2              | 2    2
+--R   (3)  - log(\|x  - a   + x) - log(\|x  - a   - x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 4
+logmul1:=rule(c*log(a)+c*log(b) == c*log(a*b))
+--R
+--I   (4)  c log(b) + c log(a) + %I == c log(a b) + %I
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 5      14:210 Schaums and Axiom differ by a constant
+dd:=logmul1 cc
+--R
+--R                 2
+--R   (5)  - log(- a )
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.xxx~~~~~$\displaystyle\int{\frac{x~dx}{\sqrt{x^2-a^2}}}$}
@@ -31,7 +64,7 @@ $$\int{\frac{x}{\sqrt{x^2-a^2}}}=\sqrt{x^2-a^2}$$
 <<*>>=
 )clear all
 
---S 2 of 28
+--S 6
 aa:=integrate(x/(sqrt(x^2-a^2)),x)
 --R 
 --R
@@ -44,6 +77,22 @@ aa:=integrate(x/(sqrt(x^2-a^2)),x)
 --R             \|x  - a   - x
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 7
+bb:=sqrt(x^2-a^2)
+--R
+--R         +-------+
+--R         | 2    2
+--R   (2)  \|x  - a
+--R                                                     Type: Expression Integer
+--E
+
+--S 8      14:xxx Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.211~~~~~$\displaystyle
@@ -54,7 +103,7 @@ $$
 <<*>>=
 )clear all
 
---S 3 of 28
+--S 9
 aa:=integrate(x^2/sqrt(x^2-a^2),x)
 --R 
 --R
@@ -72,6 +121,29 @@ aa:=integrate(x^2/sqrt(x^2-a^2),x)
 --R     4x\|x  - a   - 4x  + 2a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 10
+bb:=(x*sqrt(x^2-a^2))/2+a^2/2*log(x+sqrt(x^2-a^2))
+--R
+--R               +-------+          +-------+
+--R         2     | 2    2           | 2    2
+--R        a log(\|x  - a   + x) + x\|x  - a
+--R   (2)  -----------------------------------
+--R                         2
+--R                                                     Type: Expression Integer
+--E
+
+--S 11     14:211 Axiom cannot simplify this expression
+cc:=aa-bb
+--R
+--R                 +-------+               +-------+
+--R           2     | 2    2          2     | 2    2
+--R        - a log(\|x  - a   + x) - a log(\|x  - a   - x)
+--R   (3)  -----------------------------------------------
+--R                               2
+--R                                                     Type: Expression Integer
+--E
+
 @
 
 \section{\cite{1}:14.212~~~~~$\displaystyle
@@ -82,7 +154,7 @@ $$
 <<*>>=
 )clear all
 
---S 4 of 28
+--S 12
 aa:=integrate(x^3/sqrt(x^2-a^2),x)
 --R 
 --R
@@ -95,6 +167,24 @@ aa:=integrate(x^3/sqrt(x^2-a^2),x)
 --R                    (12x  - 3a )\|x  - a   - 12x  + 9a x
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 13
+bb:=(x^2-a^2)^(3/2)/3+a^2*sqrt(x^2-a^2)
+--R
+--R                   +-------+
+--R          2     2  | 2    2
+--R        (x  + 2a )\|x  - a
+--R   (2)  --------------------
+--R                  3
+--R                                                     Type: Expression Integer
+--E
+
+--S 14     14:212 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.213~~~~~$\displaystyle\int{\frac{dx}{x\sqrt{x^2-a^2}}}$}
@@ -104,7 +194,7 @@ $$
 <<*>>=
 )clear all
 
---S 5 of 28
+--S 15
 aa:=integrate(1/(x*sqrt(x^2-a^2)),x)
 --R 
 --R
@@ -117,6 +207,30 @@ aa:=integrate(1/(x*sqrt(x^2-a^2)),x)
 --R                  a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 16
+bb:=1/a*asec(abs(x/a))
+--R
+--R                 x
+--R        asec(abs(-))
+--R                 a
+--R   (2)  ------------
+--R              a
+--R                                                     Type: Expression Integer
+--E
+
+--S 17     14:213 Axiom cannot simplify this expression
+cc:=aa-bb
+--R
+--R               +-------+
+--R               | 2    2
+--R              \|x  - a   - x             x
+--R        2atan(--------------) - asec(abs(-))
+--R                     a                   a
+--R   (3)  ------------------------------------
+--R                          a
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.214~~~~~$\displaystyle
@@ -127,7 +241,7 @@ $$
 <<*>>=
 )clear all
 
---S 6 of 28
+--S 18
 aa:=integrate(1/(x^2*sqrt(x^2-a^2)),x)
 --R 
 --R
@@ -138,6 +252,28 @@ aa:=integrate(1/(x^2*sqrt(x^2-a^2)),x)
 --R          x\|x  - a   - x
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 19
+bb:=sqrt(x^2-a^2)/(a^2*x)
+--R
+--R         +-------+
+--R         | 2    2
+--R        \|x  - a
+--R   (2)  ----------
+--R             2
+--R            a x
+--R                                                     Type: Expression Integer
+--E
+
+--S 20     14:214 Schaums and Axiom differ by a constant
+cc:=aa-bb
+--R
+--R         1
+--R   (3)  --
+--R         2
+--R        a
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.215~~~~~$\displaystyle\int{\frac{dx}{x^3\sqrt{x^2-a^2}}}$}
@@ -148,7 +284,7 @@ $$
 <<*>>=
 )clear all
 
---S 7 of 28
+--S 21
 aa:=integrate(1/(x^3*sqrt(x^2-a^2)),x)
 --R 
 --R
@@ -168,6 +304,34 @@ aa:=integrate(1/(x^3*sqrt(x^2-a^2)),x)
 --R     4a x \|x  - a   - 4a x  + 2a x
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 22
+bb:=sqrt(x^2-a^2)/(2*a^2*x^2)+1/(2*a^3)*asec(abs(x/a))
+--R
+--R                           +-------+
+--R         2         x       | 2    2
+--R        x asec(abs(-)) + a\|x  - a
+--R                   a
+--R   (2)  ----------------------------
+--R                      3 2
+--R                    2a x
+--R                                                     Type: Expression Integer
+--E
+
+--S 23     14:215 Axiom cannot simplify this expression
+cc:=aa-bb
+--R
+--R               +-------+
+--R               | 2    2
+--R              \|x  - a   - x             x
+--R        2atan(--------------) - asec(abs(-))
+--R                     a                   a
+--R   (3)  ------------------------------------
+--R                           3
+--R                         2a
+--R                                                     Type: Expression Integer
+--E
+
 @
 
 \section{\cite{1}:14.216~~~~~$\displaystyle\int{\sqrt{x^2-a^2}}~dx$}
@@ -177,7 +341,7 @@ $$
 <<*>>=
 )clear all
 
---S 8 of 28
+--S 24
 aa:=integrate(sqrt(x^2-a^2),x)
 --R 
 --R
@@ -195,6 +359,29 @@ aa:=integrate(sqrt(x^2-a^2),x)
 --R     4x\|x  - a   - 4x  + 2a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 25
+bb:=(x*sqrt(x^2-a^2))/2-a^2/2*log(x+sqrt(x^2-a^2))
+--R
+--R                 +-------+          +-------+
+--R           2     | 2    2           | 2    2
+--R        - a log(\|x  - a   + x) + x\|x  - a
+--R   (2)  -------------------------------------
+--R                          2
+--R                                                     Type: Expression Integer
+--E
+
+--S 26     14:216 Axiom cannot simplify this expression
+cc:=aa-bb
+--R
+--R               +-------+               +-------+
+--R         2     | 2    2          2     | 2    2
+--R        a log(\|x  - a   + x) + a log(\|x  - a   - x)
+--R   (3)  ---------------------------------------------
+--R                              2
+--R                                                     Type: Expression Integer
+--E
+
 @
 
 \section{\cite{1}:14.217~~~~~$\displaystyle\int{x\sqrt{x^2-a^2}}~dx$}
@@ -204,7 +391,7 @@ $$
 <<*>>=
 )clear all
 
---S 9 of 28
+--S 27
 aa:=integrate(x*sqrt(x^2-a^2),x)
 --R 
 --R
@@ -217,6 +404,24 @@ aa:=integrate(x*sqrt(x^2-a^2),x)
 --R                    (12x  - 3a )\|x  - a   - 12x  + 9a x
 --R                                          Type: Union(Expression Integer,...)
 --E
+
+--S 28
+bb:=(x^2-a^2)^(3/2)/3
+--R
+--R                  +-------+
+--R          2    2  | 2    2
+--R        (x  - a )\|x  - a
+--R   (2)  -------------------
+--R                 3
+--R                                                     Type: Expression Integer
+--E
+
+--S 29     14:217 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.218~~~~~$\displaystyle
@@ -228,7 +433,7 @@ $$
 <<*>>=
 )clear all
 
---S 10 of 28
+--S 30
 aa:=integrate(x^2*sqrt(x^2-a^2),x)
 --R 
 --R
@@ -246,6 +451,28 @@ aa:=integrate(x^2*sqrt(x^2-a^2),x)
 --R     (64x  - 32a x)\|x  - a   - 64x  + 64a x  - 8a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 31
+bb:=(x*(x^2-a^2)^(3/2))/4+(a^2*x*sqrt(x^2-a^2))/8-a^4/8*log(x+sqrt(x^2-a^2))
+--R
+--R                 +-------+                    +-------+
+--R           4     | 2    2            3    2   | 2    2
+--R        - a log(\|x  - a   + x) + (2x  - a x)\|x  - a
+--R   (2)  -----------------------------------------------
+--R                               8
+--R                                                     Type: Expression Integer
+--E
+
+--S 32     14:218 Axiom cannot simplify this expression
+cc:=aa-bb
+--R
+--R               +-------+               +-------+
+--R         4     | 2    2          4     | 2    2
+--R        a log(\|x  - a   + x) + a log(\|x  - a   - x)
+--R   (3)  ---------------------------------------------
+--R                              8
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.219~~~~~$\displaystyle
@@ -256,7 +483,7 @@ $$
 <<*>>=
 )clear all
 
---S 11 of 28
+--S 33
 aa:=integrate(x^3*sqrt(x^2-a^2),x)
 --R 
 --R
@@ -273,6 +500,24 @@ aa:=integrate(x^3*sqrt(x^2-a^2),x)
 --R     (240x  - 180a x  + 15a )\|x  - a   - 240x  + 300a x  - 75a x
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 34
+bb:=(x^2-a^2)^(5/2)/5+(a^2*(x^2-a^2)^(3/2))/3
+--R
+--R                           +-------+
+--R           4    2 2     4  | 2    2
+--R        (3x  - a x  - 2a )\|x  - a
+--R   (2)  ----------------------------
+--R                     15
+--R                                                     Type: Expression Integer
+--E
+
+--S 35     14:219 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.220~~~~~$\displaystyle
@@ -283,7 +528,7 @@ $$
 <<*>>=
 )clear all
 
---S 12 of 28
+--S 36
 aa:=integrate(sqrt(x^2-a^2)/x,x)
 --R 
 --R
@@ -298,6 +543,27 @@ aa:=integrate(sqrt(x^2-a^2)/x,x)
 --R                                   \|x  - a   - x
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 37
+bb:=sqrt(x^2-a^2)-a*asec(abs(x/a))
+--R
+--R                            +-------+
+--R                     x      | 2    2
+--R   (2)  - a asec(abs(-)) + \|x  - a
+--R                     a
+--R                                                     Type: Expression Integer
+--E
+
+--S 38     14:220 Axiom cannot simplify this expression
+cc:=aa-bb
+--R
+--R                   +-------+
+--R                   | 2    2
+--R                  \|x  - a   - x               x
+--R   (3)  - 2a atan(--------------) + a asec(abs(-))
+--R                         a                     a
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.221~~~~~$\displaystyle
@@ -308,7 +574,7 @@ $$
 <<*>>=
 )clear all
 
---S 13 of 28
+--S 39
 aa:=integrate(sqrt(x^2-a^2)/x^2,x)
 --R 
 --R
@@ -321,6 +587,27 @@ aa:=integrate(sqrt(x^2-a^2)/x^2,x)
 --R                      x\|x  - a   - x
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 40
+bb:=-sqrt(x^2-a^2)/x+log(x+sqrt(x^2-a^2))
+--R
+--R               +-------+         +-------+
+--R               | 2    2          | 2    2
+--R        x log(\|x  - a   + x) - \|x  - a
+--R   (2)  ----------------------------------
+--R                         x
+--R                                                     Type: Expression Integer
+--E
+
+--S 41     14:221 Axiom cannot simplify this expression
+cc:=aa-bb
+--R
+--R               +-------+             +-------+
+--R               | 2    2              | 2    2
+--R   (3)  - log(\|x  - a   + x) - log(\|x  - a   - x) - 1
+--R                                                     Type: Expression Integer
+--E
+
 @
 
 \section{\cite{1}:14.222~~~~~$\displaystyle
@@ -332,7 +619,7 @@ $$
 <<*>>=
 )clear all
 
---S 14 of 28
+--S 42
 aa:=integrate(sqrt(x^2-a^2)/x^3,x)
 --R 
 --R
@@ -352,6 +639,32 @@ aa:=integrate(sqrt(x^2-a^2)/x^3,x)
 --R     4a x \|x  - a   - 4a x  + 2a x
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 43
+bb:=-sqrt(x^2-a^2)/(2*x^2)+1/(2*a)*asec(abs(x/a))
+--R
+--R                           +-------+
+--R         2         x       | 2    2
+--R        x asec(abs(-)) - a\|x  - a
+--R                   a
+--R   (2)  ----------------------------
+--R                        2
+--R                    2a x
+--R                                                     Type: Expression Integer
+--E
+
+--S 44     14:222 Axiom cannot simplify this expression
+cc:=aa-bb
+--R
+--R               +-------+
+--R               | 2    2
+--R              \|x  - a   - x             x
+--R        2atan(--------------) - asec(abs(-))
+--R                     a                   a
+--R   (3)  ------------------------------------
+--R                         2a
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.223~~~~~$\displaystyle\int{\frac{dx}{(x^2-a^2)^{3/2}}}$}
@@ -361,7 +674,7 @@ $$
 <<*>>=
 )clear all
 
---S 15 of 28
+--S 45
 aa:=integrate(1/(x^2-a^2)^(3/2),x)
 --R 
 --R
@@ -372,6 +685,27 @@ aa:=integrate(1/(x^2-a^2)^(3/2),x)
 --R          x\|x  - a   - x  + a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 46
+bb:=-x/(a^2*sqrt(x^2-a^2))
+--R
+--R                x
+--R   (2)  - ------------
+--R             +-------+
+--R           2 | 2    2
+--R          a \|x  - a
+--R                                                     Type: Expression Integer
+--E
+
+--S 47     14:223 Schaums and Axiom differ by a constant
+cc:=aa-bb
+--R
+--R           1
+--R   (3)  - --
+--R           2
+--R          a
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.224~~~~~$\displaystyle
@@ -382,7 +716,7 @@ $$
 <<*>>=
 )clear all
 
---S 16 of 28
+--S 48
 aa:=integrate(x/(x^2-a^2)^(3/2),x)
 --R 
 --R
@@ -395,6 +729,24 @@ aa:=integrate(x/(x^2-a^2)^(3/2),x)
 --R        x\|x  - a   - x  + a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 49
+bb:=-1/sqrt(x^2-a^2)
+--R
+--R               1
+--R   (2)  - ----------
+--R           +-------+
+--R           | 2    2
+--R          \|x  - a
+--R                                                     Type: Expression Integer
+--E
+
+--S 50     14:224 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.225~~~~~$\displaystyle
@@ -405,7 +757,7 @@ $$
 <<*>>=
 )clear all
 
---S 17 of 28
+--S 51
 aa:=integrate(x^2/(x^2-a^2)^(3/2),x)
 --R 
 --R
@@ -418,6 +770,28 @@ aa:=integrate(x^2/(x^2-a^2)^(3/2),x)
 --R                      x\|x  - a   - x  + a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 52
+bb:=-x/sqrt(x^2-a^2)+log(x+sqrt(x^2-a^2))
+--R
+--R         +-------+     +-------+
+--R         | 2    2      | 2    2
+--R        \|x  - a  log(\|x  - a   + x) - x
+--R   (2)  ---------------------------------
+--R                     +-------+
+--R                     | 2    2
+--R                    \|x  - a
+--R                                                     Type: Expression Integer
+--E
+
+--S 53     14:225 Axiom cannot simplify this expression
+cc:=aa-bb
+--R
+--R               +-------+             +-------+
+--R               | 2    2              | 2    2
+--R   (3)  - log(\|x  - a   + x) - log(\|x  - a   - x) - 1
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.226~~~~~$\displaystyle
@@ -428,7 +802,7 @@ $$
 <<*>>=
 )clear all
 
---S 18 of 28
+--S 54
 aa:=integrate(x^3/(x^2-a^2)^(3/2),x)
 --R 
 --R
@@ -441,6 +815,25 @@ aa:=integrate(x^3/(x^2-a^2)^(3/2),x)
 --R              (2x  - a )\|x  - a   - 2x  + 2a x
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 55
+bb:=sqrt(x^2-a^2)-a^2/sqrt(x^2-a^2)
+--R
+--R          2     2
+--R         x  - 2a
+--R   (2)  ----------
+--R         +-------+
+--R         | 2    2
+--R        \|x  - a
+--R                                                     Type: Expression Integer
+--E
+
+--S 56     14:226 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.227~~~~~$\displaystyle
@@ -452,7 +845,7 @@ $$
 <<*>>=
 )clear all
 
---S 19 of 28
+--S 57
 aa:=integrate(1/(x*(x^2-a^2)^(3/2)),x)
 --R 
 --R
@@ -467,6 +860,34 @@ aa:=integrate(1/(x*(x^2-a^2)^(3/2)),x)
 --R                              a x\|x  - a   - a x  + a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 58
+bb:=-1/(a^2*sqrt(x^2-a^2))-1/a^3*asec(abs(x/a))
+--R
+--R           +-------+
+--R           | 2    2          x
+--R        - \|x  - a  asec(abs(-)) - a
+--R                             a
+--R   (2)  ----------------------------
+--R                   +-------+
+--R                 3 | 2    2
+--R                a \|x  - a
+--R                                                     Type: Expression Integer
+--E
+
+--S 59     14:227 Axiom cannot simplify this expression
+cc:=aa-bb
+--R
+--R                 +-------+
+--R                 | 2    2
+--R                \|x  - a   - x             x
+--R        - 2atan(--------------) + asec(abs(-))
+--R                       a                   a
+--R   (3)  --------------------------------------
+--R                           3
+--R                          a
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.228~~~~~$\displaystyle
@@ -477,7 +898,7 @@ $$
 <<*>>=
 )clear all
 
---S 20 of 28
+--S 60
 aa:=integrate(1/(x^2*(x^2-a^2)^(3/2)),x)
 --R 
 --R
@@ -488,6 +909,29 @@ aa:=integrate(1/(x^2*(x^2-a^2)^(3/2)),x)
 --R          (2x  - a x)\|x  - a   - 2x  + 2a x
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 61
+bb:=-sqrt(x^2-a^2)/(a^4*x)-x/(a^4*sqrt(x^2-a^2))
+--R
+--R              2    2
+--R          - 2x  + a
+--R   (2)  -------------
+--R            +-------+
+--R         4  | 2    2
+--R        a x\|x  - a
+--R                                                     Type: Expression Integer
+--E
+
+--S 62     14:228 Schaums and Axiom differ by a constant
+cc:=aa-bb
+--R
+--R           2
+--R   (3)  - --
+--R           4
+--R          a
+--R                                                     Type: Expression Integer
+--E
+
 @
 
 \section{\cite{1}:14.229~~~~~$\displaystyle
@@ -500,7 +944,7 @@ $$
 <<*>>=
 )clear all
 
---S 21 of 28
+--S 63
 aa:=integrate(1/(x^3*(x^2-a^2)^(3/2)),x)
 --R 
 --R
@@ -520,6 +964,34 @@ aa:=integrate(1/(x^3*(x^2-a^2)^(3/2)),x)
 --R     (8a x  - 6a x )\|x  - a   - 8a x  + 10a x  - 2a x
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 64
+bb:=1/(2*a^2*x^2*sqrt(x^2-a^2))-3/(2*a^4*sqrt(x^2-a^2))-3/(2*a^5)*asec(abs(x/a))
+--R
+--R              +-------+
+--R            2 | 2    2          x         2    3
+--R        - 3x \|x  - a  asec(abs(-)) - 3a x  + a
+--R                                a
+--R   (2)  ----------------------------------------
+--R                           +-------+
+--R                       5 2 | 2    2
+--R                     2a x \|x  - a
+--R                                                     Type: Expression Integer
+--E
+
+--S 65     14:229 Axiom cannot simplify this expression
+cc:=aa-bb
+--R
+--R                 +-------+
+--R                 | 2    2
+--R                \|x  - a   - x              x
+--R        - 6atan(--------------) + 3asec(abs(-))
+--R                       a                    a
+--R   (3)  ---------------------------------------
+--R                            5
+--R                          2a
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.230~~~~~$\displaystyle\int{(x^2-a^2)^{3/2}}~dx$}
@@ -530,7 +1002,7 @@ $$
 <<*>>=
 )clear all
 
---S 22 of 28
+--S 66
 aa:=integrate((x^2-a^2)^(3/2),x)
 --R 
 --R
@@ -551,6 +1023,29 @@ aa:=integrate((x^2-a^2)^(3/2),x)
 --R     (64x  - 32a x)\|x  - a   - 64x  + 64a x  - 8a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 67
+bb:=(x*(x^2-a^2)^(3/2))/4-(3*a^2*x*sqrt(x^2-a^2))/8+3/8*a^4*log(x+sqrt(x^2-a^2))
+--R
+--R                +-------+                     +-------+
+--R          4     | 2    2            3     2   | 2    2
+--R        3a log(\|x  - a   + x) + (2x  - 5a x)\|x  - a
+--R   (2)  -----------------------------------------------
+--R                               8
+--R                                                     Type: Expression Integer
+--E
+
+--S 68     14:230 Axiom cannot simplify this expression
+cc:=aa-bb
+--R
+--R                  +-------+                +-------+
+--R            4     | 2    2           4     | 2    2
+--R        - 3a log(\|x  - a   + x) - 3a log(\|x  - a   - x)
+--R   (3)  -------------------------------------------------
+--R                                8
+--R                                                     Type: Expression Integer
+--E
+
 @
 
 \section{\cite{1}:14.231~~~~~$\displaystyle\int{x(x^2-a^2)^{3/2}}~dx$}
@@ -558,7 +1053,7 @@ $$\int{x(x^2-a^2)^{3/2}}=\frac{(x^2-a^2)^{5/2}}{5}$$
 <<*>>=
 )clear all
 
---S 23 of 28
+--S 69
 aa:=integrate(x*(x^2-a^2)^(3/2),x)
 --R 
 --R
@@ -575,6 +1070,24 @@ aa:=integrate(x*(x^2-a^2)^(3/2),x)
 --R     (80x  - 60a x  + 5a )\|x  - a   - 80x  + 100a x  - 25a x
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 70
+bb:=(x^2-a^2)^(5/2)/5
+--R
+--R                          +-------+
+--R          4     2 2    4  | 2    2
+--R        (x  - 2a x  + a )\|x  - a
+--R   (2)  ---------------------------
+--R                     5
+--R                                                     Type: Expression Integer
+--E
+
+--S 71     14:231 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.232~~~~~$\displaystyle\int{x^2(x^2-a^2)^{3/2}}~dx$}
@@ -586,7 +1099,7 @@ $$
 <<*>>=
 )clear all
 
---S 24 of 28
+--S 72
 aa:=integrate(x^2*(x^2-a^2)^(3/2),x)
 --R 
 --R
@@ -614,6 +1127,28 @@ aa:=integrate(x^2*(x^2-a^2)^(3/2),x)
 --R     (1536x  - 1536a x  + 288a x)\|x  - a   - 1536x  + 2304a x  - 864a x  + 48a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 73
+bb:=(x*(x^2-a^2)^(5/2))/6+(a^2*x*(x^2-a^2)^(3/2))/24-(a^4*x*sqrt(x^2-a^2))/16+a^6/16*log(x+sqrt(x^2-a^2))
+--R
+--R                +-------+                              +-------+
+--R          6     | 2    2            5      2 3     4   | 2    2
+--R        3a log(\|x  - a   + x) + (8x  - 14a x  + 3a x)\|x  - a
+--R   (2)  --------------------------------------------------------
+--R                                   48
+--R                                                     Type: Expression Integer
+--E
+
+--S 74     14:232 Axiom cannot simplify this expression
+cc:=aa-bb
+--R
+--R                 +-------+               +-------+
+--R           6     | 2    2          6     | 2    2
+--R        - a log(\|x  - a   + x) - a log(\|x  - a   - x)
+--R   (3)  -----------------------------------------------
+--R                               16
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.233~~~~~$\displaystyle\int{x^3(x^2-a^2)^{3/2}}~dx$}
@@ -623,7 +1158,7 @@ $$
 <<*>>=
 )clear all
 
---S 25 of 28
+--S 75
 aa:=integrate(x^3*(x^2-a^2)^(3/2),x)
 --R 
 --R
@@ -652,6 +1187,24 @@ aa:=integrate(x^3*(x^2-a^2)^(3/2),x)
 --R       - 1960a x  + 245a x
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 76
+bb:=(x^2-a^2)^(7/2)/7+(a^2*(x^2-a^2)^(5/2))/5
+--R
+--R                                   +-------+
+--R           6     2 4    4 2     6  | 2    2
+--R        (5x  - 8a x  + a x  + 2a )\|x  - a
+--R   (2)  ------------------------------------
+--R                         35
+--R                                                     Type: Expression Integer
+--E
+
+--S 77     14:233 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.234~~~~~$\displaystyle
@@ -663,7 +1216,7 @@ $$
 <<*>>=
 )clear all
 
---S 26 of 28
+--S 78
 aa:=integrate((x^2-a^2)^(3/2)/x,x)
 --R 
 --R
@@ -683,6 +1236,29 @@ aa:=integrate((x^2-a^2)^(3/2)/x,x)
 --R     (12x  - 3a )\|x  - a   - 12x  + 9a x
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 79
+bb:=(x^2-a^2)^(3/2)/3-a^2*sqrt(x^2-a^2)+a^3*asec(abs(x/a))
+--R
+--R                                     +-------+
+--R          3         x       2     2  | 2    2
+--R        3a asec(abs(-)) + (x  - 4a )\|x  - a
+--R                    a
+--R   (2)  --------------------------------------
+--R                           3
+--R                                                     Type: Expression Integer
+--E
+
+--S 80     14:234 Axiom cannot simplify this expression
+cc:=aa-bb
+--R
+--R                 +-------+
+--R                 | 2    2
+--R          3     \|x  - a   - x     3         x
+--R   (3)  2a atan(--------------) - a asec(abs(-))
+--R                       a                     a
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.235~~~~~$\displaystyle
@@ -694,7 +1270,7 @@ $$
 <<*>>=
 )clear all
 
---S 27 of 28
+--S 81
 aa:=integrate((x^2-a^2)^{3/2}/x^2,x)
 --R 
 --R
@@ -712,6 +1288,28 @@ aa:=integrate((x^2-a^2)^{3/2}/x^2,x)
 --R     (8x  - 2a x)\|x  - a   - 8x  + 6a x
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 82
+bb:=-(x^2-a^2)^(3/2)/x+3*x*sqrt(x^2-a^2)/2-3/2*a^2*log(x+sqrt(x^2-a^2))
+--R
+--R                    +-------+                   +-------+
+--R            2       | 2    2           2     2  | 2    2
+--R        - 3a x log(\|x  - a   + x) + (x  + 2a )\|x  - a
+--R   (2)  -------------------------------------------------
+--R                                2x
+--R                                                     Type: Expression Integer
+--E
+
+--S 83     14:235 Axiom cannot simplify this expression
+cc:=aa-bb
+--R
+--R                +-------+                +-------+
+--R          2     | 2    2           2     | 2    2           2
+--R        3a log(\|x  - a   + x) + 3a log(\|x  - a   - x) + 2a
+--R   (3)  -----------------------------------------------------
+--R                                  2
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.236~~~~~$\displaystyle
@@ -723,7 +1321,7 @@ $$
 <<*>>=
 )clear all
 
---S 28 of 28
+--S 84
 aa:=integrate((x^2-a^2)^(3/2)/x^3,x)
 --R 
 --R
@@ -744,6 +1342,31 @@ aa:=integrate((x^2-a^2)^(3/2)/x^3,x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
 
+--S 85
+bb:=-(x^2-a^2)^(3/2)/(2*x^2)+(3*sqrt(x^2-a^2))/2-3/2*a*asec(abs(x/a))
+--R
+--R                                         +-------+
+--R              2         x        2    2  | 2    2
+--R        - 3a x asec(abs(-)) + (2x  + a )\|x  - a
+--R                        a
+--R   (2)  ------------------------------------------
+--R                              2
+--R                            2x
+--R                                                     Type: Expression Integer
+--E
+
+--S 86     14:236 Axiom cannot simplify this expression
+cc:=aa-bb
+--R
+--R                   +-------+
+--R                   | 2    2
+--R                  \|x  - a   - x                x
+--R        - 6a atan(--------------) + 3a asec(abs(-))
+--R                         a                      a
+--R   (3)  -------------------------------------------
+--R                             2
+--R                                                     Type: Expression Integer
+--E
 )spool
 )lisp (bye)
 @
diff --git a/src/input/schaum8.input.pamphlet b/src/input/schaum8.input.pamphlet
index a5c0c7e..778d135 100644
--- a/src/input/schaum8.input.pamphlet
+++ b/src/input/schaum8.input.pamphlet
@@ -16,7 +16,7 @@ $$\int{\frac{1}{a^2-x^2}}=-\frac{1}{a}\coth^{-1}\frac{x}{a}$$
 )set message auto off
 )clear all
 
---S 1 of 19
+--S 1
 aa:=integrate(1/(a^2-x^2),x)
 --R 
 --R
@@ -25,6 +25,63 @@ aa:=integrate(1/(a^2-x^2),x)
 --R                   2a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 2
+bb:=1/(2*a)*log((a+x)/(a-x))
+--R
+--R            - x - a
+--R        log(-------)
+--R             x - a
+--R   (2)  ------------
+--R             2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 3
+cc:=aa-bb
+--R
+--R                                      - x - a
+--R        log(x + a) - log(x - a) - log(-------)
+--R                                       x - a
+--R   (3)  --------------------------------------
+--R                          2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 4
+divlog:=rule(log(a/b) == log(a) - log(b))
+--R
+--R            a
+--R   (4)  log(-) == - log(b) + log(a)
+--R            b
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 5      
+dd:=divlog cc
+--R
+--R        log(x + a) - log(- x - a)
+--R   (5)  -------------------------
+--R                    2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 6
+logminus:=rule(log(x + a) - log(- x - a) == log(-1))
+--R
+--I   (6)  log(x + a) - log(- x - a) + %I == log(- 1) + %I
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 7      14:163 Schaums and Axiom differ by a constant
+ee:=logminus dd
+--R
+--R        log(- 1)
+--R   (7)  --------
+--R           2a
+--R                                                     Type: Expression Integer
+--E
+
 @
 
 \section{\cite{1}:14.164~~~~~$\displaystyle\int{\frac{x~dx}{a^2-x^2}}$}
@@ -32,7 +89,7 @@ $$\int{\frac{x}{a^2-x^2}}=-\frac{1}{2}\ln(a^2-x^2)$$
 <<*>>=
 )clear all
 
---S 2 of 19
+--S 8
 aa:=integrate(x/(a^2-x^2),x)
 --R 
 --R
@@ -42,6 +99,43 @@ aa:=integrate(x/(a^2-x^2),x)
 --R                2
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 9
+bb:=-1/2*log(a^2-x^2)
+--R
+--R                 2    2
+--R          log(- x  + a )
+--R   (2)  - --------------
+--R                 2
+--R                                                     Type: Expression Integer
+--E
+
+--S 10
+cc:=aa-bb
+--R
+--R               2    2           2    2
+--R        - log(x  - a ) + log(- x  + a )
+--R   (3)  -------------------------------
+--R                       2
+--R                                                     Type: Expression Integer
+--E
+
+--S 11
+logminus1:=rule(-log(x^2-a^2)+log(-x^2+a^2) == log(-1))
+--R
+--R               2    2           2    2
+--I   (4)  - log(x  - a ) + log(- x  + a ) + %H == log(- 1) + %H
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 12     14:164 Schaums and Axiom differ by a constant
+dd:=logminus1 cc
+--R
+--R        log(- 1)
+--R   (5)  --------
+--R            2
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.165~~~~~$\displaystyle\int{\frac{x^2~dx}{a^2-x^2}}$}
@@ -49,7 +143,7 @@ $$\int{\frac{x^2}{a^2-x^2}}=-x+\frac{a}{2}\ln\left(\frac{a+x}{a-x}\right)$$
 <<*>>=
 )clear all
 
---S 3 of 19
+--S 13
 aa:=integrate(x^2/(a^2-x^2),x)
 --R 
 --R
@@ -58,6 +152,62 @@ aa:=integrate(x^2/(a^2-x^2),x)
 --R                        2
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 14
+bb:=-x+a/2*log((a+x)/(a-x))
+--R
+--R              - x - a
+--R        a log(-------) - 2x
+--R               x - a
+--R   (2)  -------------------
+--R                 2
+--R                                                     Type: Expression Integer
+--E
+
+--S 15
+cc:=aa-bb
+--R
+--R                                            - x - a
+--R        a log(x + a) - a log(x - a) - a log(-------)
+--R                                             x - a
+--R   (3)  --------------------------------------------
+--R                              2
+--R                                                     Type: Expression Integer
+--E
+
+--S 16
+divlog:=rule(log(a/b) == log(a) - log(b))
+--R
+--R            a
+--R   (4)  log(-) == - log(b) + log(a)
+--R            b
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 17
+dd:=divlog cc
+--R
+--R        a log(x + a) - a log(- x - a)
+--R   (5)  -----------------------------
+--R                      2
+--R                                                     Type: Expression Integer
+--E
+
+--S 18
+logminusa:=rule(b*log(x + a) - b*log(- x - a) == b*log(-1))
+--R
+--I   (6)  b log(x + a) - b log(- x - a) + %M == b log(- 1) + %M
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 19     14:165 Schaums and Axiom differ by a constant
+ee:=logminusa dd
+--R
+--R        a log(- 1)
+--R   (7)  ----------
+--R             2
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.166~~~~~$\displaystyle\int{\frac{x^3~dx}{a^2-x^2}}$}
@@ -66,7 +216,7 @@ $$\int{\frac{x^3}{a^2-x^2}}=-\frac{x^2}{2}-\frac{a^2}{2}\ln(a^2-x^2)$$
 <<*>>=
 )clear all
 
---S 4 of 19
+--S 20
 aa:=integrate(x^3/(a^2-x^2),x)
 --R 
 --R
@@ -76,6 +226,45 @@ aa:=integrate(x^3/(a^2-x^2),x)
 --R                  2
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 21
+bb:=-x^2/2-a^2/2*log(a^2-x^2)
+--R
+--R           2       2    2     2
+--R        - a log(- x  + a ) - x
+--R   (2)  -----------------------
+--R                   2
+--R                                                     Type: Expression Integer
+--E
+
+--S 22
+cc:=aa-bb
+--R
+--R           2     2    2     2       2    2
+--R        - a log(x  - a ) + a log(- x  + a )
+--R   (3)  -----------------------------------
+--R                         2
+--R                                                     Type: Expression Integer
+--E
+
+--S 23
+logminus1b:=rule(-b*log(x^2-a^2)+b*log(-x^2+a^2) == b*log(-1))
+--R
+--R                 2    2             2    2
+--I   (4)  - b log(x  - a ) + b log(- x  + a ) + %N == b log(- 1) + %N
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 24     14:166 Schaums and Axiom differ by a constant
+dd:=logminus1b cc
+--R
+--R         2
+--R        a log(- 1)
+--R   (5)  ----------
+--R             2
+--R                                                     Type: Expression Integer
+--E
+
 @
 
 \section{\cite{1}:14.167~~~~~$\displaystyle\int{\frac{dx}{x(a^2-x^2)}}$}
@@ -85,7 +274,7 @@ $$
 <<*>>=
 )clear all
 
---S 5 of 19
+--S 25
 aa:=integrate(1/(x*(a^2-x^2)),x)
 --R 
 --R
@@ -96,6 +285,72 @@ aa:=integrate(1/(x*(a^2-x^2)),x)
 --R                   2a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 26
+bb:=1/(2*a^2)*log(x^2/(a^2-x^2))
+--R
+--R                  2
+--R                 x
+--R        log(- -------)
+--R               2    2
+--R              x  - a
+--R   (2)  --------------
+--R                2
+--R              2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 27
+cc:=aa-bb
+--R
+--R                                             2
+--R               2    2                       x
+--R        - log(x  - a ) + 2log(x) - log(- -------)
+--R                                          2    2
+--R                                         x  - a
+--R   (3)  -----------------------------------------
+--R                             2
+--R                           2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 28
+divlog:=rule(log(a/b) == log(a) - log(b))
+--R
+--R            a
+--R   (4)  log(-) == - log(b) + log(a)
+--R            b
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 29
+dd:=divlog cc
+--R
+--R                         2
+--R        2log(x) - log(- x )
+--R   (5)  -------------------
+--R                  2
+--R                2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 30
+logpowminus:=rule(log(-a^n) == n*log(a)+log(-1))
+--R
+--R               n
+--R   (6)  log(- a ) == n log(a) + log(- 1)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 31     14:167 Schaums and Axiom differ by a constant
+ee:=logpowminus dd
+--R
+--R          log(- 1)
+--R   (7)  - --------
+--R               2
+--R             2a
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.168~~~~~$\displaystyle\int{\frac{dx}{x^2(a^2-x^2)}}$}
@@ -105,7 +360,7 @@ $$
 <<*>>=
 )clear all
 
---S 6 of 19
+--S 32
 aa:=integrate(1/(x^2*(a^2-x^2)),x)
 --R 
 --R
@@ -115,6 +370,67 @@ aa:=integrate(1/(x^2*(a^2-x^2)),x)
 --R                      2a x
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 33
+bb:=-1/(a^2*x)+1/(2*a^3)*log((a+x)/(a-x))
+--R
+--R              - x - a
+--R        x log(-------) - 2a
+--R               x - a
+--R   (2)  -------------------
+--R                  3
+--R                2a x
+--R                                                     Type: Expression Integer
+--E
+
+--S 34
+cc:=aa-bb
+--R
+--R                                      - x - a
+--R        log(x + a) - log(x - a) - log(-------)
+--R                                       x - a
+--R   (3)  --------------------------------------
+--R                            3
+--R                          2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 35
+divlog:=rule(log(a/b) == log(a) - log(b))
+--R
+--R            a
+--R   (4)  log(-) == - log(b) + log(a)
+--R            b
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 36
+dd:=divlog cc
+--R
+--R        log(x + a) - log(- x - a)
+--R   (5)  -------------------------
+--R                     3
+--R                   2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 37
+logminus:=rule(log(x + a) - log(- x - a) == log(-1))
+--R
+--I   (6)  log(x + a) - log(- x - a) + %O == log(- 1) + %O
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 38     14:168 Schaums and Axiom differ by a constant
+ee:=logminus dd
+--R
+--R        log(- 1)
+--R   (7)  --------
+--R             3
+--R           2a
+--R                                                     Type: Expression Integer
+--E
+
 @
 
 \section{\cite{1}:14.169~~~~~$\displaystyle\int{\frac{dx}{x^3(a^2-x^2)}}$}
@@ -124,7 +440,7 @@ $$
 <<*>>=
 )clear all
 
---S 7 of 19
+--S 39
 aa:=integrate(1/(x^3*(a^2-x^2)),x)
 --R 
 --R
@@ -135,6 +451,70 @@ aa:=integrate(1/(x^3*(a^2-x^2)),x)
 --R                      2a x
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 40
+bb:=-1/(2*a^2*x^2)+1/(2*a^4)*log(x^2/(a^2-x^2))
+--R
+--R                    2
+--R         2         x        2
+--R        x log(- -------) - a
+--R                 2    2
+--R                x  - a
+--R   (2)  ---------------------
+--R                  4 2
+--R                2a x
+--R                                                     Type: Expression Integer
+--E
+
+--S 41
+divlog:=rule(log(a/b) == log(a) - log(b))
+--R
+--R            a
+--R   (3)  log(-) == - log(b) + log(a)
+--R            b
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 42
+bb1:=divlog bb
+--R
+--R           2     2    2     2       2     2
+--R        - x log(x  - a ) + x log(- x ) - a
+--R   (4)  -----------------------------------
+--R                         4 2
+--R                       2a x
+--R                                                     Type: Expression Integer
+--E
+
+--S 43
+cc:=aa-bb1
+--R
+--R                         2
+--R        2log(x) - log(- x )
+--R   (5)  -------------------
+--R                  4
+--R                2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 44
+logminuspow:=rule(log(-x^n) == n*log(x)+log(-1))
+--R
+--R               n
+--R   (6)  log(- x ) == n log(x) + log(- 1)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 45     14:169 Schaums and Axiom differ by a constant
+dd:=logminuspow cc
+--R
+--R          log(- 1)
+--R   (7)  - --------
+--R               4
+--R             2a
+--R                                                     Type: Expression Integer
+--E
+
 @
 
 \section{\cite{1}:14.170~~~~~$\displaystyle\int{\frac{dx}{(a^2-x^2)^2}}$}
@@ -144,7 +524,7 @@ $$
 <<*>>=
 )clear all
 
---S 8 of 19
+--S 46
 aa:=integrate(1/((a^2-x^2)^2),x)
 --R 
 --R
@@ -155,6 +535,66 @@ aa:=integrate(1/((a^2-x^2)^2),x)
 --R                            4a x  - 4a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 47
+bb:=x/(2*a^2*(a^2-x^2))+1/(4*a^3)*log((a+x)/(a-x))
+--R
+--R          2    2     - x - a
+--R        (x  - a )log(-------) - 2a x
+--R                      x - a
+--R   (2)  ----------------------------
+--R                   3 2     5
+--R                 4a x  - 4a
+--R                                                     Type: Expression Integer
+--E
+
+--S 48
+divlog:=rule(log(a/b) == log(a) - log(b))
+--R
+--R            a
+--R   (3)  log(-) == - log(b) + log(a)
+--R            b
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 49
+bb1:=divlog bb
+--R
+--R            2    2                2    2
+--R        (- x  + a )log(x - a) + (x  - a )log(- x - a) - 2a x
+--R   (4)  ----------------------------------------------------
+--R                               3 2     5
+--R                             4a x  - 4a
+--R                                                     Type: Expression Integer
+--E
+
+--S 50
+cc:=aa-bb1
+--R
+--R        log(x + a) - log(- x - a)
+--R   (5)  -------------------------
+--R                     3
+--R                   4a
+--R                                                     Type: Expression Integer
+--E
+
+--S 51
+logminus:=rule(log(x + a) - log(- x - a) == log(-1))
+--R
+--I   (6)  log(x + a) - log(- x - a) + %P == log(- 1) + %P
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 52     14:170 Schaums and Axiom differ by a constant
+dd:=logminus cc
+--R
+--R        log(- 1)
+--R   (7)  --------
+--R             3
+--R           4a
+--R                                                     Type: Expression Integer
+--E
+
 @
 
 \section{\cite{1}:14.171~~~~~$\displaystyle\int{\frac{x~dx}{(a^2-x^2)^2}}$}
@@ -164,7 +604,7 @@ $$
 <<*>>=
 )clear all
 
---S 9 of 19
+--S 53
 aa:=integrate(x/((a^2-x^2)^2),x)
 --R 
 --R
@@ -174,6 +614,24 @@ aa:=integrate(x/((a^2-x^2)^2),x)
 --R          2x  - 2a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 54
+bb:=1/(2*(a^2-x^2))
+--R
+--R              1
+--R   (2)  - ---------
+--R            2     2
+--R          2x  - 2a
+--R                                            Type: Fraction Polynomial Integer
+--E
+
+--S 55     14:171 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
+
 @
 
 \section{\cite{1}:14.172~~~~~$\displaystyle\int{\frac{x^2dx}{(a^2-x^2)^2}}$}
@@ -183,7 +641,7 @@ $$
 <<*>>=
 )clear all
 
---S 10 of 19
+--S 56
 aa:=integrate(x^2/((a^2-x^2)^2),x)
 --R 
 --R
@@ -194,6 +652,63 @@ aa:=integrate(x^2/((a^2-x^2)^2),x)
 --R                            4a x  - 4a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 57
+bb:=x/(2*(a^2-x^2))-1/(4*a)*log((a+x)/(a-x))
+--R
+--R            2    2     - x - a
+--R        (- x  + a )log(-------) - 2a x
+--R                        x - a
+--R   (2)  ------------------------------
+--R                      2     3
+--R                  4a x  - 4a
+--R                                                     Type: Expression Integer
+--E
+
+--S 58
+divlog:=rule(log(a/b) == log(a) - log(b))
+--R
+--R            a
+--R   (3)  log(-) == - log(b) + log(a)
+--R            b
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 59
+bb1:=divlog bb
+--R
+--R          2    2                  2    2
+--R        (x  - a )log(x - a) + (- x  + a )log(- x - a) - 2a x
+--R   (4)  ----------------------------------------------------
+--R                                 2     3
+--R                             4a x  - 4a
+--R                                                     Type: Expression Integer
+--E
+
+--S 60
+cc:=aa-bb1
+--R
+--R        - log(x + a) + log(- x - a)
+--R   (5)  ---------------------------
+--R                     4a
+--R                                                     Type: Expression Integer
+--E
+
+--S 61
+logminus2:=rule(-log(x + a) + log(- x - a) == log(-1))
+--R
+--I   (6)  - log(x + a) + log(- x - a) + %S == log(- 1) + %S
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 62     14:172 Schaums and Axiom differ by a constant
+dd:=logminus2 cc
+--R
+--R        log(- 1)
+--R   (7)  --------
+--R           4a
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.173~~~~~$\displaystyle\int{\frac{x^3dx}{(a^2-x^2)^2}}$}
@@ -203,7 +718,7 @@ $$
 <<*>>=
 )clear all
 
---S 11 of 19
+--S 63
 aa:=integrate(x^3/((a^2-x^2)^2),x)
 --R 
 --R
@@ -214,6 +729,45 @@ aa:=integrate(x^3/((a^2-x^2)^2),x)
 --R                 2x  - 2a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 64
+bb:=a^2/(2*(a^2-x^2))+1/2*log(a^2-x^2)
+--R
+--R          2    2        2    2     2
+--R        (x  - a )log(- x  + a ) - a
+--R   (2)  ----------------------------
+--R                    2     2
+--R                  2x  - 2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 65
+cc:=aa-bb
+--R
+--R             2    2           2    2
+--R        log(x  - a ) - log(- x  + a )
+--R   (3)  -----------------------------
+--R                      2
+--R                                                     Type: Expression Integer
+--E
+
+--S 66
+logminus3:=rule(log(x^2-a^2)-log(-x^2+a^2) == log(-1))
+--R
+--R             2    2           2    2
+--I   (4)  log(x  - a ) - log(- x  + a ) + %T == log(- 1) + %T
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 67     14:173 Schaums and Axiom differ by a constant
+dd:=logminus3 cc
+--R
+--R        log(- 1)
+--R   (5)  --------
+--R            2
+--R                                                     Type: Expression Integer
+--E
+
 @
 
 \section{\cite{1}:14.174~~~~~$\displaystyle\int{\frac{dx}{x(a^2-x^2)^2}}$}
@@ -223,7 +777,7 @@ $$
 <<*>>=
 )clear all
 
---S 12 of 19
+--S 68
 aa:=integrate(1/(x*(a^2-x^2)^2),x)
 --R 
 --R
@@ -234,6 +788,70 @@ aa:=integrate(1/(x*(a^2-x^2)^2),x)
 --R                           2a x  - 2a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 69
+bb:=1/(2*a^2*(a^2-x^2))+1/(2*a^4)*log(x^2/(a^2-x^2))
+--R
+--R                           2
+--R          2    2          x        2
+--R        (x  - a )log(- -------) - a
+--R                        2    2
+--R                       x  - a
+--R   (2)  ----------------------------
+--R                   4 2     6
+--R                 2a x  - 2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 70
+divlog:=rule(log(a/b) == log(a) - log(b))
+--R
+--R            a
+--R   (3)  log(-) == - log(b) + log(a)
+--R            b
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 71
+bb1:=divlog bb
+--R
+--R            2    2      2    2      2    2        2     2
+--R        (- x  + a )log(x  - a ) + (x  - a )log(- x ) - a
+--R   (4)  -------------------------------------------------
+--R                             4 2     6
+--R                           2a x  - 2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 72
+cc:=aa-bb1
+--R
+--R                         2
+--R        2log(x) - log(- x )
+--R   (5)  -------------------
+--R                  4
+--R                2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 73
+logpowminus:=rule(log(-a^n) == n*log(a)+log(-1))
+--R
+--R               n
+--R   (6)  log(- a ) == n log(a) + log(- 1)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 74     14:174 Schaums and Axiom differ by a constant
+dd:=logpowminus cc
+--R
+--R          log(- 1)
+--R   (7)  - --------
+--R               4
+--R             2a
+--R                                                     Type: Expression Integer
+--E
+
 @
 
 \section{\cite{1}:14.175~~~~~$\displaystyle\int{\frac{dx}{x^2(a^2-x^2)^2}}$}
@@ -244,17 +862,88 @@ $$
 <<*>>=
 )clear all
 
---S 13 of 19
-aa:=integrate(1/((a^2-x^2)^2),x)
---R 
+--S 75
+aa:=integrate(1/(x^2*(a^2-x^2)^2),x)
 --R
---R          2    2                  2    2
---R        (x  - a )log(x + a) + (- x  + a )log(x - a) - 2a x
---R   (1)  --------------------------------------------------
---R                              3 2     5
---R                            4a x  - 4a
+--R           3     2                    3     2                   2     3
+--R        (3x  - 3a x)log(x + a) + (- 3x  + 3a x)log(x - a) - 6a x  + 4a
+--R   (1)  ---------------------------------------------------------------
+--R                                    5 3     7
+--R                                  4a x  - 4a x
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 76
+bb:=-1/(a^4*x)+x/(2*a^4*(a^2-x^2))+3/(4*a^5)*log((a+x)/(a-x))
+--R
+--R           3     2      - x - a        2     3
+--R        (3x  - 3a x)log(-------) - 6a x  + 4a
+--R                         x - a
+--R   (2)  --------------------------------------
+--R                       5 3     7
+--R                     4a x  - 4a x
+--R                                                     Type: Expression Integer
+--E
+
+--S 77
+divlog:=rule(log(a/b) == log(a) - log(b))
+--R
+--R            a
+--R   (3)  log(-) == - log(b) + log(a)
+--R            b
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 78
+bb1:=divlog bb
+--R
+--R             3     2                  3     2                     2     3
+--R        (- 3x  + 3a x)log(x - a) + (3x  - 3a x)log(- x - a) - 6a x  + 4a
+--R   (4)  -----------------------------------------------------------------
+--R                                     5 3     7
+--R                                   4a x  - 4a x
+--R                                                     Type: Expression Integer
+--E
+
+--S 79
+cc:=aa-bb
+--R
+--R                                         - x - a
+--R        3log(x + a) - 3log(x - a) - 3log(-------)
+--R                                          x - a
+--R   (5)  -----------------------------------------
+--R                             5
+--R                           4a
+--R                                                     Type: Expression Integer
+--E
+
+--S 80
+dd:=divlog cc
+--R
+--R        3log(x + a) - 3log(- x - a)
+--R   (6)  ---------------------------
+--R                      5
+--R                    4a
+--R                                                     Type: Expression Integer
+--E
+
+--S 81
+logminusb:=rule(b*log(x + a) - b*log(- x - a) == b*log(-1))
+--R
+--I   (7)  b log(x + a) - b log(- x - a) + %U == b log(- 1) + %U
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 82     14:175 Schaums and Axiom differ by a constant
+ee:=logminusb dd
+--R
+--R        3log(- 1)
+--R   (8)  ---------
+--R             5
+--R           4a
+--R                                                     Type: Expression Integer
+--E
+
 @
 
 \section{\cite{1}:14.176~~~~~$\displaystyle\int{\frac{dx}{x^3(a^2-x^2)^2}}$}
@@ -265,7 +954,7 @@ $$
 <<*>>=
 )clear all
 
---S 14 of 19
+--S 83
 aa:=integrate(1/(x^3*(a^2-x^2)^2),x)
 --R 
 --R
@@ -276,6 +965,70 @@ aa:=integrate(1/(x^3*(a^2-x^2)^2),x)
 --R                                 2a x  - 2a x
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 84
+bb:=-1/(2*a^4*x^2)+1/(2*a^4*(a^2-x^2))+1/a^6*log(x^2/(a^2-x^2))
+--R
+--R                               2
+--R           4     2 2          x         2 2    4
+--R        (2x  - 2a x )log(- -------) - 2a x  + a
+--R                            2    2
+--R                           x  - a
+--R   (2)  ----------------------------------------
+--R                        6 4     8 2
+--R                      2a x  - 2a x
+--R                                                     Type: Expression Integer
+--E
+
+--S 85
+divlog:=rule(log(a/b) == log(a) - log(b))
+--R
+--R            a
+--R   (3)  log(-) == - log(b) + log(a)
+--R            b
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 86
+bb1:=divlog bb
+--R
+--R             4     2 2      2    2       4     2 2        2      2 2    4
+--R        (- 2x  + 2a x )log(x  - a ) + (2x  - 2a x )log(- x ) - 2a x  + a
+--R   (4)  -----------------------------------------------------------------
+--R                                    6 4     8 2
+--R                                  2a x  - 2a x
+--R                                                     Type: Expression Integer
+--E
+
+--S 87
+cc:=aa-bb1
+--R
+--R                         2
+--R        2log(x) - log(- x )
+--R   (5)  -------------------
+--R                  6
+--R                 a
+--R                                                     Type: Expression Integer
+--E
+
+--S 88
+logpowminus:=rule(log(-a^n) == n*log(a)+log(-1))
+--R
+--R               n
+--R   (6)  log(- a ) == n log(a) + log(- 1)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 89     14:176 Schaums and Axiom differ by a constant
+dd:=logpowminus cc
+--R
+--R          log(- 1)
+--R   (7)  - --------
+--R              6
+--R             a
+--R                                                     Type: Expression Integer
+--E
+
 @
 
 \section{\cite{1}:14.177~~~~~$\displaystyle\int{\frac{dx}{(a^2-x^2)^n}}$}
@@ -286,7 +1039,7 @@ $$
 <<*>>=
 )clear all
 
---S 15 of 19
+--S 90     14:177 Axiom cannot do this integration
 aa:=integrate(1/((a^2-x^2)^n),x)
 --R 
 --R
@@ -306,7 +1059,7 @@ $$
 <<*>>=
 )clear all
 
---S 16 of 19
+--S 91
 aa:=integrate(x/((a^2-x^2)^n),x)
 --R 
 --R
@@ -318,6 +1071,49 @@ aa:=integrate(x/((a^2-x^2)^n),x)
 --R        (2n - 2)%e
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 92
+bb:=1/(2*(n-1)*(a^2-x^2)^(n-1))
+--R
+--R                    1
+--R   (2)  ------------------------
+--R                    2    2 n - 1
+--R        (2n - 2)(- x  + a )
+--R                                                     Type: Expression Integer
+--E
+
+--S 93
+cc:=aa-bb
+--R
+--R                     2    2
+--R            n log(- x  + a )       2    2     2    2 n - 1
+--R        - %e                 + (- x  + a )(- x  + a )
+--R   (3)  --------------------------------------------------
+--R                                               2    2
+--R                        2    2 n - 1  n log(- x  + a )
+--R            (2n - 2)(- x  + a )     %e
+--R                                                     Type: Expression Integer
+--E
+
+--S 94
+explog:=rule(%e^(n*log(x)) == x^n)
+--R
+--R          n log(x)     n
+--R   (4)  %e         == x
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 95     14:178 Axiom cannot simplify this expression
+dd:=explog cc
+--R
+--R              2    2 n       2    2     2    2 n - 1
+--R        - (- x  + a )  + (- x  + a )(- x  + a )
+--R   (5)  --------------------------------------------
+--R                        2    2 n - 1    2    2 n
+--R            (2n - 2)(- x  + a )     (- x  + a )
+--R                                                     Type: Expression Integer
+--E
+
 @
 
 \section{\cite{1}:14.179~~~~~$\displaystyle\int{\frac{dx}{x(a^2-x^2)^n}}$}
@@ -328,7 +1124,7 @@ $$
 <<*>>=
 )clear all
 
---S 17 of 19
+--S 96     14:179 Axiom cannot integrate this expression
 aa:=integrate(1/(x*(a^2-x^2)^n),x)
 --R 
 --R
@@ -349,7 +1145,7 @@ $$
 <<*>>=
 )clear all
 
---S 18 of 19
+--S 97     14:180 Axiom cannot integrate this expression
 aa:=integrate(x^m/((a^2-x^2)^n),x)
 --R 
 --R
@@ -370,7 +1166,7 @@ $$
 <<*>>=
 )clear all
 
---S 19 of 19
+--S 98     14:181 Axiom cannot integrate this expression
 aa:=integrate(1/(x^m*(a^2-x^2)^n),x)
 --R 
 --R
diff --git a/src/input/schaum9.input.pamphlet b/src/input/schaum9.input.pamphlet
index 6610811..fceb094 100644
--- a/src/input/schaum9.input.pamphlet
+++ b/src/input/schaum9.input.pamphlet
@@ -16,7 +16,7 @@ $$\int{\frac{1}{\sqrt{x^2+a^2}}}=\sinh^{-1}\frac{x}{a}$$
 )set message auto off
 )clear all
 
---S 1 of 28
+--S 1
 aa:=integrate(1/(sqrt(x^2+a^2)),x)
 --R 
 --R
@@ -25,14 +25,33 @@ aa:=integrate(1/(sqrt(x^2+a^2)),x)
 --R   (1)  - log(\|x  + a   - x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 2
+bb:=log(x+sqrt(x^2+a^2))
+--R
+--R             +-------+
+--R             | 2    2
+--R   (2)  log(\|x  + a   + x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 3      14:182 Axiom cannot simplify this expression
+cc:=aa-bb
+--R
+--R               +-------+             +-------+
+--R               | 2    2              | 2    2
+--R   (3)  - log(\|x  + a   + x) - log(\|x  + a   - x)
+--R                                                     Type: Expression Integer
+--E
 @
+This is equal to $-\log(a^2)$ but Axiom cannot prove it.
 
 \section{\cite{1}:14.183~~~~~$\displaystyle\int{\frac{x~dx}{\sqrt{x^2+a^2}}}$}
 $$\int{\frac{x}{\sqrt{x^2+a^2}}}=\sqrt{x^2+a^2}$$
 <<*>>=
 )clear all
 
---S 2 of 28
+--S 4
 aa:=integrate(x/(sqrt(x^2+a^2)),x)
 --R 
 --R
@@ -45,6 +64,22 @@ aa:=integrate(x/(sqrt(x^2+a^2)),x)
 --R             \|x  + a   - x
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 5
+bb:=sqrt(x^2+a^2)
+--R
+--R         +-------+
+--R         | 2    2
+--R   (2)  \|x  + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 6      14:183 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.184~~~~~$\displaystyle
@@ -55,7 +90,7 @@ $$
 <<*>>=
 )clear all
 
---S 3 of 28
+--S 7
 aa:=integrate(x^2/sqrt(x^2+a^2),x)
 --R 
 --R
@@ -73,6 +108,46 @@ aa:=integrate(x^2/sqrt(x^2+a^2),x)
 --R     4x\|x  + a   - 4x  - 2a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 8
+bb:=(x*sqrt(x^2+a^2))/2-a^2/2*log(x+sqrt(x^2+a^2))
+--R
+--R                 +-------+          +-------+
+--R           2     | 2    2           | 2    2
+--R        - a log(\|x  + a   + x) + x\|x  + a
+--R   (2)  -------------------------------------
+--R                          2
+--R                                                     Type: Expression Integer
+--E
+
+--S 9
+cc:=aa-bb
+--R
+--R               +-------+               +-------+
+--R         2     | 2    2          2     | 2    2
+--R        a log(\|x  + a   + x) + a log(\|x  + a   - x)
+--R   (3)  ---------------------------------------------
+--R                              2
+--R                                                     Type: Expression Integer
+--E
+
+--S 10
+logmul1:=rule(c*log(a)+c*log(b) == c*log(a*b))
+--R
+--I   (4)  c log(b) + c log(a) + %K == c log(a b) + %K
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 11     14:184 Schaums and Axiom differ by a constant
+dd:=logmul1 cc
+--R
+--R         2     2
+--R        a log(a )
+--R   (5)  ---------
+--R            2
+--R                                                     Type: Expression Integer
+--E
+
 @
 
 \section{\cite{1}:14.185~~~~~$\displaystyle
@@ -83,7 +158,7 @@ $$
 <<*>>=
 )clear all
 
---S 4 of 28
+--S 12
 aa:=integrate(x^3/sqrt(x^2+a^2),x)
 --R 
 --R
@@ -96,6 +171,24 @@ aa:=integrate(x^3/sqrt(x^2+a^2),x)
 --R                    (12x  + 3a )\|x  + a   - 12x  - 9a x
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 13
+bb:=(x^2+a^2)^(3/2)/3-a^2*sqrt(x^2+a^2)
+--R
+--R                   +-------+
+--R          2     2  | 2    2
+--R        (x  - 2a )\|x  + a
+--R   (2)  --------------------
+--R                  3
+--R                                                     Type: Expression Integer
+--E
+
+--S 14     14:185 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.186~~~~~$\displaystyle\int{\frac{dx}{x\sqrt{x^2+a^2}}}$}
@@ -105,7 +198,7 @@ $$
 <<*>>=
 )clear all
 
---S 5 of 28
+--S 15
 aa:=integrate(1/(x*sqrt(x^2+a^2)),x)
 --R 
 --R
@@ -116,6 +209,57 @@ aa:=integrate(1/(x*sqrt(x^2+a^2)),x)
 --R                                 a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 16
+bb:=-1/a*log((a+sqrt(x^2+a^2))/x)
+--R
+--R               +-------+
+--R               | 2    2
+--R              \|x  + a   + a
+--R          log(--------------)
+--R                     x
+--R   (2)  - -------------------
+--R                   a
+--R                                                     Type: Expression Integer
+--E
+
+--S 17
+cc:=aa-bb
+--R
+--R   (3)
+--R                                                              +-------+
+--R          +-------+                 +-------+                 | 2    2
+--R          | 2    2                  | 2    2                 \|x  + a   + a
+--R   - log(\|x  + a   - x + a) + log(\|x  + a   - x - a) + log(--------------)
+--R                                                                    x
+--R   -------------------------------------------------------------------------
+--R                                       a
+--R                                                     Type: Expression Integer
+--E
+
+--S 18
+divlog:=rule(log(a/b) == log(a) - log(b))
+--R
+--R            a
+--R   (4)  log(-) == - log(b) + log(a)
+--R            b
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 19     14:186 Axiom cannot simplify this expression
+dd:=divlog cc
+--R
+--R   (5)
+--R            +-------+             +-------+                 +-------+
+--R            | 2    2              | 2    2                  | 2    2
+--R       log(\|x  + a   + a) - log(\|x  + a   - x + a) + log(\|x  + a   - x - a)
+--R     + 
+--R       - log(x)
+--R  /
+--R     a
+--R                                                     Type: Expression Integer
+--E
+
 @
 
 \section{\cite{1}:14.187~~~~~$\displaystyle
@@ -126,7 +270,7 @@ $$
 <<*>>=
 )clear all
 
---S 6 of 28
+--S 20
 aa:=integrate(1/(x^2*sqrt(x^2+a^2)),x)
 --R 
 --R
@@ -137,6 +281,29 @@ aa:=integrate(1/(x^2*sqrt(x^2+a^2)),x)
 --R          x\|x  + a   - x
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 21
+bb:=-sqrt(x^2+a^2)/(a^2*x)
+--R
+--R           +-------+
+--R           | 2    2
+--R          \|x  + a
+--R   (2)  - ----------
+--R               2
+--R              a x
+--R                                                     Type: Expression Integer
+--E
+
+--S 22     14:187 Schaums and Axiom differ by a constant
+cc:=aa-bb
+--R
+--R           1
+--R   (3)  - --
+--R           2
+--R          a
+--R                                                     Type: Expression Integer
+--E
+
 @
 
 \section{\cite{1}:14.188~~~~~$\displaystyle\int{\frac{dx}{x^3\sqrt{x^2+a^2}}}$}
@@ -147,7 +314,7 @@ $$
 <<*>>=
 )clear all
 
---S 7 of 28
+--S 23
 aa:=integrate(1/(x^3*sqrt(x^2+a^2)),x)
 --R 
 --R
@@ -169,6 +336,59 @@ aa:=integrate(1/(x^3*sqrt(x^2+a^2)),x)
 --R     4a x \|x  + a   - 4a x  - 2a x
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 24
+bb:=-sqrt(x^2+a^2)/(2*a^2*x^2)+1/(2*a^3)*log((a+sqrt(x^2+a^2))/x)
+--R
+--R               +-------+
+--R               | 2    2           +-------+
+--R         2    \|x  + a   + a      | 2    2
+--R        x log(--------------) - a\|x  + a
+--R                     x
+--R   (2)  -----------------------------------
+--R                         3 2
+--R                       2a x
+--R                                                     Type: Expression Integer
+--E
+
+--S 25
+cc:=aa-bb
+--R
+--R   (3)
+--R                                                            +-------+
+--R        +-------+                 +-------+                 | 2    2
+--R        | 2    2                  | 2    2                 \|x  + a   + a
+--R   log(\|x  + a   - x + a) - log(\|x  + a   - x - a) - log(--------------)
+--R                                                                  x
+--R   -----------------------------------------------------------------------
+--R                                       3
+--R                                     2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 26
+divlog:=rule(log(a/b) == log(a) - log(b))
+--R
+--R            a
+--R   (4)  log(-) == - log(b) + log(a)
+--R            b
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 27     14:188 Axiom cannot simplify this expression
+dd:=divlog cc
+--R
+--R   (5)
+--R              +-------+             +-------+                 +-------+
+--R              | 2    2              | 2    2                  | 2    2
+--R       - log(\|x  + a   + a) + log(\|x  + a   - x + a) - log(\|x  + a   - x - a)
+--R     + 
+--R       log(x)
+--R  /
+--R       3
+--R     2a
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.189~~~~~$\displaystyle\int{\sqrt{x^2+a^2}}~dx$}
@@ -178,7 +398,7 @@ $$
 <<*>>=
 )clear all
 
---S 8 of 28
+--S 28
 aa:=integrate(sqrt(x^2+a^2),x)
 --R 
 --R
@@ -196,6 +416,28 @@ aa:=integrate(sqrt(x^2+a^2),x)
 --R     4x\|x  + a   - 4x  - 2a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 29
+bb:=(x*sqrt(x^2+a^2))/2+a^2/2*log(x+sqrt(x^2+a^2))
+--R
+--R               +-------+          +-------+
+--R         2     | 2    2           | 2    2
+--R        a log(\|x  + a   + x) + x\|x  + a
+--R   (2)  -----------------------------------
+--R                         2
+--R                                                     Type: Expression Integer
+--E
+
+--S 30     14:189 Axiom cannot simplify this expression
+cc:=aa-bb
+--R
+--R                 +-------+               +-------+
+--R           2     | 2    2          2     | 2    2
+--R        - a log(\|x  + a   + x) - a log(\|x  + a   - x)
+--R   (3)  -----------------------------------------------
+--R                               2
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.190~~~~~$\displaystyle\int{x\sqrt{x^2+a^2}}~dx$}
@@ -205,7 +447,7 @@ $$
 <<*>>=
 )clear all
 
---S 9 of 28
+--S 31
 aa:=integrate(x*sqrt(x^2+a^2),x)
 --R 
 --R
@@ -218,6 +460,24 @@ aa:=integrate(x*sqrt(x^2+a^2),x)
 --R                    (12x  + 3a )\|x  + a   - 12x  - 9a x
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 32
+bb:=(x^2+a^2)^(3/2)/3
+--R
+--R                  +-------+
+--R          2    2  | 2    2
+--R        (x  + a )\|x  + a
+--R   (2)  -------------------
+--R                 3
+--R                                                     Type: Expression Integer
+--E
+
+--S 33     14:190 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.191~~~~~$\displaystyle
@@ -229,7 +489,7 @@ $$
 <<*>>=
 )clear all
 
---S 10 of 28
+--S 34
 aa:=integrate(x^2*sqrt(x^2+a^2),x)
 --R 
 --R
@@ -247,6 +507,28 @@ aa:=integrate(x^2*sqrt(x^2+a^2),x)
 --R     (64x  + 32a x)\|x  + a   - 64x  - 64a x  - 8a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 35
+bb:=(x*(x^2+a^2)^(3/2))/4-(a^2*x*sqrt(x^2+a^2))/8-a^4/8*log(x+sqrt(x^2+a^2))
+--R
+--R                 +-------+                    +-------+
+--R           4     | 2    2            3    2   | 2    2
+--R        - a log(\|x  + a   + x) + (2x  + a x)\|x  + a
+--R   (2)  -----------------------------------------------
+--R                               8
+--R                                                     Type: Expression Integer
+--E
+
+--S 36     14:191 Axiom cannot simplify this expression
+cc:=aa-bb
+--R
+--R               +-------+               +-------+
+--R         4     | 2    2          4     | 2    2
+--R        a log(\|x  + a   + x) + a log(\|x  + a   - x)
+--R   (3)  ---------------------------------------------
+--R                              8
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.192~~~~~$\displaystyle
@@ -257,7 +539,7 @@ $$
 <<*>>=
 )clear all
 
---S 11 of 28
+--S 37
 aa:=integrate(x^3*sqrt(x^2+a^2),x)
 --R 
 --R
@@ -274,6 +556,24 @@ aa:=integrate(x^3*sqrt(x^2+a^2),x)
 --R     (240x  + 180a x  + 15a )\|x  + a   - 240x  - 300a x  - 75a x
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 38
+bb:=(x^2+a^2)^(5/2)/5-(a^2*(x^2+a^2)^(3/2))/3
+--R
+--R                           +-------+
+--R           4    2 2     4  | 2    2
+--R        (3x  + a x  - 2a )\|x  + a
+--R   (2)  ----------------------------
+--R                     15
+--R                                                     Type: Expression Integer
+--E
+
+--S 39     14:192 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.193~~~~~$\displaystyle
@@ -284,7 +584,7 @@ $$
 <<*>>=
 )clear all
 
---S 12 of 28
+--S 40
 aa:=integrate(sqrt(x^2+a^2)/x,x)
 --R 
 --R
@@ -302,6 +602,33 @@ aa:=integrate(sqrt(x^2+a^2)/x,x)
 --R     \|x  + a   - x
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 41
+bb:=sqrt(x^2+a^2)-a*log((a+sqrt(x^2+a^2))/x)
+--R
+--R                 +-------+
+--R                 | 2    2          +-------+
+--R                \|x  + a   + a     | 2    2
+--R   (2)  - a log(--------------) + \|x  + a
+--R                       x
+--R                                                     Type: Expression Integer
+--E
+
+--S 42     14:193 Axiom cannot simplify this expression
+cc:=aa-bb
+--R
+--R   (3)
+--R              +-------+                   +-------+
+--R              | 2    2                    | 2    2
+--R     - a log(\|x  + a   - x + a) + a log(\|x  + a   - x - a)
+--R   + 
+--R            +-------+
+--R            | 2    2
+--R           \|x  + a   + a
+--R     a log(--------------)
+--R                  x
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.194~~~~~$\displaystyle
@@ -312,7 +639,7 @@ $$
 <<*>>=
 )clear all
 
---S 13 of 28
+--S 43
 aa:=integrate(sqrt(x^2+a^2)/x^2,x)
 --R 
 --R
@@ -325,6 +652,26 @@ aa:=integrate(sqrt(x^2+a^2)/x^2,x)
 --R                      x\|x  + a   - x
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 44
+bb:=-sqrt(x^2+a^2)/x+log(x+sqrt(x^2+a^2))
+--R
+--R               +-------+         +-------+
+--R               | 2    2          | 2    2
+--R        x log(\|x  + a   + x) - \|x  + a
+--R   (2)  ----------------------------------
+--R                         x
+--R                                                     Type: Expression Integer
+--E
+
+--S 45     14:194 Axiom cannot simplify this expression
+cc:=aa-bb
+--R
+--R               +-------+             +-------+
+--R               | 2    2              | 2    2
+--R   (3)  - log(\|x  + a   + x) - log(\|x  + a   - x) - 1
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.195~~~~~$\displaystyle
@@ -336,7 +683,7 @@ $$
 <<*>>=
 )clear all
 
---S 14 of 28
+--S 46
 aa:=integrate(sqrt(x^2+a^2)/x^3,x)
 --R 
 --R
@@ -358,6 +705,57 @@ aa:=integrate(sqrt(x^2+a^2)/x^3,x)
 --R     4a x \|x  + a   - 4a x  - 2a x
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 47
+bb:=-sqrt(x^2+a^2)/(2*x^2)-1/(2*a)*log((a+sqrt(x^2+a^2))/x)
+--R
+--R                 +-------+
+--R                 | 2    2           +-------+
+--R           2    \|x  + a   + a      | 2    2
+--R        - x log(--------------) - a\|x  + a
+--R                       x
+--R   (2)  -------------------------------------
+--R                            2
+--R                        2a x
+--R                                                     Type: Expression Integer
+--E
+
+--S 48
+cc:=aa-bb
+--R
+--R   (3)
+--R                                                              +-------+
+--R          +-------+                 +-------+                 | 2    2
+--R          | 2    2                  | 2    2                 \|x  + a   + a
+--R   - log(\|x  + a   - x + a) + log(\|x  + a   - x - a) + log(--------------)
+--R                                                                    x
+--R   -------------------------------------------------------------------------
+--R                                       2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 49
+divlog:=rule(log(a/b) == log(a) - log(b))
+--R
+--R            a
+--R   (4)  log(-) == - log(b) + log(a)
+--R            b
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 50     14:195 Axiom cannot simplify this expression
+dd:=divlog cc
+--R
+--R   (5)
+--R            +-------+             +-------+                 +-------+
+--R            | 2    2              | 2    2                  | 2    2
+--R       log(\|x  + a   + a) - log(\|x  + a   - x + a) + log(\|x  + a   - x - a)
+--R     + 
+--R       - log(x)
+--R  /
+--R     2a
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.196~~~~~$\displaystyle\int{\frac{dx}{(x^2+a^2)^{3/2}}}$}
@@ -367,7 +765,7 @@ $$
 <<*>>=
 )clear all
 
---S 15 of 28
+--S 51
 aa:=integrate(1/(x^2+a^2)^(3/2),x)
 --R 
 --R
@@ -378,6 +776,27 @@ aa:=integrate(1/(x^2+a^2)^(3/2),x)
 --R          x\|x  + a   - x  - a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 52
+bb:=x/(a^2*sqrt(x^2+a^2))
+--R
+--R              x
+--R   (2)  ------------
+--R           +-------+
+--R         2 | 2    2
+--R        a \|x  + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 53     14:196 Schaums and Axiom differ by a constant
+cc:=aa-bb
+--R
+--R         1
+--R   (3)  --
+--R         2
+--R        a
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.197~~~~~$\displaystyle
@@ -388,7 +807,7 @@ $$
 <<*>>=
 )clear all
 
---S 16 of 28
+--S 54
 aa:=integrate(x/(x^2+a^2)^(3/2),x)
 --R 
 --R
@@ -401,6 +820,25 @@ aa:=integrate(x/(x^2+a^2)^(3/2),x)
 --R        x\|x  + a   - x  - a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 55
+bb:=-1/sqrt(x^2+a^2)
+--R
+--R               1
+--R   (2)  - ----------
+--R           +-------+
+--R           | 2    2
+--R          \|x  + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 56     14:197 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
+
 @
 
 \section{\cite{1}:14.198~~~~~$\displaystyle
@@ -411,7 +849,7 @@ $$
 <<*>>=
 )clear all
 
---S 17 of 28
+--S 57
 aa:=integrate(x^2/(x^2+a^2)^(3/2),x)
 --R 
 --R
@@ -424,6 +862,28 @@ aa:=integrate(x^2/(x^2+a^2)^(3/2),x)
 --R                      x\|x  + a   - x  - a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 58
+bb:=-x/sqrt(x^2+a^2)+log(x+sqrt(x^2+a^2))
+--R
+--R         +-------+     +-------+
+--R         | 2    2      | 2    2
+--R        \|x  + a  log(\|x  + a   + x) - x
+--R   (2)  ---------------------------------
+--R                     +-------+
+--R                     | 2    2
+--R                    \|x  + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 59     14:198 Axiom cannot simplify this expression
+cc:=aa-bb
+--R
+--R               +-------+             +-------+
+--R               | 2    2              | 2    2
+--R   (3)  - log(\|x  + a   + x) - log(\|x  + a   - x) - 1
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.199~~~~~$\displaystyle
@@ -434,7 +894,7 @@ $$
 <<*>>=
 )clear all
 
---S 18 of 28
+--S 60
 aa:=integrate(x^3/(x^2+a^2)^(3/2),x)
 --R 
 --R
@@ -447,6 +907,25 @@ aa:=integrate(x^3/(x^2+a^2)^(3/2),x)
 --R              (2x  + a )\|x  + a   - 2x  - 2a x
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 61
+bb:=sqrt(x^2+a^2)+a^2/sqrt(x^2+a^2)
+--R
+--R          2     2
+--R         x  + 2a
+--R   (2)  ----------
+--R         +-------+
+--R         | 2    2
+--R        \|x  + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 62     14:199 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.200~~~~~$\displaystyle
@@ -458,7 +937,7 @@ $$
 <<*>>=
 )clear all
 
---S 19 of 28
+--S 63
 aa:=integrate(1/(x*(x^2+a^2)^(3/2)),x)
 --R 
 --R
@@ -476,6 +955,60 @@ aa:=integrate(1/(x*(x^2+a^2)^(3/2)),x)
 --R     a x\|x  + a   - a x  - a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 64
+bb:=1/(a^2*sqrt(x^2+a^2))-1/a^3*log((a+sqrt(x^2+a^2))/x)
+--R
+--R                         +-------+
+--R           +-------+     | 2    2
+--R           | 2    2     \|x  + a   + a
+--R        - \|x  + a  log(--------------) + a
+--R                               x
+--R   (2)  -----------------------------------
+--R                       +-------+
+--R                     3 | 2    2
+--R                    a \|x  + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 65
+cc:=aa-bb
+--R
+--R   (3)
+--R                                                              +-------+
+--R          +-------+                 +-------+                 | 2    2
+--R          | 2    2                  | 2    2                 \|x  + a   + a
+--R   - log(\|x  + a   - x + a) + log(\|x  + a   - x - a) + log(--------------)
+--R                                                                    x
+--R   -------------------------------------------------------------------------
+--R                                        3
+--R                                       a
+--R                                                     Type: Expression Integer
+--E
+
+--S 66
+divlog:=rule(log(a/b) == log(a) - log(b))
+--R
+--R            a
+--R   (4)  log(-) == - log(b) + log(a)
+--R            b
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 67     14:200 Axiom cannot simplify this expression
+dd:=divlog cc
+--R
+--R   (5)
+--R            +-------+             +-------+                 +-------+
+--R            | 2    2              | 2    2                  | 2    2
+--R       log(\|x  + a   + a) - log(\|x  + a   - x + a) + log(\|x  + a   - x - a)
+--R     + 
+--R       - log(x)
+--R  /
+--R      3
+--R     a
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.201~~~~~$\displaystyle
@@ -486,7 +1019,7 @@ $$
 <<*>>=
 )clear all
 
---S 20 of 28
+--S 68
 aa:=integrate(1/(x^2*(x^2+a^2)^(3/2)),x)
 --R 
 --R
@@ -497,6 +1030,28 @@ aa:=integrate(1/(x^2*(x^2+a^2)^(3/2)),x)
 --R          (2x  + a x)\|x  + a   - 2x  - 2a x
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 69
+bb:=-sqrt(x^2+a^2)/(a^4*x)-x/(a^4*sqrt(x^2+a^2))
+--R
+--R              2    2
+--R          - 2x  - a
+--R   (2)  -------------
+--R            +-------+
+--R         4  | 2    2
+--R        a x\|x  + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 70     14:201 Schaums and Axiom differ by a constant
+cc:=aa-bb
+--R
+--R           2
+--R   (3)  - --
+--R           4
+--R          a
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.202~~~~~$\displaystyle
@@ -509,7 +1064,7 @@ $$
 <<*>>=
 )clear all
 
---S 21 of 28
+--S 71
 aa:=integrate(1/(x^3*(x^2+a^2)^(3/2)),x)
 --R 
 --R
@@ -535,6 +1090,62 @@ aa:=integrate(1/(x^3*(x^2+a^2)^(3/2)),x)
 --R     (8a x  + 6a x )\|x  + a   - 8a x  - 10a x  - 2a x
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 72
+bb:=-1/(2*a^2*x^2*sqrt(x^2+a^2))-3/(2*a^4*sqrt(x^2+a^2))+3/(2*a^5)*log((a+sqrt(x^2+a^2))/x)
+--R
+--R                          +-------+
+--R            +-------+     | 2    2
+--R          2 | 2    2     \|x  + a   + a        2    3
+--R        3x \|x  + a  log(--------------) - 3a x  - a
+--R                                x
+--R   (2)  ---------------------------------------------
+--R                             +-------+
+--R                         5 2 | 2    2
+--R                       2a x \|x  + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 73
+cc:=aa-bb
+--R
+--R   (3)
+--R                                                               +-------+
+--R         +-------+                  +-------+                  | 2    2
+--R         | 2    2                   | 2    2                  \|x  + a   + a
+--R   3log(\|x  + a   - x + a) - 3log(\|x  + a   - x - a) - 3log(--------------)
+--R                                                                     x
+--R   --------------------------------------------------------------------------
+--R                                         5
+--R                                       2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 74
+divlog:=rule(log(a/b) == log(a) - log(b))
+--R
+--R            a
+--R   (4)  log(-) == - log(b) + log(a)
+--R            b
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 75     14:202 Axiom cannot simplify this expression
+dd:=divlog cc
+--R
+--R   (5)
+--R               +-------+              +-------+
+--R               | 2    2               | 2    2
+--R       - 3log(\|x  + a   + a) + 3log(\|x  + a   - x + a)
+--R     + 
+--R               +-------+
+--R               | 2    2
+--R       - 3log(\|x  + a   - x - a) + 3log(x)
+--R  /
+--R       5
+--R     2a
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.203~~~~~$\displaystyle\int{(x^2+a^2)^{3/2}}~dx$}
@@ -545,9 +1156,8 @@ $$
 <<*>>=
 )clear all
 
---S 22 of 28
+--S 76
 aa:=integrate((x^2+a^2)^(3/2),x)
---R 
 --R
 --R   (1)
 --R                           +-------+                              +-------+
@@ -566,6 +1176,28 @@ aa:=integrate((x^2+a^2)^(3/2),x)
 --R     (64x  + 32a x)\|x  + a   - 64x  - 64a x  - 8a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 77
+bb:=(x*(x^2+a^2)^(3/2))/4+(3*a^2*x*sqrt(x^2+a^2))/8+3/8*a^4*log(x+sqrt(x^2+a^2))
+--R
+--R                +-------+                     +-------+
+--R          4     | 2    2            3     2   | 2    2
+--R        3a log(\|x  + a   + x) + (2x  + 5a x)\|x  + a
+--R   (2)  -----------------------------------------------
+--R                               8
+--R                                                     Type: Expression Integer
+--E
+
+--S 78     14:203 Axiom cannot simplify this expression
+cc:=aa-bb
+--R
+--R                  +-------+                +-------+
+--R            4     | 2    2           4     | 2    2
+--R        - 3a log(\|x  + a   + x) - 3a log(\|x  + a   - x)
+--R   (3)  -------------------------------------------------
+--R                                8
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.204~~~~~$\displaystyle\int{x(x^2+a^2)^{3/2}}~dx$}
@@ -573,7 +1205,7 @@ $$\int{x(x^2+a^2)^{3/2}}=\frac{(x^2+a^2)^{5/2}}{5}$$
 <<*>>=
 )clear all
 
---S 23 of 28
+--S 79
 aa:=integrate(x*(x^2+a^2)^(3/2),x)
 --R 
 --R
@@ -590,6 +1222,24 @@ aa:=integrate(x*(x^2+a^2)^(3/2),x)
 --R     (80x  + 60a x  + 5a )\|x  + a   - 80x  - 100a x  - 25a x
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 80
+bb:=(x^2+a^2)^(5/2)/5
+--R
+--R                          +-------+
+--R          4     2 2    4  | 2    2
+--R        (x  + 2a x  + a )\|x  + a
+--R   (2)  ---------------------------
+--R                     5
+--R                                                     Type: Expression Integer
+--E
+
+--S 81     14:204 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.205~~~~~$\displaystyle\int{x^2(x^2+a^2)^{3/2}}~dx$}
@@ -601,7 +1251,7 @@ $$
 <<*>>=
 )clear all
 
---S 24 of 28
+--S 82
 aa:=integrate(x^2*(x^2+a^2)^(3/2),x)
 --R 
 --R
@@ -629,6 +1279,28 @@ aa:=integrate(x^2*(x^2+a^2)^(3/2),x)
 --R     (1536x  + 1536a x  + 288a x)\|x  + a   - 1536x  - 2304a x  - 864a x  - 48a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 83
+bb:=(x*(x^2+a^2)^(5/2))/6-(a^2*x*(x^2+a^2)^(3/2))/24-(a^4*x*sqrt(x^2+a^2))/16-a^6/16*log(x+sqrt(x^2+a^2))
+--R
+--R                  +-------+                              +-------+
+--R            6     | 2    2            5      2 3     4   | 2    2
+--R        - 3a log(\|x  + a   + x) + (8x  + 14a x  + 3a x)\|x  + a
+--R   (2)  ----------------------------------------------------------
+--R                                    48
+--R                                                     Type: Expression Integer
+--E
+
+--S 84     14:205 Axiom cannot simplify this expression
+cc:=aa-bb
+--R
+--R               +-------+               +-------+
+--R         6     | 2    2          6     | 2    2
+--R        a log(\|x  + a   + x) + a log(\|x  + a   - x)
+--R   (3)  ---------------------------------------------
+--R                              16
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.206~~~~~$\displaystyle\int{x^3(x^2+a^2)^{3/2}}~dx$}
@@ -638,7 +1310,7 @@ $$
 <<*>>=
 )clear all
 
---S 25 of 28
+--S 85
 aa:=integrate(x^3*(x^2+a^2)^(3/2),x)
 --R 
 --R
@@ -667,6 +1339,24 @@ aa:=integrate(x^3*(x^2+a^2)^(3/2),x)
 --R       - 1960a x  - 245a x
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 86
+bb:=(x^2+a^2)^(7/2)/7-(a^2*(x^2+a^2)^(5/2))/5
+--R
+--R                                   +-------+
+--R           6     2 4    4 2     6  | 2    2
+--R        (5x  + 8a x  + a x  - 2a )\|x  + a
+--R   (2)  ------------------------------------
+--R                         35
+--R                                                     Type: Expression Integer
+--E
+
+--S 87     14:206 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.207~~~~~$\displaystyle
@@ -678,7 +1368,7 @@ $$
 <<*>>=
 )clear all
 
---S 26 of 28
+--S 88
 aa:=integrate((x^2+a^2)^(3/2)/x,x)
 --R 
 --R
@@ -700,6 +1390,58 @@ aa:=integrate((x^2+a^2)^(3/2)/x,x)
 --R     (12x  + 3a )\|x  + a   - 12x  - 9a x
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 89
+bb:=(x^2+a^2)^(3/2)/3+a^2*sqrt(x^2+a^2)-a^3*log((a+sqrt(x^2+a^2))/x)
+--R
+--R                  +-------+
+--R                  | 2    2                    +-------+
+--R            3    \|x  + a   + a      2     2  | 2    2
+--R        - 3a log(--------------) + (x  + 4a )\|x  + a
+--R                        x
+--R   (2)  -----------------------------------------------
+--R                               3
+--R                                                     Type: Expression Integer
+--E
+
+--S 90
+cc:=aa-bb
+--R
+--R   (3)
+--R              +-------+                   +-------+
+--R        3     | 2    2              3     | 2    2
+--R     - a log(\|x  + a   - x + a) + a log(\|x  + a   - x - a)
+--R   + 
+--R            +-------+
+--R            | 2    2
+--R      3    \|x  + a   + a
+--R     a log(--------------)
+--R                  x
+--R                                                     Type: Expression Integer
+--E
+
+--S 91
+divlog:=rule(log(a/b) == log(a) - log(b))
+--R
+--R            a
+--R   (4)  log(-) == - log(b) + log(a)
+--R            b
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 92     14:207 Axiom cannot simplify this expression
+dd:=divlog cc
+--R
+--R   (5)
+--R            +-------+               +-------+
+--R      3     | 2    2          3     | 2    2
+--R     a log(\|x  + a   + a) - a log(\|x  + a   - x + a)
+--R   + 
+--R            +-------+
+--R      3     | 2    2              3
+--R     a log(\|x  + a   - x - a) - a log(x)
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.208~~~~~$\displaystyle
@@ -711,7 +1453,7 @@ $$
 <<*>>=
 )clear all
 
---S 27 of 28
+--S 93
 aa:=integrate((x^2+a^2)^{3/2}/x^2,x)
 --R 
 --R
@@ -729,6 +1471,28 @@ aa:=integrate((x^2+a^2)^{3/2}/x^2,x)
 --R     (8x  + 2a x)\|x  + a   - 8x  - 6a x
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 94
+bb:=-(x^2+a^2)^(3/2)/x+(3*x*sqrt(x^2+a^2))/2+3/2*a^2*log(x+sqrt(x^2+a^2))
+--R
+--R                  +-------+                   +-------+
+--R          2       | 2    2           2     2  | 2    2
+--R        3a x log(\|x  + a   + x) + (x  - 2a )\|x  + a
+--R   (2)  -----------------------------------------------
+--R                               2x
+--R                                                     Type: Expression Integer
+--E
+
+--S 95     14:208 Axiom cannot simplify this expression
+cc:=aa-bb
+--R
+--R                  +-------+                +-------+
+--R            2     | 2    2           2     | 2    2           2
+--R        - 3a log(\|x  + a   + x) - 3a log(\|x  + a   - x) - 2a
+--R   (3)  -------------------------------------------------------
+--R                                   2
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.209~~~~~$\displaystyle
@@ -740,7 +1504,7 @@ $$
 <<*>>=
 )clear all
 
---S 28 of 28
+--S 96
 aa:=integrate((x^2+a^2)^(3/2)/x^3,x)
 --R 
 --R
@@ -763,6 +1527,51 @@ aa:=integrate((x^2+a^2)^(3/2)/x^3,x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
 
+--S 97
+bb:=-(x^2+a^2)^(3/2)/(2*x^3)+3/2*sqrt(x^2+a^2)-3/2*a*log((a+sqrt(x^2+a^2))/x)
+--R
+--R                    +-------+
+--R                    | 2    2                         +-------+
+--R              3    \|x  + a   + a       3    2    2  | 2    2
+--R        - 3a x log(--------------) + (3x  - x  - a )\|x  + a
+--R                          x
+--R   (2)  ------------------------------------------------------
+--R                                    3
+--R                                  2x
+--R                                                     Type: Expression Integer
+--E
+
+--S 98     14:209 Axiom cannot simplify this expression
+cc:=aa-bb
+--R
+--R   (3)
+--R                           +-------+                       +-------+
+--R                5     3 3  | 2    2         6     3 4      | 2    2
+--R       ((- 12a x  - 3a x )\|x  + a   + 12a x  + 9a x )log(\|x  + a   - x + a)
+--R     + 
+--R                         +-------+                       +-------+
+--R              5     3 3  | 2    2         6     3 4      | 2    2
+--R       ((12a x  + 3a x )\|x  + a   - 12a x  - 9a x )log(\|x  + a   - x - a)
+--R     + 
+--R                                                         +-------+
+--R                         +-------+                       | 2    2
+--R              5     3 3  | 2    2         6     3 4     \|x  + a   + a
+--R       ((12a x  + 3a x )\|x  + a   - 12a x  - 9a x )log(--------------)
+--R                                                               x
+--R     + 
+--R                                                  +-------+
+--R          6     5     2 4     2 3     4 2     4   | 2    2      7     6     2 5
+--R       (4x  - 4x  + 7a x  - 7a x  + 3a x  - 3a x)\|x  + a   - 4x  + 4x  - 9a x
+--R     + 
+--R         2 4     4 3     4 2    6     6
+--R       9a x  - 6a x  + 6a x  - a x + a
+--R  /
+--R                   +-------+
+--R        5     2 3  | 2    2      6     2 4
+--R     (8x  + 2a x )\|x  + a   - 8x  - 6a x
+--R                                                     Type: Expression Integer
+--E
+
 )spool
 )lisp (bye)
 @



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Subject: [Axiom-developer] 20080418.01.tpd.patch (CATS Schaums-Axiom
	equivalence testing (1-11))
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This patch revises several old files where it was claimed that Axiom 
could not factor the results. As Shakespeare once said (but never 
wrote down), "The fault, Dear Brutus, is not in our software but 
in ourselves". Now that I'm a tad wiser about simplification in Axiom
I was able to simplify most of the results.

Also of interest, I believe that there is a typo in the Schaums book
for problem 14:91. Axiom cannot simplify this expression. It appears
that the trailing sqrt factor should be 
   sqrt((a*x+b)^3)
not 
   sqrt((a+b*x)^3)
For more information look at schaum2.input.pamphlet,--S 56 where I
factor the numerator of the Axiom result. Note that I'm using the
Schaums book published in 1968.

Other than 14:91, where Axiom could compute the integral, the results
to date have agreed with Schaums to within a constant of integration.


schaum11.input.pamphlet is new work. The other changes are rework
of prior results.

The new cumulative results are:

schaum1.input.pamphet
  14:59 Schaums and Axiom agree
  14:60 Schaums and Axiom agree
  14:61 Schaums and Axiom differ by a constant
  14:62 Schaums and Axiom differ by a constant
  14:63 Schaums and Axiom agree
  14:64 Schaums and Axiom agree
  14:65 Schaums and Axiom agree
  14:66 Schaums and Axiom agree
  14:67 Schaums and Axiom agree
  14:68 Schaums and Axiom differ by a constant
  14:69 Schaums and Axiom differ by a constant
  14:70 Schaums and Axiom agree
  14:71 Schaums and Axiom agree
  14:72 Schaums and Axiom differ by a constant
  14:73 Schaums and Axiom differ by a constant
  14:74 Schaums and Axiom agree
  14:75 Schaums and Axiom agree
  14:76 Schaums and Axiom agree
  14:77 Schaums and Axiom differ by a constant
  14:78 Schaums and Axiom agree
  14:79 Schaums and Axiom agree
  14:80 Schaums and Axiom agree
  14:82 Schaums and Axiom agree
  14:83 Axiom cannot do this integration

schaum2.input.pamphet
  14:84 Schaums and Axiom agree
  14:85 Schaums and Axiom agree
  14:86 Schaums and Axiom agree
  14:87a Schaums and Axiom differ by a constant
  14:87b Schaums and Axiom differ by a constant
  14:88 Schaums and Axiom differ by a constant
  14:89 Schaums and Axiom differ by a constant
  14:90 Schaums and Axiom agree
  14:91 Axiom cannot simplify this expression. Schaums typo?
  14:92 Axiom cannot simplify this expression
  14:93 Schaums and Axiom agree
  14:94 Axiom cannot do this integral
  14:95 Axiom cannot do this integral
  14:96 Axiom cannot do this integral
  14:97 Axiom cannot do this integral
  14:98 Axiom cannot do this integral
  14:99 Schaums and Axiom agree
  14:100 Schaums and Axiom agree
  14:101 Schaums and Axiom agree
  14:102 Axiom cannot do this integral
  14:103 Axiom cannot do this integral
  14:104 Axiom cannot do this integral

schaum3.input.pamphet
  14:105 Schaums and Axiom agree
  14:106 Schaums and Axiom agree
  14:107 Schaums and Axiom agree
  14:108 Schaums and Axiom agree
  14:109 Schaums and Axiom agree
  14:110 Axiom cannot do this integral
  14:111 Schaums and Axiom agree
  14:112 Axiom cannot do this integral

schaum4.input.pamphet
  14:113 Schaums and Axiom agree
  14:114 Axiom cannot simplify these answers
  14:115 Axiom cannot simplify these answers
  14:116 Axiom cannot compute this integral
  14:117 Axiom cannot compute this integral
  14:118 Axiom cannot compute this integral
  14:119 Axiom cannot compute this integral

schaum5.input.pamphet
  14:120 Axiom cannot simplify these answers
  14:121 Axiom cannot simplify this answer
  14:122 Axiom cannot simplify this answer
  14:123 Axiom cannot simplify these results
  14:124 Axiom cannot simplify this result

schaum6.input.pamphet
  14:125 Schaums and Axiom agree
  14:126 Schaums and Axiom agree
  14:127 Schaums and Axiom agree
  14:128 Schaums and Axiom agree
  14:129 Schaums and Axiom agree
  14:130 Schaums and Axiom agree
  14:131 Schaums and Axiom agree
  14:132 Schaums and Axiom agree
  14:133 Schaums and Axiom agree
  14:134 Schaums and Axiom differ by a constant
  14:135 Schaums and Axiom agree
  14:136 Schaums and Axiom agree
  14:137 Schaums and Axiom agree
  14:138 Schaums and Axiom agree
  14:139 Axiom cannot do this integral
  14:140 Schaums and Axiom agree
  14:141 Axiom cannot do this integral
  14:142 Axiom cannot do this integral
  14:143 Axiom cannot do this integral

schaum7.input.pamphet
  14:144 Schaums and Axiom agree
  14:145 Schaums and Axiom agree
  14:146 Schaums and Axiom agree
  14:147 Schaums and Axiom agree
  14:148 Schaums and Axiom agree
  14:149 Schaums and Axiom agree
  14:150 Schaums and Axiom agree
  14:151 Schaums and Axiom agree
  14:152 Schaums and Axiom agree
  14:153 Schaums and Axiom agree
  14:154 Schaums and Axiom agree
  14:155 Schaums and Axiom agree
  14:156 Schaums and Axiom agree
  14:157 Schaums and Axiom agree
  14:158 Axiom cannot do this integral
  14:159 Schaums and Axiom agree
  14:160 Axiom cannot compute this integral
  14:161 Axiom cannot compute this integral
  14:162 Axiom cannot compute this integral

schaum8.input.pamphet
  14:163 Schaums and Axiom differ by a constant
  14:164 Schaums and Axiom differ by a constant
  14:165 Schaums and Axiom differ by a constant
  14:166 Schaums and Axiom differ by a constant
  14:167 Schaums and Axiom differ by a constant
  14:168 Schaums and Axiom differ by a constant
  14:169 Schaums and Axiom differ by a constant
  14:170 Schaums and Axiom differ by a constant
  14:171 Schaums and Axiom agree
  14:172 Schaums and Axiom differ by a constant
  14:173 Schaums and Axiom differ by a constant
  14:174 Schaums and Axiom differ by a constant
  14:175 Schaums and Axiom differ by a constant
  14:176 Schaums and Axiom differ by a constant
  14:177 Axiom cannot do this integration
  14:178 Schaums and Axiom agree
  14:179 Axiom cannot integrate this expression
  14:180 Axiom cannot integrate this expression
  14:181 Axiom cannot integrate this expression

schaum9.input.pamphet
  14:182 Schaums and Axiom differ by a constant
  14:183 Schaums and Axiom agree
  14:184 Schaums and Axiom differ by a constant
  14:185 Schaums and Axiom agree
  14:186 Schaums and Axiom differ by a constant
  14:187 Schaums and Axiom differ by a constant
  14:188 Schaums and Axiom differ by a constant
  14:189 Schaums and Axiom differ by a constant
  14:190 Schaums and Axiom agree
  14:191 Schaums and Axiom differ by a constant
  14:192 Schaums and Axiom agree
  14:193 Schaums and Axiom differ by a constant
  14:194 Schaums and Axiom differ by a constant
  14:195 Schaums and Axiom differ by a constant
  14:196 Schaums and Axiom differ by a constant
  14:197 Schaums and Axiom agree
  14:198 Schaums and Axiom differ by a constant
  14:199 Schaums and Axiom agree
  14:200 Schaums and Axiom differ by a constant
  14:201 Schaums and Axiom differ by a constant
  14:202 Schaums and Axiom differ by a constant
  14:203 Schaums and Axiom differ by a constant
  14:204 Schaums and Axiom agree
  14:205 Schaums and Axiom differ by a constant
  14:206 Schaums and Axiom agree
  14:207 Schaums and Axiom differ by a constant
  14:208 Schaums and Axiom differ by a constant
  14:209 Schaums and Axiom differ by a constant

schaum10.input.pamphet
  14:210 Schaums and Axiom differ by a constant
  14:xxx Schaums and Axiom agree
  14:211 Schaums and Axiom differ by a constant
  14:212 Schaums and Axiom agree
  14:213 Schaums and Axiom differ by a constant
  14:214 Schaums and Axiom differ by a constant
  14:215 Schaums and Axiom differ by a constant
  14:216 Schaums and Axiom differ by a constant 
  14:217 Schaums and Axiom agree
  14:218 Schaums and Axiom differ by a constant
  14:219 Schaums and Axiom agree
  14:220 Schaums and Axiom differ by a constant
  14:221 Schaums and Axiom differ by a constant
  14:222 Schaums and Axiom differ by a constant
  14:223 Schaums and Axiom differ by a constant
  14:224 Schaums and Axiom agree
  14:225 Schaums and Axiom differ by a constant
  14:226 Schaums and Axiom agree
  14:227 Schaums and Axiom differ by a constant
  14:228 Schaums and Axiom differ by a constant
  14:229 Schaums and Axiom differ by a constant
  14:230 Schaums and Axiom differ by a constant
  14:231 Schaums and Axiom agree
  14:232 Schaums and Axiom differ by a constant
  14:233 Schaums and Axiom agree
  14:234 Schaums and Axiom differ by a constant
  14:235 Schaums and Axiom differ by a constant
  14:236 Schaums and Axiom differ by a constant

schaum11.input.pamphet
  14:238 Schaums and Axiom agree
  14:238 Schaums and Axiom differ by a constant
  14:239 Schaums and Axiom agree
  14:240 Schaums and Axiom differ by a constant
  14:241 Schaums and Axiom differ by a constant
  14:242 Schaums and Axiom agree
  14:243 Schaums and Axiom differ by a constant
  14:244 Schaums and Axiom agree
  14:245 Schaums and Axiom differ by a constant
  14:246 Schaums and Axiom agree
  14:247 Schaums and Axiom differ by a constant
  14:248 Schaums and Axiom differ by a constant
  14:249 Schaums and Axiom agree
  14:250 Schaums and Axiom differ by a constant
  14:251 Schaums and Axiom agree
  14:252 Schaums and Axiom differ by a constant
  14:253 Schaums and Axiom agree
  14:254 Schaums and Axiom differ by a constant
  14:255 Schaums and Axiom differ by a constant
  14:256 Schaums and Axiom agree
  14:257 Schaums and Axiom differ by a constant
  14:258 Schaums and Axiom agree
  14:259 Schaums and Axiom differ by a constant
  14:260 Schaums and Axiom agree
  14:261 Schaums and Axiom differ by a constant
  14:262 Schaums and Axiom differ by a constant
  14:263 Schaums and Axiom agree
  14:264 Schaums and Axiom differ by a constant


=========================================================================
diff --git a/changelog b/changelog
index 502aa1e..c10550c 100644
--- a/changelog
+++ b/changelog
@@ -1,3 +1,11 @@
+20080418 tpd src/input/schaum11.input show Schaums-Axiom equivalence
+20080418 tpd src/input/schaum10.input fix Schaums-Axiom equivalence
+20080418 tpd src/input/schaum9.input fix Schaums-Axiom equivalence
+20080418 tpd src/input/schaum8.input fix Schaums-Axiom equivalence
+20080418 tpd src/input/schaum7.input fix Schaums-Axiom equivalence
+20080418 tpd src/input/schaum6.input fix Schaums-Axiom equivalence
+20080418 tpd src/input/schaum2.input fix Schaums-Axiom equivalence
+20080418 tpd src/input/schaum1.input fix Schaums-Axiom equivalence
 20080417 tpd src/input/schaum10.input show Schaums-Axiom equivalence
 20080417 tpd src/input/schaum9.input show Schaums-Axiom equivalence
 20080417 tpd src/input/schaum8.input show Schaums-Axiom equivalence
diff --git a/src/input/schaum1.input.pamphlet b/src/input/schaum1.input.pamphlet
index 7e7e8c4..615d907 100644
--- a/src/input/schaum1.input.pamphlet
+++ b/src/input/schaum1.input.pamphlet
@@ -1201,7 +1201,7 @@ explog:=rule(%e^(n*log(x)) == x^n)
 --R                        Type: RewriteRule(Integer,Integer,Expression Integer)
 --E
 
---S 94     14:80 Schaums and Axiom agree
+--S 94
 dd:=explog cc
 --R
 --R                   n + 1                     n
@@ -1210,8 +1210,14 @@ dd:=explog cc
 --R                        a n + a
 --R                                                     Type: Expression Integer
 --E
+
+--S 95     14:80 Schaums and Axiom agree
+ee:=complexNormalize dd
+--R
+--R   (6)  0
+--R                                                     Type: Expression Integer
+--E
 @
-The numerator is clearly zero but I cannot get Axiom to simplify it.
 
 \section{\cite{1}:14.81~~~~~$\displaystyle
 \int{x(ax+b)^n~dx}$}
@@ -1221,7 +1227,7 @@ $$\int{x(ax+b)^n}=
 $$
 <<*>>=
 )clear all
---S 95
+--S 96
 aa:=integrate(x*(a*x+b)^n,x)
 --R
 --R           2     2  2              2   n log(a x + b)
@@ -1232,7 +1238,7 @@ aa:=integrate(x*(a*x+b)^n,x)
 --R                                          Type: Union(Expression Integer,...)
 --E
 
---S 96
+--S 97
 bb:=((a*x+b)^(n+2))/((n+2)*a^2)-(b*(a*x+b)^(n+1))/((n+1)*a^2)
 --R
 --R                        n + 2                        n + 1
@@ -1243,7 +1249,7 @@ bb:=((a*x+b)^(n+2))/((n+2)*a^2)-(b*(a*x+b)^(n+1))/((n+1)*a^2)
 --R                                                     Type: Expression Integer
 --E
 
---S 97
+--S 98
 cc:=aa-bb
 --R
 --R   (3)
@@ -1258,7 +1264,7 @@ cc:=aa-bb
 --R                                                     Type: Expression Integer
 --E
 
---S 98
+--S 99
 explog:=rule(%e^(n*log(x)) == x^n)
 --R
 --R          n log(x)     n
@@ -1266,7 +1272,7 @@ explog:=rule(%e^(n*log(x)) == x^n)
 --R                        Type: RewriteRule(Integer,Integer,Expression Integer)
 --E
 
---S 99     14:81 Schaums and Axiom agreement cannot be determined
+--S 100
 dd:=explog cc
 --R
 --R   (5)
@@ -1280,6 +1286,13 @@ dd:=explog cc
 --R     a n  + 3a n + 2a
 --R                                                     Type: Expression Integer
 --E
+
+--S 101
+ee:=complexNormalize dd
+--R
+--R   (6)  0
+--R                                                     Type: Expression Integer
+--E
 @
 \section{\cite{1}:14.82~~~~~$\displaystyle
 \int{x^2(ax+b)^n~dx}$}
@@ -1292,7 +1305,7 @@ $$
 
 <<*>>=
 )clear all
---S 100
+--S 102
 aa:=integrate(x^2*(a*x+b)^n,x)
 --R
 --R   (1)
@@ -1304,7 +1317,7 @@ aa:=integrate(x^2*(a*x+b)^n,x)
 --R                                          Type: Union(Expression Integer,...)
 --E
 
---S 101
+--S 103
 bb:=(a*x+b)^(n+3)/((n+3)*a^3)-(2*b*(a*x+b)^(n+2))/((n+2)*a^3)+(b^2*(a*x+b)^(n+1))/((n+1)*a^3)
 --R
 --R   (2)
@@ -1319,7 +1332,7 @@ bb:=(a*x+b)^(n+3)/((n+3)*a^3)-(2*b*(a*x+b)^(n+2))/((n+2)*a^3)+(b^2*(a*x+b)^(n+1)
 --R                                                     Type: Expression Integer
 --E
 
---S 102    14:82 Schaums and Axiom agreement cannot be determined
+--S 104
 cc:=aa-bb
 --R
 --R   (3)
@@ -1339,6 +1352,39 @@ cc:=aa-bb
 --R     a n  + 6a n  + 11a n + 6a
 --R                                                     Type: Expression Integer
 --E
+
+--S 105
+explog:=rule(%e^(n*log(x)) == x^n)
+--R
+--R          n log(x)     n
+--R   (4)  %e         == x
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 106
+dd:=explog cc
+--R
+--R   (5)
+--R           2                   n + 3        2                      n + 2
+--R       (- n  - 3n - 2)(a x + b)      + (2b n  + 8b n + 6b)(a x + b)
+--R     + 
+--R           2 2     2      2          n + 1
+--R       (- b n  - 5b n - 6b )(a x + b)
+--R     + 
+--R          3 2     3      3  3     2   2    2     2       2        3          n
+--R       ((a n  + 3a n + 2a )x  + (a b n  + a b n)x  - 2a b n x + 2b )(a x + b)
+--R  /
+--R      3 3     3 2      3      3
+--R     a n  + 6a n  + 11a n + 6a
+--R                                                     Type: Expression Integer
+--E
+
+--S 107    14:82 Schaums and Axiom agree
+ee:=complexNormalize dd
+--R
+--R   (6)  0
+--R                                                     Type: Expression Integer
+--E
 @
 \section{\cite{1}:14.83~~~~~$\displaystyle
 \int{x^m(ax+b)^n}~dx$}
@@ -1361,7 +1407,7 @@ $$\int{x^m(ax+b)^n}
 $$
 
 <<*>>=
---S 103    14:83 Axiom cannot do this integration
+--S 108    14:83 Axiom cannot do this integration
 aa:=integrate(x^m*(a*x+b)^n,x)
 --R
 --R           x
diff --git a/src/input/schaum10.input.pamphlet b/src/input/schaum10.input.pamphlet
index d0ba7d9..6149cc0 100644
--- a/src/input/schaum10.input.pamphlet
+++ b/src/input/schaum10.input.pamphlet
@@ -133,7 +133,7 @@ bb:=(x*sqrt(x^2-a^2))/2+a^2/2*log(x+sqrt(x^2-a^2))
 --R                                                     Type: Expression Integer
 --E
 
---S 11     14:211 Axiom cannot simplify this expression
+--S 11     
 cc:=aa-bb
 --R
 --R                 +-------+               +-------+
@@ -144,6 +144,16 @@ cc:=aa-bb
 --R                                                     Type: Expression Integer
 --E
 
+--S 12     14:211 Schaums and Axiom differ by a constant
+dd:=complexNormalize cc
+--R
+--R           2       2
+--R          a log(- a )
+--R   (4)  - -----------
+--R               2
+--R                                                     Type: Expression Integer
+--E
+
 @
 
 \section{\cite{1}:14.212~~~~~$\displaystyle
@@ -154,7 +164,7 @@ $$
 <<*>>=
 )clear all
 
---S 12
+--S 13
 aa:=integrate(x^3/sqrt(x^2-a^2),x)
 --R 
 --R
@@ -168,7 +178,7 @@ aa:=integrate(x^3/sqrt(x^2-a^2),x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
 
---S 13
+--S 14
 bb:=(x^2-a^2)^(3/2)/3+a^2*sqrt(x^2-a^2)
 --R
 --R                   +-------+
@@ -179,7 +189,7 @@ bb:=(x^2-a^2)^(3/2)/3+a^2*sqrt(x^2-a^2)
 --R                                                     Type: Expression Integer
 --E
 
---S 14     14:212 Schaums and Axiom agree
+--S 15     14:212 Schaums and Axiom agree
 cc:=aa-bb
 --R
 --R   (3)  0
@@ -194,7 +204,7 @@ $$
 <<*>>=
 )clear all
 
---S 15
+--S 16
 aa:=integrate(1/(x*sqrt(x^2-a^2)),x)
 --R 
 --R
@@ -208,29 +218,134 @@ aa:=integrate(1/(x*sqrt(x^2-a^2)),x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
 
---S 16
-bb:=1/a*asec(abs(x/a))
+--S 17
+bb:=1/a*asec(x/a)
 --R
---R                 x
---R        asec(abs(-))
---R                 a
---R   (2)  ------------
---R              a
+--R             x
+--R        asec(-)
+--R             a
+--R   (2)  -------
+--R           a
 --R                                                     Type: Expression Integer
 --E
 
---S 17     14:213 Axiom cannot simplify this expression
+--S 18
 cc:=aa-bb
 --R
 --R               +-------+
 --R               | 2    2
---R              \|x  - a   - x             x
---R        2atan(--------------) - asec(abs(-))
---R                     a                   a
---R   (3)  ------------------------------------
---R                          a
+--R              \|x  - a   - x         x
+--R        2atan(--------------) - asec(-)
+--R                     a               a
+--R   (3)  -------------------------------
+--R                       a
 --R                                                     Type: Expression Integer
 --E
+
+--S 19
+asecrule:=rule(asec(x) == 1/2*%pi+%i*log(sqrt(1-1/x^2)+%i/x))
+--R
+--R                             +------+
+--R                             | 2
+--R                             |x  - 1
+--R                           x |------  + %i
+--R                             |   2
+--R                            \|  x
+--R                   2%i log(---------------) + %pi
+--R                                  x
+--R   (4)  asec(x) == ------------------------------
+--R                                  2
+--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
+--E
+
+--S 20
+dd:=asecrule cc
+--R
+--R                    +-------+
+--R                    | 2    2
+--R                    |x  - a
+--R                  x |-------  + %i a           +-------+
+--R                    |    2                     | 2    2
+--R                   \|   x                     \|x  - a   - x
+--R        - 2%i log(------------------) + 4atan(--------------) - %pi
+--R                           x                         a
+--R   (5)  -----------------------------------------------------------
+--R                                     2a
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 21
+atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
+--R
+--R                            - x + %i
+--R                     %i log(--------)
+--R                             x + %i
+--R   (6)  atan(x) == - ----------------
+--R                             2
+--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
+--E
+
+--S 22
+ee:=atanrule dd
+--R
+--R                    +-------+
+--R                    | 2    2
+--R                    |x  - a
+--R                  x |-------  + %i a               +-------+
+--R                    |    2                         | 2    2
+--R                   \|   x                       - \|x  - a   + x + %i a
+--R        - 2%i log(------------------) - 2%i log(-----------------------) - %pi
+--R                           x                      +-------+
+--R                                                  | 2    2
+--R                                                 \|x  - a   - x + %i a
+--R   (7)  ----------------------------------------------------------------------
+--R                                          2a
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 23
+ff:=expandLog ee
+--R
+--R   (8)
+--R                +-------+                        +-------+
+--R                | 2    2                         | 2    2
+--R       2%i log(\|x  - a   - x + %i a) - 2%i log(\|x  - a   - x - %i a)
+--R     + 
+--R                   +-------+
+--R                   | 2    2
+--R                   |x  - a
+--R       - 2%i log(x |-------  + %i a) + 2%i log(x) - 2%i log(- 1) - %pi
+--R                   |    2
+--R                  \|   x
+--R  /
+--R     2a
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 24
+gg:=rootSimp ff
+--R
+--R   (9)
+--R                  +-------+                    +-------+
+--R                  | 2    2                     | 2    2
+--R       - 2%i log(\|x  - a   + %i a) + 2%i log(\|x  - a   - x + %i a)
+--R     + 
+--R                  +-------+
+--R                  | 2    2
+--R       - 2%i log(\|x  - a   - x - %i a) + 2%i log(x) - 2%i log(- 1) - %pi
+--R  /
+--R     2a
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 25     14:213 Schaums and Axiom differ by a constant
+hh:=complexNormalize gg
+--R
+--R           %pi
+--R   (10)  - ---
+--R            2a
+--R                                             Type: Expression Complex Integer
+--E
 @
 
 \section{\cite{1}:14.214~~~~~$\displaystyle
@@ -241,7 +356,7 @@ $$
 <<*>>=
 )clear all
 
---S 18
+--S 26
 aa:=integrate(1/(x^2*sqrt(x^2-a^2)),x)
 --R 
 --R
@@ -253,7 +368,7 @@ aa:=integrate(1/(x^2*sqrt(x^2-a^2)),x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
 
---S 19
+--S 27
 bb:=sqrt(x^2-a^2)/(a^2*x)
 --R
 --R         +-------+
@@ -265,7 +380,7 @@ bb:=sqrt(x^2-a^2)/(a^2*x)
 --R                                                     Type: Expression Integer
 --E
 
---S 20     14:214 Schaums and Axiom differ by a constant
+--S 28     14:214 Schaums and Axiom differ by a constant
 cc:=aa-bb
 --R
 --R         1
@@ -284,7 +399,7 @@ $$
 <<*>>=
 )clear all
 
---S 21
+--S 29
 aa:=integrate(1/(x^3*sqrt(x^2-a^2)),x)
 --R 
 --R
@@ -305,33 +420,143 @@ aa:=integrate(1/(x^3*sqrt(x^2-a^2)),x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
 
---S 22
-bb:=sqrt(x^2-a^2)/(2*a^2*x^2)+1/(2*a^3)*asec(abs(x/a))
+--S 30
+bb:=sqrt(x^2-a^2)/(2*a^2*x^2)+1/(2*a^3)*asec(x/a)
 --R
---R                           +-------+
---R         2         x       | 2    2
---R        x asec(abs(-)) + a\|x  - a
---R                   a
---R   (2)  ----------------------------
---R                      3 2
---R                    2a x
+--R          +-------+
+--R          | 2    2     2     x
+--R        a\|x  - a   + x asec(-)
+--R                             a
+--R   (2)  -----------------------
+--R                   3 2
+--R                 2a x
 --R                                                     Type: Expression Integer
 --E
 
---S 23     14:215 Axiom cannot simplify this expression
+--S 31
 cc:=aa-bb
+--R 
 --R
 --R               +-------+
 --R               | 2    2
---R              \|x  - a   - x             x
---R        2atan(--------------) - asec(abs(-))
---R                     a                   a
---R   (3)  ------------------------------------
---R                           3
---R                         2a
+--R              \|x  - a   - x         x
+--R        2atan(--------------) - asec(-)
+--R                     a               a
+--R   (3)  -------------------------------
+--R                        3
+--R                      2a
 --R                                                     Type: Expression Integer
 --E
 
+--S 32
+atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
+--R
+--R                            - x + %i
+--R                     %i log(--------)
+--R                             x + %i
+--R   (4)  atan(x) == - ----------------
+--R                             2
+--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
+--E
+
+--S 33
+dd:=atanrule cc
+--R
+--R                    +-------+
+--R                    | 2    2
+--R                 - \|x  - a   + x + %i a         x
+--R        - %i log(-----------------------) - asec(-)
+--R                   +-------+                     a
+--R                   | 2    2
+--R                  \|x  - a   - x + %i a
+--R   (5)  -------------------------------------------
+--R                              3
+--R                            2a
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 34
+asecrule:=rule(asec(x) == 1/2*%pi+%i*log(sqrt(1-1/x^2)+%i/x))
+--R
+--R                             +------+
+--R                             | 2
+--R                             |x  - 1
+--R                           x |------  + %i
+--R                             |   2
+--R                            \|  x
+--R                   2%i log(---------------) + %pi
+--R                                  x
+--R   (6)  asec(x) == ------------------------------
+--R                                  2
+--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
+--E
+
+--S 35
+ee:=asecrule dd
+--R
+--R                    +-------+
+--R                    | 2    2
+--R                    |x  - a
+--R                  x |-------  + %i a               +-------+
+--R                    |    2                         | 2    2
+--R                   \|   x                       - \|x  - a   + x + %i a
+--R        - 2%i log(------------------) - 2%i log(-----------------------) - %pi
+--R                           x                      +-------+
+--R                                                  | 2    2
+--R                                                 \|x  - a   - x + %i a
+--R   (7)  ----------------------------------------------------------------------
+--R                                            3
+--R                                          4a
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 36
+ff:=expandLog ee
+--R
+--R   (8)
+--R                +-------+                        +-------+
+--R                | 2    2                         | 2    2
+--R       2%i log(\|x  - a   - x + %i a) - 2%i log(\|x  - a   - x - %i a)
+--R     + 
+--R                   +-------+
+--R                   | 2    2
+--R                   |x  - a
+--R       - 2%i log(x |-------  + %i a) + 2%i log(x) - 2%i log(- 1) - %pi
+--R                   |    2
+--R                  \|   x
+--R  /
+--R       3
+--R     4a
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 37
+gg:=rootSimp ff
+--R
+--R   (9)
+--R                  +-------+                    +-------+
+--R                  | 2    2                     | 2    2
+--R       - 2%i log(\|x  - a   + %i a) + 2%i log(\|x  - a   - x + %i a)
+--R     + 
+--R                  +-------+
+--R                  | 2    2
+--R       - 2%i log(\|x  - a   - x - %i a) + 2%i log(x) - 2%i log(- 1) - %pi
+--R  /
+--R       3
+--R     4a
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 38     14:215 Schaums and Axiom differ by a constant
+hh:=complexNormalize gg
+--R
+--R           %pi
+--R   (10)  - ---
+--R             3
+--R           4a
+--R                                             Type: Expression Complex Integer
+--E
+
 @
 
 \section{\cite{1}:14.216~~~~~$\displaystyle\int{\sqrt{x^2-a^2}}~dx$}
@@ -341,7 +566,7 @@ $$
 <<*>>=
 )clear all
 
---S 24
+--S 39
 aa:=integrate(sqrt(x^2-a^2),x)
 --R 
 --R
@@ -360,7 +585,7 @@ aa:=integrate(sqrt(x^2-a^2),x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
 
---S 25
+--S 40
 bb:=(x*sqrt(x^2-a^2))/2-a^2/2*log(x+sqrt(x^2-a^2))
 --R
 --R                 +-------+          +-------+
@@ -371,7 +596,7 @@ bb:=(x*sqrt(x^2-a^2))/2-a^2/2*log(x+sqrt(x^2-a^2))
 --R                                                     Type: Expression Integer
 --E
 
---S 26     14:216 Axiom cannot simplify this expression
+--S 41
 cc:=aa-bb
 --R
 --R               +-------+               +-------+
@@ -382,6 +607,15 @@ cc:=aa-bb
 --R                                                     Type: Expression Integer
 --E
 
+--S 42     14:216 Schaums and Axiom differ by a constant 
+dd:=complexNormalize cc
+--R
+--R         2       2
+--R        a log(- a )
+--R   (4)  -----------
+--R             2
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.217~~~~~$\displaystyle\int{x\sqrt{x^2-a^2}}~dx$}
@@ -391,7 +625,7 @@ $$
 <<*>>=
 )clear all
 
---S 27
+--S 43
 aa:=integrate(x*sqrt(x^2-a^2),x)
 --R 
 --R
@@ -405,7 +639,7 @@ aa:=integrate(x*sqrt(x^2-a^2),x)
 --R                                          Type: Union(Expression Integer,...)
 --E
 
---S 28
+--S 44
 bb:=(x^2-a^2)^(3/2)/3
 --R
 --R                  +-------+
@@ -416,7 +650,7 @@ bb:=(x^2-a^2)^(3/2)/3
 --R                                                     Type: Expression Integer
 --E
 
---S 29     14:217 Schaums and Axiom agree
+--S 45     14:217 Schaums and Axiom agree
 cc:=aa-bb
 --R
 --R   (3)  0
@@ -433,7 +667,7 @@ $$
 <<*>>=
 )clear all
 
---S 30
+--S 46
 aa:=integrate(x^2*sqrt(x^2-a^2),x)
 --R 
 --R
@@ -452,7 +686,7 @@ aa:=integrate(x^2*sqrt(x^2-a^2),x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
 
---S 31
+--S 47
 bb:=(x*(x^2-a^2)^(3/2))/4+(a^2*x*sqrt(x^2-a^2))/8-a^4/8*log(x+sqrt(x^2-a^2))
 --R
 --R                 +-------+                    +-------+
@@ -463,7 +697,7 @@ bb:=(x*(x^2-a^2)^(3/2))/4+(a^2*x*sqrt(x^2-a^2))/8-a^4/8*log(x+sqrt(x^2-a^2))
 --R                                                     Type: Expression Integer
 --E
 
---S 32     14:218 Axiom cannot simplify this expression
+--S 48     
 cc:=aa-bb
 --R
 --R               +-------+               +-------+
@@ -473,6 +707,16 @@ cc:=aa-bb
 --R                              8
 --R                                                     Type: Expression Integer
 --E
+
+--S 49     14:218 Schaums and Axiom differ by a constant
+dd:=complexNormalize cc
+--R
+--R         4       2
+--R        a log(- a )
+--R   (4)  -----------
+--R             8
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.219~~~~~$\displaystyle
@@ -483,7 +727,7 @@ $$
 <<*>>=
 )clear all
 
---S 33
+--S 50
 aa:=integrate(x^3*sqrt(x^2-a^2),x)
 --R 
 --R
@@ -501,7 +745,7 @@ aa:=integrate(x^3*sqrt(x^2-a^2),x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
 
---S 34
+--S 51
 bb:=(x^2-a^2)^(5/2)/5+(a^2*(x^2-a^2)^(3/2))/3
 --R
 --R                           +-------+
@@ -512,7 +756,7 @@ bb:=(x^2-a^2)^(5/2)/5+(a^2*(x^2-a^2)^(3/2))/3
 --R                                                     Type: Expression Integer
 --E
 
---S 35     14:219 Schaums and Axiom agree
+--S 52     14:219 Schaums and Axiom agree
 cc:=aa-bb
 --R
 --R   (3)  0
@@ -528,7 +772,7 @@ $$
 <<*>>=
 )clear all
 
---S 36
+--S 53
 aa:=integrate(sqrt(x^2-a^2)/x,x)
 --R 
 --R
@@ -544,26 +788,129 @@ aa:=integrate(sqrt(x^2-a^2)/x,x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
 
---S 37
-bb:=sqrt(x^2-a^2)-a*asec(abs(x/a))
+--S 54
+bb:=sqrt(x^2-a^2)-a*asec(x/a)
 --R
---R                            +-------+
---R                     x      | 2    2
---R   (2)  - a asec(abs(-)) + \|x  - a
---R                     a
+--R         +-------+
+--R         | 2    2           x
+--R   (2)  \|x  - a   - a asec(-)
+--R                            a
 --R                                                     Type: Expression Integer
 --E
 
---S 38     14:220 Axiom cannot simplify this expression
+--S 55
 cc:=aa-bb
 --R
 --R                   +-------+
 --R                   | 2    2
---R                  \|x  - a   - x               x
---R   (3)  - 2a atan(--------------) + a asec(abs(-))
---R                         a                     a
+--R                  \|x  - a   - x           x
+--R   (3)  - 2a atan(--------------) + a asec(-)
+--R                         a                 a
 --R                                                     Type: Expression Integer
 --E
+
+--S 56
+atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
+--R
+--R                            - x + %i
+--R                     %i log(--------)
+--R                             x + %i
+--R   (4)  atan(x) == - ----------------
+--R                             2
+--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
+--E
+
+--S 57
+dd:=atanrule cc
+--R
+--R                    +-------+
+--R                    | 2    2
+--R                 - \|x  - a   + x + %i a           x
+--R   (5)  %i a log(-----------------------) + a asec(-)
+--R                   +-------+                       a
+--R                   | 2    2
+--R                  \|x  - a   - x + %i a
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 58
+asecrule:=rule(asec(x) == 1/2*%pi+%i*log(sqrt(1-1/x^2)+%i/x))
+--R
+--R                             +------+
+--R                             | 2
+--R                             |x  - 1
+--R                           x |------  + %i
+--R                             |   2
+--R                            \|  x
+--R                   2%i log(---------------) + %pi
+--R                                  x
+--R   (6)  asec(x) == ------------------------------
+--R                                  2
+--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
+--E
+
+--S 59
+ee:=asecrule dd
+--R
+--R   (7)
+--R               +-------+
+--R               | 2    2
+--R               |x  - a
+--R             x |-------  + %i a                 +-------+
+--R               |    2                           | 2    2
+--R              \|   x                         - \|x  - a   + x + %i a
+--R   2%i a log(------------------) + 2%i a log(-----------------------) + a %pi
+--R                      x                        +-------+
+--R                                               | 2    2
+--R                                              \|x  - a   - x + %i a
+--R   --------------------------------------------------------------------------
+--R                                        2
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 60
+ff:=expandLog ee
+--R
+--R   (8)
+--R                    +-------+                          +-------+
+--R                    | 2    2                           | 2    2
+--R       - 2%i a log(\|x  - a   - x + %i a) + 2%i a log(\|x  - a   - x - %i a)
+--R     + 
+--R                   +-------+
+--R                   | 2    2
+--R                   |x  - a
+--R       2%i a log(x |-------  + %i a) - 2%i a log(x) + 2%i a log(- 1) + a %pi
+--R                   |    2
+--R                  \|   x
+--R  /
+--R     2
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 61
+gg:=rootSimp ff
+--R
+--R   (9)
+--R                  +-------+                      +-------+
+--R                  | 2    2                       | 2    2
+--R       2%i a log(\|x  - a   + %i a) - 2%i a log(\|x  - a   - x + %i a)
+--R     + 
+--R                  +-------+
+--R                  | 2    2
+--R       2%i a log(\|x  - a   - x - %i a) - 2%i a log(x) + 2%i a log(- 1) + a %pi
+--R  /
+--R     2
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 62     14:220 Schaums and Axiom differ by a constant
+hh:=complexNormalize gg
+--R
+--R         a %pi
+--R   (10)  -----
+--R           2
+--R                                             Type: Expression Complex Integer
+--E
 @
 
 \section{\cite{1}:14.221~~~~~$\displaystyle
@@ -574,7 +921,7 @@ $$
 <<*>>=
 )clear all
 
---S 39
+--S 63
 aa:=integrate(sqrt(x^2-a^2)/x^2,x)
 --R 
 --R
@@ -588,7 +935,7 @@ aa:=integrate(sqrt(x^2-a^2)/x^2,x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
 
---S 40
+--S 64
 bb:=-sqrt(x^2-a^2)/x+log(x+sqrt(x^2-a^2))
 --R
 --R               +-------+         +-------+
@@ -599,7 +946,7 @@ bb:=-sqrt(x^2-a^2)/x+log(x+sqrt(x^2-a^2))
 --R                                                     Type: Expression Integer
 --E
 
---S 41     14:221 Axiom cannot simplify this expression
+--S 65
 cc:=aa-bb
 --R
 --R               +-------+             +-------+
@@ -608,6 +955,14 @@ cc:=aa-bb
 --R                                                     Type: Expression Integer
 --E
 
+--S 66     14:221 Schaums and Axiom differ by a constant
+dd:=complexNormalize cc
+--R
+--R                 2
+--R   (4)  - log(- a ) - 1
+--R                                                     Type: Expression Integer
+--E
+
 @
 
 \section{\cite{1}:14.222~~~~~$\displaystyle
@@ -619,7 +974,7 @@ $$
 <<*>>=
 )clear all
 
---S 42
+--S 67
 aa:=integrate(sqrt(x^2-a^2)/x^3,x)
 --R 
 --R
@@ -640,31 +995,136 @@ aa:=integrate(sqrt(x^2-a^2)/x^3,x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
 
---S 43
-bb:=-sqrt(x^2-a^2)/(2*x^2)+1/(2*a)*asec(abs(x/a))
+--S 68
+bb:=-sqrt(x^2-a^2)/(2*x^2)+1/(2*a)*asec(x/a)
 --R
---R                           +-------+
---R         2         x       | 2    2
---R        x asec(abs(-)) - a\|x  - a
---R                   a
---R   (2)  ----------------------------
---R                        2
---R                    2a x
+--R            +-------+
+--R            | 2    2     2     x
+--R        - a\|x  - a   + x asec(-)
+--R                               a
+--R   (2)  -------------------------
+--R                      2
+--R                  2a x
 --R                                                     Type: Expression Integer
 --E
 
---S 44     14:222 Axiom cannot simplify this expression
+--S 69
 cc:=aa-bb
 --R
 --R               +-------+
 --R               | 2    2
---R              \|x  - a   - x             x
---R        2atan(--------------) - asec(abs(-))
---R                     a                   a
---R   (3)  ------------------------------------
---R                         2a
+--R              \|x  - a   - x         x
+--R        2atan(--------------) - asec(-)
+--R                     a               a
+--R   (3)  -------------------------------
+--R                       2a
 --R                                                     Type: Expression Integer
 --E
+
+--S 70
+asecrule:=rule(asec(x) == 1/2*%pi+%i*log(sqrt(1-1/x^2)+%i/x))
+--R
+--R                             +------+
+--R                             | 2
+--R                             |x  - 1
+--R                           x |------  + %i
+--R                             |   2
+--R                            \|  x
+--R                   2%i log(---------------) + %pi
+--R                                  x
+--R   (4)  asec(x) == ------------------------------
+--R                                  2
+--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
+--E
+
+--S 71
+dd:=asecrule cc
+--R
+--R                    +-------+
+--R                    | 2    2
+--R                    |x  - a
+--R                  x |-------  + %i a           +-------+
+--R                    |    2                     | 2    2
+--R                   \|   x                     \|x  - a   - x
+--R        - 2%i log(------------------) + 4atan(--------------) - %pi
+--R                           x                         a
+--R   (5)  -----------------------------------------------------------
+--R                                     4a
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 72
+atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
+--R
+--R                            - x + %i
+--R                     %i log(--------)
+--R                             x + %i
+--R   (6)  atan(x) == - ----------------
+--R                             2
+--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
+--E
+
+--S 73
+ee:=atanrule dd
+--R
+--R                    +-------+
+--R                    | 2    2
+--R                    |x  - a
+--R                  x |-------  + %i a               +-------+
+--R                    |    2                         | 2    2
+--R                   \|   x                       - \|x  - a   + x + %i a
+--R        - 2%i log(------------------) - 2%i log(-----------------------) - %pi
+--R                           x                      +-------+
+--R                                                  | 2    2
+--R                                                 \|x  - a   - x + %i a
+--R   (7)  ----------------------------------------------------------------------
+--R                                          4a
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 74
+ff:=expandLog ee
+--R
+--R   (8)
+--R                +-------+                        +-------+
+--R                | 2    2                         | 2    2
+--R       2%i log(\|x  - a   - x + %i a) - 2%i log(\|x  - a   - x - %i a)
+--R     + 
+--R                   +-------+
+--R                   | 2    2
+--R                   |x  - a
+--R       - 2%i log(x |-------  + %i a) + 2%i log(x) - 2%i log(- 1) - %pi
+--R                   |    2
+--R                  \|   x
+--R  /
+--R     4a
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 75
+gg:=rootSimp ff
+--R
+--R   (9)
+--R                  +-------+                    +-------+
+--R                  | 2    2                     | 2    2
+--R       - 2%i log(\|x  - a   + %i a) + 2%i log(\|x  - a   - x + %i a)
+--R     + 
+--R                  +-------+
+--R                  | 2    2
+--R       - 2%i log(\|x  - a   - x - %i a) + 2%i log(x) - 2%i log(- 1) - %pi
+--R  /
+--R     4a
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 76     14:222 Schaums and Axiom differ by a constant
+hh:=complexNormalize gg
+--R
+--R           %pi
+--R   (10)  - ---
+--R            4a
+--R                                             Type: Expression Complex Integer
+--E
 @
 
 \section{\cite{1}:14.223~~~~~$\displaystyle\int{\frac{dx}{(x^2-a^2)^{3/2}}}$}
@@ -674,7 +1134,7 @@ $$
 <<*>>=
 )clear all
 
---S 45
+--S 77
 aa:=integrate(1/(x^2-a^2)^(3/2),x)
 --R 
 --R
@@ -686,7 +1146,7 @@ aa:=integrate(1/(x^2-a^2)^(3/2),x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
 
---S 46
+--S 78
 bb:=-x/(a^2*sqrt(x^2-a^2))
 --R
 --R                x
@@ -697,7 +1157,7 @@ bb:=-x/(a^2*sqrt(x^2-a^2))
 --R                                                     Type: Expression Integer
 --E
 
---S 47     14:223 Schaums and Axiom differ by a constant
+--S 79     14:223 Schaums and Axiom differ by a constant
 cc:=aa-bb
 --R
 --R           1
@@ -716,7 +1176,7 @@ $$
 <<*>>=
 )clear all
 
---S 48
+--S 80
 aa:=integrate(x/(x^2-a^2)^(3/2),x)
 --R 
 --R
@@ -730,7 +1190,7 @@ aa:=integrate(x/(x^2-a^2)^(3/2),x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
 
---S 49
+--S 81
 bb:=-1/sqrt(x^2-a^2)
 --R
 --R               1
@@ -741,7 +1201,7 @@ bb:=-1/sqrt(x^2-a^2)
 --R                                                     Type: Expression Integer
 --E
 
---S 50     14:224 Schaums and Axiom agree
+--S 82     14:224 Schaums and Axiom agree
 cc:=aa-bb
 --R
 --R   (3)  0
@@ -757,7 +1217,7 @@ $$
 <<*>>=
 )clear all
 
---S 51
+--S 83
 aa:=integrate(x^2/(x^2-a^2)^(3/2),x)
 --R 
 --R
@@ -771,7 +1231,7 @@ aa:=integrate(x^2/(x^2-a^2)^(3/2),x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
 
---S 52
+--S 84
 bb:=-x/sqrt(x^2-a^2)+log(x+sqrt(x^2-a^2))
 --R
 --R         +-------+     +-------+
@@ -784,7 +1244,7 @@ bb:=-x/sqrt(x^2-a^2)+log(x+sqrt(x^2-a^2))
 --R                                                     Type: Expression Integer
 --E
 
---S 53     14:225 Axiom cannot simplify this expression
+--S 85     
 cc:=aa-bb
 --R
 --R               +-------+             +-------+
@@ -792,6 +1252,14 @@ cc:=aa-bb
 --R   (3)  - log(\|x  - a   + x) - log(\|x  - a   - x) - 1
 --R                                                     Type: Expression Integer
 --E
+
+--S 86     14:225 Schaums and Axiom differ by a constant
+dd:=complexNormalize cc
+--R
+--R                 2
+--R   (4)  - log(- a ) - 1
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.226~~~~~$\displaystyle
@@ -802,7 +1270,7 @@ $$
 <<*>>=
 )clear all
 
---S 54
+--S 87
 aa:=integrate(x^3/(x^2-a^2)^(3/2),x)
 --R 
 --R
@@ -816,7 +1284,7 @@ aa:=integrate(x^3/(x^2-a^2)^(3/2),x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
 
---S 55
+--S 88
 bb:=sqrt(x^2-a^2)-a^2/sqrt(x^2-a^2)
 --R
 --R          2     2
@@ -828,7 +1296,7 @@ bb:=sqrt(x^2-a^2)-a^2/sqrt(x^2-a^2)
 --R                                                     Type: Expression Integer
 --E
 
---S 56     14:226 Schaums and Axiom agree
+--S 89     14:226 Schaums and Axiom agree
 cc:=aa-bb
 --R
 --R   (3)  0
@@ -845,7 +1313,7 @@ $$
 <<*>>=
 )clear all
 
---S 57
+--S 90
 aa:=integrate(1/(x*(x^2-a^2)^(3/2)),x)
 --R 
 --R
@@ -861,33 +1329,143 @@ aa:=integrate(1/(x*(x^2-a^2)^(3/2)),x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
 
---S 58
-bb:=-1/(a^2*sqrt(x^2-a^2))-1/a^3*asec(abs(x/a))
+--S 91
+bb:=-1/(a^2*sqrt(x^2-a^2))-1/a^3*asec(x/a)
 --R
---R           +-------+
---R           | 2    2          x
---R        - \|x  - a  asec(abs(-)) - a
---R                             a
---R   (2)  ----------------------------
---R                   +-------+
---R                 3 | 2    2
---R                a \|x  - a
+--R                  +-------+
+--R               x  | 2    2
+--R        - asec(-)\|x  - a   - a
+--R               a
+--R   (2)  -----------------------
+--R                 +-------+
+--R               3 | 2    2
+--R              a \|x  - a
 --R                                                     Type: Expression Integer
 --E
 
---S 59     14:227 Axiom cannot simplify this expression
+--S 92
 cc:=aa-bb
 --R
 --R                 +-------+
 --R                 | 2    2
---R                \|x  - a   - x             x
---R        - 2atan(--------------) + asec(abs(-))
---R                       a                   a
---R   (3)  --------------------------------------
---R                           3
---R                          a
+--R                \|x  - a   - x         x
+--R        - 2atan(--------------) + asec(-)
+--R                       a               a
+--R   (3)  ---------------------------------
+--R                         3
+--R                        a
 --R                                                     Type: Expression Integer
 --E
+
+--S 93
+atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
+--R
+--R                            - x + %i
+--R                     %i log(--------)
+--R                             x + %i
+--R   (4)  atan(x) == - ----------------
+--R                             2
+--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
+--E
+
+--S 94
+dd:=atanrule cc
+--R
+--R                  +-------+
+--R                  | 2    2
+--R               - \|x  - a   + x + %i a         x
+--R        %i log(-----------------------) + asec(-)
+--R                 +-------+                     a
+--R                 | 2    2
+--R                \|x  - a   - x + %i a
+--R   (5)  -----------------------------------------
+--R                             3
+--R                            a
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 95
+asecrule:=rule(asec(x) == 1/2*%pi+%i*log(sqrt(1-1/x^2)+%i/x))
+--R
+--R                             +------+
+--R                             | 2
+--R                             |x  - 1
+--R                           x |------  + %i
+--R                             |   2
+--R                            \|  x
+--R                   2%i log(---------------) + %pi
+--R                                  x
+--R   (6)  asec(x) == ------------------------------
+--R                                  2
+--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
+--E
+
+--S 96
+ee:=asecrule dd
+--R
+--R                  +-------+
+--R                  | 2    2
+--R                  |x  - a
+--R                x |-------  + %i a               +-------+
+--R                  |    2                         | 2    2
+--R                 \|   x                       - \|x  - a   + x + %i a
+--R        2%i log(------------------) + 2%i log(-----------------------) + %pi
+--R                         x                      +-------+
+--R                                                | 2    2
+--R                                               \|x  - a   - x + %i a
+--R   (7)  --------------------------------------------------------------------
+--R                                           3
+--R                                         2a
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 97
+ff:=expandLog ee
+--R
+--R   (8)
+--R                  +-------+                        +-------+
+--R                  | 2    2                         | 2    2
+--R       - 2%i log(\|x  - a   - x + %i a) + 2%i log(\|x  - a   - x - %i a)
+--R     + 
+--R                 +-------+
+--R                 | 2    2
+--R                 |x  - a
+--R       2%i log(x |-------  + %i a) - 2%i log(x) + 2%i log(- 1) + %pi
+--R                 |    2
+--R                \|   x
+--R  /
+--R       3
+--R     2a
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 98
+gg:=rootSimp ff
+--R
+--R   (9)
+--R                +-------+                    +-------+
+--R                | 2    2                     | 2    2
+--R       2%i log(\|x  - a   + %i a) - 2%i log(\|x  - a   - x + %i a)
+--R     + 
+--R                +-------+
+--R                | 2    2
+--R       2%i log(\|x  - a   - x - %i a) - 2%i log(x) + 2%i log(- 1) + %pi
+--R  /
+--R       3
+--R     2a
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 99     14:227 Schaums and Axiom differ by a constant
+hh:=complexNormalize gg
+--R
+--R         %pi
+--R   (10)  ---
+--R           3
+--R         2a
+--R                                             Type: Expression Complex Integer
+--E
+
 @
 
 \section{\cite{1}:14.228~~~~~$\displaystyle
@@ -898,7 +1476,7 @@ $$
 <<*>>=
 )clear all
 
---S 60
+--S 100
 aa:=integrate(1/(x^2*(x^2-a^2)^(3/2)),x)
 --R 
 --R
@@ -910,7 +1488,7 @@ aa:=integrate(1/(x^2*(x^2-a^2)^(3/2)),x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
 
---S 61
+--S 101
 bb:=-sqrt(x^2-a^2)/(a^4*x)-x/(a^4*sqrt(x^2-a^2))
 --R
 --R              2    2
@@ -922,7 +1500,7 @@ bb:=-sqrt(x^2-a^2)/(a^4*x)-x/(a^4*sqrt(x^2-a^2))
 --R                                                     Type: Expression Integer
 --E
 
---S 62     14:228 Schaums and Axiom differ by a constant
+--S 102    14:228 Schaums and Axiom differ by a constant
 cc:=aa-bb
 --R
 --R           2
@@ -944,7 +1522,7 @@ $$
 <<*>>=
 )clear all
 
---S 63
+--S 103
 aa:=integrate(1/(x^3*(x^2-a^2)^(3/2)),x)
 --R 
 --R
@@ -965,35 +1543,143 @@ aa:=integrate(1/(x^3*(x^2-a^2)^(3/2)),x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
 
---S 64
-bb:=1/(2*a^2*x^2*sqrt(x^2-a^2))-3/(2*a^4*sqrt(x^2-a^2))-3/(2*a^5)*asec(abs(x/a))
+--S 104
+bb:=1/(2*a^2*x^2*sqrt(x^2-a^2))-3/(2*a^4*sqrt(x^2-a^2))-3/(2*a^5)*asec(x/a)
 --R
---R              +-------+
---R            2 | 2    2          x         2    3
---R        - 3x \|x  - a  asec(abs(-)) - 3a x  + a
---R                                a
---R   (2)  ----------------------------------------
---R                           +-------+
---R                       5 2 | 2    2
---R                     2a x \|x  - a
+--R                     +-------+
+--R            2     x  | 2    2        2    3
+--R        - 3x asec(-)\|x  - a   - 3a x  + a
+--R                  a
+--R   (2)  -----------------------------------
+--R                        +-------+
+--R                    5 2 | 2    2
+--R                  2a x \|x  - a
 --R                                                     Type: Expression Integer
 --E
 
---S 65     14:229 Axiom cannot simplify this expression
+--S 105
 cc:=aa-bb
 --R
 --R                 +-------+
 --R                 | 2    2
---R                \|x  - a   - x              x
---R        - 6atan(--------------) + 3asec(abs(-))
---R                       a                    a
---R   (3)  ---------------------------------------
---R                            5
---R                          2a
+--R                \|x  - a   - x          x
+--R        - 6atan(--------------) + 3asec(-)
+--R                       a                a
+--R   (3)  ----------------------------------
+--R                          5
+--R                        2a
 --R                                                     Type: Expression Integer
 --E
-@
 
+--S 106
+atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
+--R
+--R                            - x + %i
+--R                     %i log(--------)
+--R                             x + %i
+--R   (4)  atan(x) == - ----------------
+--R                             2
+--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
+--E
+
+--S 107
+dd:=atanrule cc
+--R
+--R                   +-------+
+--R                   | 2    2
+--R                - \|x  - a   + x + %i a          x
+--R        3%i log(-----------------------) + 3asec(-)
+--R                  +-------+                      a
+--R                  | 2    2
+--R                 \|x  - a   - x + %i a
+--R   (5)  -------------------------------------------
+--R                              5
+--R                            2a
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 108
+asecrule:=rule(asec(x) == 1/2*%pi+%i*log(sqrt(1-1/x^2)+%i/x))
+--R
+--R                             +------+
+--R                             | 2
+--R                             |x  - 1
+--R                           x |------  + %i
+--R                             |   2
+--R                            \|  x
+--R                   2%i log(---------------) + %pi
+--R                                  x
+--R   (6)  asec(x) == ------------------------------
+--R                                  2
+--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
+--E
+
+--S 109
+ee:=asecrule dd
+--R
+--R                  +-------+
+--R                  | 2    2
+--R                  |x  - a
+--R                x |-------  + %i a               +-------+
+--R                  |    2                         | 2    2
+--R                 \|   x                       - \|x  - a   + x + %i a
+--R        6%i log(------------------) + 6%i log(-----------------------) + 3%pi
+--R                         x                      +-------+
+--R                                                | 2    2
+--R                                               \|x  - a   - x + %i a
+--R   (7)  ---------------------------------------------------------------------
+--R                                           5
+--R                                         4a
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 110
+ff:=expandLog ee
+--R
+--R   (8)
+--R                  +-------+                        +-------+
+--R                  | 2    2                         | 2    2
+--R       - 6%i log(\|x  - a   - x + %i a) + 6%i log(\|x  - a   - x - %i a)
+--R     + 
+--R                 +-------+
+--R                 | 2    2
+--R                 |x  - a
+--R       6%i log(x |-------  + %i a) - 6%i log(x) + 6%i log(- 1) + 3%pi
+--R                 |    2
+--R                \|   x
+--R  /
+--R       5
+--R     4a
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 111
+gg:=rootSimp ff
+--R
+--R   (9)
+--R                +-------+                    +-------+
+--R                | 2    2                     | 2    2
+--R       6%i log(\|x  - a   + %i a) - 6%i log(\|x  - a   - x + %i a)
+--R     + 
+--R                +-------+
+--R                | 2    2
+--R       6%i log(\|x  - a   - x - %i a) - 6%i log(x) + 6%i log(- 1) + 3%pi
+--R  /
+--R       5
+--R     4a
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 112    14:229 Schaums and Axiom differ by a constant
+hh:=complexNormalize gg
+--R
+--R         3%pi
+--R   (10)  ----
+--R            5
+--R          4a
+--R                                             Type: Expression Complex Integer
+--E
+@
 \section{\cite{1}:14.230~~~~~$\displaystyle\int{(x^2-a^2)^{3/2}}~dx$}
 $$\int{(x^2-a^2)^{3/2}}=
 \frac{x(x^2-a^2)^{3/2}}{4}-\frac{3a^2x\sqrt{x^2-a^2}}{8}+
@@ -1002,7 +1688,7 @@ $$
 <<*>>=
 )clear all
 
---S 66
+--S 113
 aa:=integrate((x^2-a^2)^(3/2),x)
 --R 
 --R
@@ -1024,7 +1710,7 @@ aa:=integrate((x^2-a^2)^(3/2),x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
 
---S 67
+--S 114
 bb:=(x*(x^2-a^2)^(3/2))/4-(3*a^2*x*sqrt(x^2-a^2))/8+3/8*a^4*log(x+sqrt(x^2-a^2))
 --R
 --R                +-------+                     +-------+
@@ -1035,7 +1721,7 @@ bb:=(x*(x^2-a^2)^(3/2))/4-(3*a^2*x*sqrt(x^2-a^2))/8+3/8*a^4*log(x+sqrt(x^2-a^2))
 --R                                                     Type: Expression Integer
 --E
 
---S 68     14:230 Axiom cannot simplify this expression
+--S 115
 cc:=aa-bb
 --R
 --R                  +-------+                +-------+
@@ -1046,6 +1732,16 @@ cc:=aa-bb
 --R                                                     Type: Expression Integer
 --E
 
+--S 116    14:230 Schaums and Axiom differ by a constant
+dd:=complexNormalize cc
+--R
+--R            4       2
+--R          3a log(- a )
+--R   (4)  - ------------
+--R                8
+--R                                                     Type: Expression Integer
+--E
+
 @
 
 \section{\cite{1}:14.231~~~~~$\displaystyle\int{x(x^2-a^2)^{3/2}}~dx$}
@@ -1053,7 +1749,7 @@ $$\int{x(x^2-a^2)^{3/2}}=\frac{(x^2-a^2)^{5/2}}{5}$$
 <<*>>=
 )clear all
 
---S 69
+--S 117
 aa:=integrate(x*(x^2-a^2)^(3/2),x)
 --R 
 --R
@@ -1071,7 +1767,7 @@ aa:=integrate(x*(x^2-a^2)^(3/2),x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
 
---S 70
+--S 118
 bb:=(x^2-a^2)^(5/2)/5
 --R
 --R                          +-------+
@@ -1082,7 +1778,7 @@ bb:=(x^2-a^2)^(5/2)/5
 --R                                                     Type: Expression Integer
 --E
 
---S 71     14:231 Schaums and Axiom agree
+--S 119    14:231 Schaums and Axiom agree
 cc:=aa-bb
 --R
 --R   (3)  0
@@ -1099,7 +1795,7 @@ $$
 <<*>>=
 )clear all
 
---S 72
+--S 120
 aa:=integrate(x^2*(x^2-a^2)^(3/2),x)
 --R 
 --R
@@ -1128,7 +1824,7 @@ aa:=integrate(x^2*(x^2-a^2)^(3/2),x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
 
---S 73
+--S 121
 bb:=(x*(x^2-a^2)^(5/2))/6+(a^2*x*(x^2-a^2)^(3/2))/24-(a^4*x*sqrt(x^2-a^2))/16+a^6/16*log(x+sqrt(x^2-a^2))
 --R
 --R                +-------+                              +-------+
@@ -1139,7 +1835,7 @@ bb:=(x*(x^2-a^2)^(5/2))/6+(a^2*x*(x^2-a^2)^(3/2))/24-(a^4*x*sqrt(x^2-a^2))/16+a^
 --R                                                     Type: Expression Integer
 --E
 
---S 74     14:232 Axiom cannot simplify this expression
+--S 122
 cc:=aa-bb
 --R
 --R                 +-------+               +-------+
@@ -1149,6 +1845,16 @@ cc:=aa-bb
 --R                               16
 --R                                                     Type: Expression Integer
 --E
+
+--S 123    14:232 Schaums and Axiom differ by a constant
+dd:=complexNormalize cc
+--R
+--R           6       2
+--R          a log(- a )
+--R   (4)  - -----------
+--R               16
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.233~~~~~$\displaystyle\int{x^3(x^2-a^2)^{3/2}}~dx$}
@@ -1158,7 +1864,7 @@ $$
 <<*>>=
 )clear all
 
---S 75
+--S 124
 aa:=integrate(x^3*(x^2-a^2)^(3/2),x)
 --R 
 --R
@@ -1188,7 +1894,7 @@ aa:=integrate(x^3*(x^2-a^2)^(3/2),x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
 
---S 76
+--S 125
 bb:=(x^2-a^2)^(7/2)/7+(a^2*(x^2-a^2)^(5/2))/5
 --R
 --R                                   +-------+
@@ -1199,7 +1905,7 @@ bb:=(x^2-a^2)^(7/2)/7+(a^2*(x^2-a^2)^(5/2))/5
 --R                                                     Type: Expression Integer
 --E
 
---S 77     14:233 Schaums and Axiom agree
+--S 126    14:233 Schaums and Axiom agree
 cc:=aa-bb
 --R
 --R   (3)  0
@@ -1216,7 +1922,7 @@ $$
 <<*>>=
 )clear all
 
---S 78
+--S 127
 aa:=integrate((x^2-a^2)^(3/2)/x,x)
 --R 
 --R
@@ -1237,28 +1943,135 @@ aa:=integrate((x^2-a^2)^(3/2)/x,x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
 
---S 79
-bb:=(x^2-a^2)^(3/2)/3-a^2*sqrt(x^2-a^2)+a^3*asec(abs(x/a))
+--S 128
+bb:=(x^2-a^2)^(3/2)/3-a^2*sqrt(x^2-a^2)+a^3*asec(x/a)
 --R
---R                                     +-------+
---R          3         x       2     2  | 2    2
---R        3a asec(abs(-)) + (x  - 4a )\|x  - a
---R                    a
---R   (2)  --------------------------------------
---R                           3
+--R                   +-------+
+--R          2     2  | 2    2      3     x
+--R        (x  - 4a )\|x  - a   + 3a asec(-)
+--R                                       a
+--R   (2)  ---------------------------------
+--R                        3
 --R                                                     Type: Expression Integer
 --E
 
---S 80     14:234 Axiom cannot simplify this expression
+--S 129
 cc:=aa-bb
 --R
 --R                 +-------+
 --R                 | 2    2
---R          3     \|x  - a   - x     3         x
---R   (3)  2a atan(--------------) - a asec(abs(-))
---R                       a                     a
+--R          3     \|x  - a   - x     3     x
+--R   (3)  2a atan(--------------) - a asec(-)
+--R                       a                 a
 --R                                                     Type: Expression Integer
 --E
+
+--S 130
+asecrule:=rule(asec(x) == 1/2*%pi+%i*log(sqrt(1-1/x^2)+%i/x))
+--R
+--R                             +------+
+--R                             | 2
+--R                             |x  - 1
+--R                           x |------  + %i
+--R                             |   2
+--R                            \|  x
+--R                   2%i log(---------------) + %pi
+--R                                  x
+--R   (4)  asec(x) == ------------------------------
+--R                                  2
+--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
+--E
+
+--S 131
+dd:=asecrule cc
+--R
+--R                      +-------+
+--R                      | 2    2
+--R                      |x  - a
+--R                    x |-------  + %i a             +-------+
+--R                      |    2                       | 2    2
+--R               3     \|   x                 3     \|x  - a   - x     3
+--R        - 2%i a log(------------------) + 4a atan(--------------) - a %pi
+--R                             x                           a
+--R   (5)  -----------------------------------------------------------------
+--R                                        2
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 132
+atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
+--R
+--R                            - x + %i
+--R                     %i log(--------)
+--R                             x + %i
+--R   (6)  atan(x) == - ----------------
+--R                             2
+--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
+--E
+
+--S 133
+ee:=atanrule dd
+--R
+--R   (7)
+--R                 +-------+
+--R                 | 2    2
+--R                 |x  - a
+--R               x |-------  + %i a                 +-------+
+--R                 |    2                           | 2    2
+--R          3     \|   x                    3    - \|x  - a   + x + %i a     3
+--R   - 2%i a log(------------------) - 2%i a log(-----------------------) - a %pi
+--R                        x                        +-------+
+--R                                                 | 2    2
+--R                                                \|x  - a   - x + %i a
+--R   ----------------------------------------------------------------------------
+--R                                         2
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 134
+ff:=expandLog ee
+--R
+--R   (8)
+--R                  +-------+                          +-------+
+--R            3     | 2    2                     3     | 2    2
+--R       2%i a log(\|x  - a   - x + %i a) - 2%i a log(\|x  - a   - x - %i a)
+--R     + 
+--R                     +-------+
+--R                     | 2    2
+--R              3      |x  - a                  3              3            3
+--R       - 2%i a log(x |-------  + %i a) + 2%i a log(x) - 2%i a log(- 1) - a %pi
+--R                     |    2
+--R                    \|   x
+--R  /
+--R     2
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 135
+gg:=rootSimp ff
+--R
+--R   (9)
+--R                    +-------+                      +-------+
+--R              3     | 2    2                 3     | 2    2
+--R       - 2%i a log(\|x  - a   + %i a) + 2%i a log(\|x  - a   - x + %i a)
+--R     + 
+--R                  +-------+
+--R            3     | 2    2                     3              3            3
+--R     - 2%i a log(\|x  - a   - x - %i a) + 2%i a log(x) - 2%i a log(- 1) - a %pi
+--R  /
+--R     2
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 136    14:234 Schaums and Axiom differ by a constant
+hh:=complexNormalize gg
+--R
+--R            3
+--R           a %pi
+--R   (10)  - -----
+--R             2
+--R                                             Type: Expression Complex Integer
+--E
 @
 
 \section{\cite{1}:14.235~~~~~$\displaystyle
@@ -1270,7 +2083,7 @@ $$
 <<*>>=
 )clear all
 
---S 81
+--S 137
 aa:=integrate((x^2-a^2)^{3/2}/x^2,x)
 --R 
 --R
@@ -1289,7 +2102,7 @@ aa:=integrate((x^2-a^2)^{3/2}/x^2,x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
 
---S 82
+--S 138
 bb:=-(x^2-a^2)^(3/2)/x+3*x*sqrt(x^2-a^2)/2-3/2*a^2*log(x+sqrt(x^2-a^2))
 --R
 --R                    +-------+                   +-------+
@@ -1300,7 +2113,7 @@ bb:=-(x^2-a^2)^(3/2)/x+3*x*sqrt(x^2-a^2)/2-3/2*a^2*log(x+sqrt(x^2-a^2))
 --R                                                     Type: Expression Integer
 --E
 
---S 83     14:235 Axiom cannot simplify this expression
+--S 139
 cc:=aa-bb
 --R
 --R                +-------+                +-------+
@@ -1310,6 +2123,17 @@ cc:=aa-bb
 --R                                  2
 --R                                                     Type: Expression Integer
 --E
+
+--S 140    14:235 Schaums and Axiom differ by a constant
+dd:=complexNormalize cc
+--R
+--R          2       2      2
+--R        3a log(- a ) + 2a
+--R   (4)  ------------------
+--R                 2
+--R                                                     Type: Expression Integer
+--E
+
 @
 
 \section{\cite{1}:14.236~~~~~$\displaystyle
@@ -1321,7 +2145,7 @@ $$
 <<*>>=
 )clear all
 
---S 84
+--S 141
 aa:=integrate((x^2-a^2)^(3/2)/x^3,x)
 --R 
 --R
@@ -1342,31 +2166,137 @@ aa:=integrate((x^2-a^2)^(3/2)/x^3,x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
 
---S 85
-bb:=-(x^2-a^2)^(3/2)/(2*x^2)+(3*sqrt(x^2-a^2))/2-3/2*a*asec(abs(x/a))
+--S 142
+bb:=-(x^2-a^2)^(3/2)/(2*x^2)+(3*sqrt(x^2-a^2))/2-3/2*a*asec(x/a)
 --R
---R                                         +-------+
---R              2         x        2    2  | 2    2
---R        - 3a x asec(abs(-)) + (2x  + a )\|x  - a
---R                        a
---R   (2)  ------------------------------------------
---R                              2
---R                            2x
+--R                   +-------+
+--R           2    2  | 2    2        2     x
+--R        (2x  + a )\|x  - a   - 3a x asec(-)
+--R                                         a
+--R   (2)  -----------------------------------
+--R                          2
+--R                        2x
 --R                                                     Type: Expression Integer
 --E
 
---S 86     14:236 Axiom cannot simplify this expression
+--S 143
 cc:=aa-bb
 --R
 --R                   +-------+
 --R                   | 2    2
---R                  \|x  - a   - x                x
---R        - 6a atan(--------------) + 3a asec(abs(-))
---R                         a                      a
---R   (3)  -------------------------------------------
---R                             2
+--R                  \|x  - a   - x            x
+--R        - 6a atan(--------------) + 3a asec(-)
+--R                         a                  a
+--R   (3)  --------------------------------------
+--R                           2
 --R                                                     Type: Expression Integer
 --E
+
+--S 144
+atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
+--R
+--R                            - x + %i
+--R                     %i log(--------)
+--R                             x + %i
+--R   (4)  atan(x) == - ----------------
+--R                             2
+--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
+--E
+
+--S 145
+dd:=atanrule cc
+--R
+--R                     +-------+
+--R                     | 2    2
+--R                  - \|x  - a   + x + %i a            x
+--R        3%i a log(-----------------------) + 3a asec(-)
+--R                    +-------+                        a
+--R                    | 2    2
+--R                   \|x  - a   - x + %i a
+--R   (5)  -----------------------------------------------
+--R                               2
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 146
+asecrule:=rule(asec(x) == 1/2*%pi+%i*log(sqrt(1-1/x^2)+%i/x))
+--R
+--R                             +------+
+--R                             | 2
+--R                             |x  - 1
+--R                           x |------  + %i
+--R                             |   2
+--R                            \|  x
+--R                   2%i log(---------------) + %pi
+--R                                  x
+--R   (6)  asec(x) == ------------------------------
+--R                                  2
+--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
+--E
+
+--S 147
+ee:=asecrule dd
+--R
+--R   (7)
+--R               +-------+
+--R               | 2    2
+--R               |x  - a
+--R             x |-------  + %i a                 +-------+
+--R               |    2                           | 2    2
+--R              \|   x                         - \|x  - a   + x + %i a
+--R   6%i a log(------------------) + 6%i a log(-----------------------) + 3a %pi
+--R                      x                        +-------+
+--R                                               | 2    2
+--R                                              \|x  - a   - x + %i a
+--R   ---------------------------------------------------------------------------
+--R                                        4
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 148
+ff:=expandLog ee
+--R
+--R   (8)
+--R                    +-------+                          +-------+
+--R                    | 2    2                           | 2    2
+--R       - 6%i a log(\|x  - a   - x + %i a) + 6%i a log(\|x  - a   - x - %i a)
+--R     + 
+--R                   +-------+
+--R                   | 2    2
+--R                   |x  - a
+--R       6%i a log(x |-------  + %i a) - 6%i a log(x) + 6%i a log(- 1) + 3a %pi
+--R                   |    2
+--R                  \|   x
+--R  /
+--R     4
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 149
+gg:=rootSimp ff
+--R
+--R   (9)
+--R                  +-------+                      +-------+
+--R                  | 2    2                       | 2    2
+--R       6%i a log(\|x  - a   + %i a) - 6%i a log(\|x  - a   - x + %i a)
+--R     + 
+--R                +-------+
+--R                | 2    2
+--R     6%i a log(\|x  - a   - x - %i a) - 6%i a log(x) + 6%i a log(- 1) + 3a %pi
+--R  /
+--R     4
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 150    14:236 Schaums and Axiom differ by a constant
+hh:=complexNormalize gg
+--R
+--R         3a %pi
+--R   (10)  ------
+--R            4
+--R                                             Type: Expression Complex Integer
+--E
+
 )spool
 )lisp (bye)
 @
diff --git a/src/input/schaum11.input.pamphlet b/src/input/schaum11.input.pamphlet
index 6cd59a6..fc3117e 100644
--- a/src/input/schaum11.input.pamphlet
+++ b/src/input/schaum11.input.pamphlet
@@ -15,7 +15,7 @@ $$\int{\frac{1}{\sqrt{a^2-x^2}}}=\ln\left(x+\sqrt{a^2-x^2}\right)$$
 )set message auto off
 )clear all
 
---S 1 of 28
+--S 1
 aa:=integrate(1/(sqrt(a^2-x^2)),x)
 --R 
 --R
@@ -26,6 +26,96 @@ aa:=integrate(1/(sqrt(a^2-x^2)),x)
 --R                        x
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 2
+bb:=asin(x/a)
+--R
+--R             x
+--R   (2)  asin(-)
+--R             a
+--R                                                     Type: Expression Integer
+--E
+
+--S 3
+cc:=aa-bb
+--R
+--R                 +---------+
+--R                 |   2    2
+--R                \|- x  + a   - a         x
+--R   (3)  - 2atan(----------------) - asin(-)
+--R                        x                a
+--R                                                     Type: Expression Integer
+--E
+
+--S 4
+atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
+--R
+--R                            - x + %i
+--R                     %i log(--------)
+--R                             x + %i
+--R   (4)  atan(x) == - ----------------
+--R                             2
+--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
+--E
+
+--S 5
+dd:=atanrule cc
+--R
+--R                  +---------+
+--R                  |   2    2
+--R               - \|- x  + a   + %i x + a         x
+--R   (5)  %i log(-------------------------) - asin(-)
+--R                 +---------+                     a
+--R                 |   2    2
+--R                \|- x  + a   + %i x - a
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 6
+asinrule:=rule(asin(x) == %i*log(-%i*x+sqrt(1-x^2)))
+--R
+--R                           +--------+
+--R                           |   2
+--R   (6)  asin(x) == %i log(\|- x  + 1  - %i x)
+--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
+--E
+
+--S 7
+ee:=asinrule dd
+--R
+--R                   +---------+
+--R                   |   2    2
+--R                   |- x  + a
+--R                 a |---------  - %i x              +---------+
+--R                   |     2                         |   2    2
+--R                  \|    a                       - \|- x  + a   + %i x + a
+--R   (7)  - %i log(--------------------) + %i log(-------------------------)
+--R                           a                      +---------+
+--R                                                  |   2    2
+--R                                                 \|- x  + a   + %i x - a
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 8
+ff:=rootSimp ee
+--R
+--R                    +-------+                     +-------+
+--R                    | 2    2                      | 2    2
+--R                 %i\|x  - a   - %i x           - \|x  - a   + x - %i a
+--R   (8)  - %i log(-------------------) + %i log(-----------------------)
+--R                          a                      +-------+
+--R                                                 | 2    2
+--R                                                \|x  - a   + x + %i a
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 9      14:238 Schaums and Axiom agree
+gg:=complexNormalize ff
+--R
+--R   (9)  0
+--R                                             Type: Expression Complex Integer
+--E
+
 @
 
 \section{\cite{1}:14.238~~~~~$\displaystyle\int{\frac{x~dx}{\sqrt{a^2-x^2}}}$}
@@ -33,7 +123,7 @@ $$\int{\frac{x}{\sqrt{a^2-x^2}}}=\sqrt{a^2-x^2}$$
 <<*>>=
 )clear all
 
---S 2 of 28
+--S 10
 aa:=integrate(x/(sqrt(a^2-x^2)),x)
 --R 
 --R
@@ -45,6 +135,22 @@ aa:=integrate(x/(sqrt(a^2-x^2)),x)
 --R        \|- x  + a   - a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 11
+bb:=-sqrt(a^2-x^2)
+--R
+--R           +---------+
+--R           |   2    2
+--R   (2)  - \|- x  + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 12     14:238 Schaums and Axiom differ by a constant
+cc:=aa-bb
+--R
+--R   (3)  - a
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.239~~~~~$\displaystyle
@@ -55,7 +161,7 @@ $$
 <<*>>=
 )clear all
 
---S 3 of 28
+--S 13
 aa:=integrate(x^2/sqrt(a^2-x^2),x)
 --R 
 --R
@@ -75,6 +181,127 @@ aa:=integrate(x^2/sqrt(a^2-x^2),x)
 --R     4a\|- x  + a   + 2x  - 4a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 14
+bb:=-(x*sqrt(a^2-x^2))/2+a^2/2*asin(x/a)
+--R
+--R            +---------+
+--R            |   2    2     2     x
+--R        - x\|- x  + a   + a asin(-)
+--R                                 a
+--R   (2)  ---------------------------
+--R                     2
+--R                                                     Type: Expression Integer
+--E
+
+--S 15
+cc:=aa-bb
+--R
+--R                   +---------+
+--R                   |   2    2
+--R            2     \|- x  + a   - a     2     x
+--R        - 2a atan(----------------) - a asin(-)
+--R                          x                  a
+--R   (3)  ---------------------------------------
+--R                           2
+--R                                                     Type: Expression Integer
+--E
+
+--S 16
+atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
+--R
+--R                            - x + %i
+--R                     %i log(--------)
+--R                             x + %i
+--R   (4)  atan(x) == - ----------------
+--R                             2
+--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
+--E
+
+--S 17
+dd:=atanrule cc
+--R
+--R                    +---------+
+--R                    |   2    2
+--R            2    - \|- x  + a   + %i x + a     2     x
+--R        %i a log(-------------------------) - a asin(-)
+--R                   +---------+                       a
+--R                   |   2    2
+--R                  \|- x  + a   + %i x - a
+--R   (5)  -----------------------------------------------
+--R                               2
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 18
+asinrule:=rule(asin(x) == %i*log(-%i*x+sqrt(1-x^2)))
+--R
+--R                           +--------+
+--R                           |   2
+--R   (6)  asin(x) == %i log(\|- x  + 1  - %i x)
+--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
+--E
+
+--S 19
+ee:=asinrule dd
+--R
+--R                     +---------+
+--R                     |   2    2
+--R                     |- x  + a
+--R                   a |---------  - %i x                +---------+
+--R                     |     2                           |   2    2
+--R              2     \|    a                    2    - \|- x  + a   + %i x + a
+--R        - %i a log(--------------------) + %i a log(-------------------------)
+--R                             a                        +---------+
+--R                                                      |   2    2
+--R                                                     \|- x  + a   + %i x - a
+--R   (7)  ----------------------------------------------------------------------
+--R                                           2
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 20
+ff:=expandLog ee
+--R
+--R   (8)
+--R                    +---------+
+--R                    |   2    2                      +---------+
+--R             2      |- x  + a                 2     |   2    2
+--R       - %i a log(a |---------  - %i x) - %i a log(\|- x  + a   + %i x - a)
+--R                    |     2
+--R                   \|    a
+--R     + 
+--R                 +---------+
+--R           2     |   2    2                    2             2
+--R       %i a log(\|- x  + a   - %i x - a) + %i a log(a) + %i a log(- 1)
+--R  /
+--R     2
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 21
+gg:=rootSimp ff
+--R
+--R   (9)
+--R                     +-------+                           +-------+
+--R             2       | 2    2                    2       | 2    2
+--R       - %i a log(%i\|x  - a   + %i x - a) - %i a log(%i\|x  - a   - %i x)
+--R     + 
+--R                   +-------+
+--R           2       | 2    2                    2             2
+--R       %i a log(%i\|x  - a   - %i x - a) + %i a log(a) + %i a log(- 1)
+--R  /
+--R     2
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 22     14:239 Schaums and Axiom agree
+hh:=complexNormalize gg
+--R
+--R   (10)  0
+--R                                             Type: Expression Complex Integer
+--E
+
 @
 
 \section{\cite{1}:14.240~~~~~$\displaystyle
@@ -85,7 +312,7 @@ $$
 <<*>>=
 )clear all
 
---S 4 of 28
+--S 23
 aa:=integrate(x^3/sqrt(a^2-x^2),x)
 --R 
 --R
@@ -98,6 +325,27 @@ aa:=integrate(x^3/sqrt(a^2-x^2),x)
 --R        (3x  - 12a )\|- x  + a   - 9a x  + 12a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 24
+bb:=(a^2-x^2)^(3/2)/3-a^2*sqrt(a^2-x^2)
+--R
+--R                     +---------+
+--R            2     2  |   2    2
+--R        (- x  - 2a )\|- x  + a
+--R   (2)  ------------------------
+--R                    3
+--R                                                     Type: Expression Integer
+--E
+
+--S 25     14:240 Schaums and Axiom differ by a constant
+cc:=aa-bb
+--R
+--R            3
+--R          2a
+--R   (3)  - ---
+--R           3
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.241~~~~~$\displaystyle\int{\frac{dx}{x\sqrt{a^2-x^2}}}$}
@@ -107,7 +355,7 @@ $$
 <<*>>=
 )clear all
 
---S 5 of 28
+--S 26
 aa:=integrate(1/(x*sqrt(a^2-x^2)),x)
 --R 
 --R
@@ -120,6 +368,66 @@ aa:=integrate(1/(x*sqrt(a^2-x^2)),x)
 --R                  a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 27
+bb:=-1/a*log((a+sqrt(a^2-x^2))/x)
+--R
+--R               +---------+
+--R               |   2    2
+--R              \|- x  + a   + a
+--R          log(----------------)
+--R                      x
+--R   (2)  - ---------------------
+--R                    a
+--R                                                     Type: Expression Integer
+--E
+
+--S 28
+cc:=aa-bb
+--R
+--R             +---------+             +---------+
+--R             |   2    2              |   2    2
+--R            \|- x  + a   + a        \|- x  + a   - a
+--R        log(----------------) + log(----------------)
+--R                    x                       x
+--R   (3)  ---------------------------------------------
+--R                              a
+--R                                                     Type: Expression Integer
+--E
+
+--S 29
+dd:=expandLog cc
+--R
+--R             +---------+             +---------+
+--R             |   2    2              |   2    2
+--R        log(\|- x  + a   + a) + log(\|- x  + a   - a) - 2log(x)
+--R   (4)  -------------------------------------------------------
+--R                                   a
+--R                                                     Type: Expression Integer
+--E
+
+--S 30
+ee:=complexNormalize dd
+--R
+--R                  x
+--R          2log(-------)
+--R                +----+
+--R                |   2
+--R               \|- x
+--R   (5)  - -------------
+--R                a
+--R                                                     Type: Expression Integer
+--E
+
+--S 31     14:241 Schaums and Axiom differ by a constant
+ff:=rootSimp ee
+--R
+--R              +---+
+--R        2log(\|- 1 )
+--R   (6)  ------------
+--R              a
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.242~~~~~$\displaystyle
@@ -130,7 +438,7 @@ $$
 <<*>>=
 )clear all
 
---S 6 of 28
+--S 32
 aa:=integrate(1/(x^2*sqrt(a^2-x^2)),x)
 --R 
 --R
@@ -143,6 +451,25 @@ aa:=integrate(1/(x^2*sqrt(a^2-x^2)),x)
 --R         a x\|- x  + a   - a x
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 33
+bb:=-sqrt(a^2-x^2)/(a^2*x)
+--R
+--R           +---------+
+--R           |   2    2
+--R          \|- x  + a
+--R   (2)  - ------------
+--R                2
+--R               a x
+--R                                                     Type: Expression Integer
+--E
+
+--S 34     14:242 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.243~~~~~$\displaystyle\int{\frac{dx}{x^3\sqrt{a^2-x^2}}}$}
@@ -153,7 +480,7 @@ $$
 <<*>>=
 )clear all
 
---S 7 of 28
+--S 35
 aa:=integrate(1/(x^3*sqrt(a^2-x^2)),x)
 --R 
 --R
@@ -173,6 +500,71 @@ aa:=integrate(1/(x^3*sqrt(a^2-x^2)),x)
 --R     4a x \|- x  + a   + 2a x  - 4a x
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 36
+bb:=-sqrt(a^2-x^2)/(2*a^2*x^2)-1/(2*a^3)*log((a+sqrt(a^2-x^2))/x)
+--R
+--R                 +---------+
+--R                 |   2    2           +---------+
+--R           2    \|- x  + a   + a      |   2    2
+--R        - x log(----------------) - a\|- x  + a
+--R                        x
+--R   (2)  -----------------------------------------
+--R                            3 2
+--R                          2a x
+--R                                                     Type: Expression Integer
+--E
+
+--S 37
+cc:=aa-bb
+--R
+--R             +---------+             +---------+
+--R             |   2    2              |   2    2
+--R            \|- x  + a   + a        \|- x  + a   - a
+--R        log(----------------) + log(----------------)
+--R                    x                       x
+--R   (3)  ---------------------------------------------
+--R                               3
+--R                             2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 38
+dd:=expandLog cc
+--R
+--R             +---------+             +---------+
+--R             |   2    2              |   2    2
+--R        log(\|- x  + a   + a) + log(\|- x  + a   - a) - 2log(x)
+--R   (4)  -------------------------------------------------------
+--R                                    3
+--R                                  2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 39
+ee:=complexNormalize dd
+--R
+--R                 x
+--R          log(-------)
+--R               +----+
+--R               |   2
+--R              \|- x
+--R   (5)  - ------------
+--R                3
+--R               a
+--R                                                     Type: Expression Integer
+--E 
+
+--S 40     14:243 Schaums and Axiom differ by a constant
+ff:=rootSimp ee
+--R
+--R             +---+
+--R        log(\|- 1 )
+--R   (6)  -----------
+--R              3
+--R             a
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.244~~~~~$\displaystyle\int{\sqrt{a^2-x^2}}~dx$}
@@ -182,7 +574,7 @@ $$
 <<*>>=
 )clear all
 
---S 8 of 28
+--S 41
 aa:=integrate(sqrt(a^2-x^2),x)
 --R 
 --R
@@ -202,6 +594,127 @@ aa:=integrate(sqrt(a^2-x^2),x)
 --R     4a\|- x  + a   + 2x  - 4a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 42
+bb:=(x*sqrt(a^2-x^2))/2+a^2/2*asin(x/a)
+--R
+--R          +---------+
+--R          |   2    2     2     x
+--R        x\|- x  + a   + a asin(-)
+--R                               a
+--R   (2)  -------------------------
+--R                    2
+--R                                                     Type: Expression Integer
+--E
+
+--S 43
+cc:=aa-bb
+--R
+--R                   +---------+
+--R                   |   2    2
+--R            2     \|- x  + a   - a     2     x
+--R        - 2a atan(----------------) - a asin(-)
+--R                          x                  a
+--R   (3)  ---------------------------------------
+--R                           2
+--R                                                     Type: Expression Integer
+--E
+
+--S 44
+asinrule:=rule(asin(x) == %i*log(-%i*x+sqrt(1-x^2)))
+--R
+--R                           +--------+
+--R                           |   2
+--R   (4)  asin(x) == %i log(\|- x  + 1  - %i x)
+--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
+--E
+
+--S 45
+dd:=asinrule cc
+--R
+--R                     +---------+
+--R                     |   2    2
+--R                     |- x  + a
+--R                   a |---------  - %i x             +---------+
+--R                     |     2                        |   2    2
+--R              2     \|    a                  2     \|- x  + a   - a
+--R        - %i a log(--------------------) - 2a atan(----------------)
+--R                             a                             x
+--R   (5)  ------------------------------------------------------------
+--R                                      2
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 46
+atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
+--R
+--R                            - x + %i
+--R                     %i log(--------)
+--R                             x + %i
+--R   (6)  atan(x) == - ----------------
+--R                             2
+--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
+--E
+
+--S 47
+ee:=atanrule dd
+--R
+--R                     +---------+
+--R                     |   2    2
+--R                     |- x  + a
+--R                   a |---------  - %i x                +---------+
+--R                     |     2                           |   2    2
+--R              2     \|    a                    2    - \|- x  + a   + %i x + a
+--R        - %i a log(--------------------) + %i a log(-------------------------)
+--R                             a                        +---------+
+--R                                                      |   2    2
+--R                                                     \|- x  + a   + %i x - a
+--R   (7)  ----------------------------------------------------------------------
+--R                                           2
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 48
+ff:=expandLog ee
+--R
+--R   (8)
+--R                    +---------+
+--R                    |   2    2                      +---------+
+--R             2      |- x  + a                 2     |   2    2
+--R       - %i a log(a |---------  - %i x) - %i a log(\|- x  + a   + %i x - a)
+--R                    |     2
+--R                   \|    a
+--R     + 
+--R                 +---------+
+--R           2     |   2    2                    2             2
+--R       %i a log(\|- x  + a   - %i x - a) + %i a log(a) + %i a log(- 1)
+--R  /
+--R     2
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 49
+gg:=rootSimp ff
+--R
+--R   (9)
+--R                     +-------+                           +-------+
+--R             2       | 2    2                    2       | 2    2
+--R       - %i a log(%i\|x  - a   + %i x - a) - %i a log(%i\|x  - a   - %i x)
+--R     + 
+--R                   +-------+
+--R           2       | 2    2                    2             2
+--R       %i a log(%i\|x  - a   - %i x - a) + %i a log(a) + %i a log(- 1)
+--R  /
+--R     2
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 50     14:244 Schaums and Axiom agree
+hh:=complexNormalize gg
+--R
+--R   (10)  0
+--R                                             Type: Expression Complex Integer
+--E
 @
 
 \section{\cite{1}:14.245~~~~~$\displaystyle\int{x\sqrt{a^2-x^2}}~dx$}
@@ -211,7 +724,7 @@ $$
 <<*>>=
 )clear all
 
---S 9 of 28
+--S 51
 aa:=integrate(x*sqrt(a^2-x^2),x)
 --R 
 --R
@@ -224,6 +737,27 @@ aa:=integrate(x*sqrt(a^2-x^2),x)
 --R              (3x  - 12a )\|- x  + a   - 9a x  + 12a
 --R                                          Type: Union(Expression Integer,...)
 --E
+
+--S 52
+bb:=-(a^2-x^2)^(3/2)/3
+--R
+--R                  +---------+
+--R          2    2  |   2    2
+--R        (x  - a )\|- x  + a
+--R   (2)  ---------------------
+--R                  3
+--R                                                     Type: Expression Integer
+--E
+
+--S 53     14:245 Schaums and Axiom differ by a constant
+cc:=aa-bb
+--R
+--R           3
+--R          a
+--R   (3)  - --
+--R           3
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.246~~~~~$\displaystyle
@@ -235,7 +769,7 @@ $$
 <<*>>=
 )clear all
 
---S 10 of 28
+--S 54
 aa:=integrate(x^2*sqrt(a^2-x^2),x)
 --R 
 --R
@@ -259,6 +793,126 @@ aa:=integrate(x^2*sqrt(a^2-x^2),x)
 --R     (32a x  - 64a )\|- x  + a   + 8x  - 64a x  + 64a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 55
+bb:=-(x*(a^2-x^2)^(3/2))/4+(a^2*x*sqrt(a^2-x^2))/8+a^4/8*asin(x/a)
+--R
+--R                    +---------+
+--R           3    2   |   2    2     4     x
+--R        (2x  - a x)\|- x  + a   + a asin(-)
+--R                                         a
+--R   (2)  -----------------------------------
+--R                         8
+--R                                                     Type: Expression Integer
+--E
+
+--S 56
+cc:=aa-bb
+--R
+--R                   +---------+
+--R                   |   2    2
+--R            4     \|- x  + a   - a     4     x
+--R        - 2a atan(----------------) - a asin(-)
+--R                          x                  a
+--R   (3)  ---------------------------------------
+--R                           8
+--R                                                     Type: Expression Integer
+--E
+
+--S 57
+atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
+--R
+--R                            - x + %i
+--R                     %i log(--------)
+--R                             x + %i
+--R   (4)  atan(x) == - ----------------
+--R                             2
+--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
+--E
+
+--S 58
+dd:=atanrule cc
+--R
+--R                    +---------+
+--R                    |   2    2
+--R            4    - \|- x  + a   + %i x + a     4     x
+--R        %i a log(-------------------------) - a asin(-)
+--R                   +---------+                       a
+--R                   |   2    2
+--R                  \|- x  + a   + %i x - a
+--R   (5)  -----------------------------------------------
+--R                               8
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 59
+asinrule:=rule(asin(x) == %i*log(-%i*x+sqrt(1-x^2)))
+--R
+--R                           +--------+
+--R                           |   2
+--R   (6)  asin(x) == %i log(\|- x  + 1  - %i x)
+--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
+--E
+
+--S 60
+ee:=asinrule dd
+--R
+--R                     +---------+
+--R                     |   2    2
+--R                     |- x  + a
+--R                   a |---------  - %i x                +---------+
+--R                     |     2                           |   2    2
+--R              4     \|    a                    4    - \|- x  + a   + %i x + a
+--R        - %i a log(--------------------) + %i a log(-------------------------)
+--R                             a                        +---------+
+--R                                                      |   2    2
+--R                                                     \|- x  + a   + %i x - a
+--R   (7)  ----------------------------------------------------------------------
+--R                                           8
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 61
+ff:=expandLog ee
+--R
+--R   (8)
+--R                    +---------+
+--R                    |   2    2                      +---------+
+--R             4      |- x  + a                 4     |   2    2
+--R       - %i a log(a |---------  - %i x) - %i a log(\|- x  + a   + %i x - a)
+--R                    |     2
+--R                   \|    a
+--R     + 
+--R                 +---------+
+--R           4     |   2    2                    4             4
+--R       %i a log(\|- x  + a   - %i x - a) + %i a log(a) + %i a log(- 1)
+--R  /
+--R     8
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 62
+gg:=rootSimp ff
+--R
+--R   (9)
+--R                     +-------+                           +-------+
+--R             4       | 2    2                    4       | 2    2
+--R       - %i a log(%i\|x  - a   + %i x - a) - %i a log(%i\|x  - a   - %i x)
+--R     + 
+--R                   +-------+
+--R           4       | 2    2                    4             4
+--R       %i a log(%i\|x  - a   - %i x - a) + %i a log(a) + %i a log(- 1)
+--R  /
+--R     8
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 63     14:246 Schaums and Axiom agree
+hh:=complexNormalize gg
+--R
+--R   (10)  0
+--R                                             Type: Expression Complex Integer
+--E
 @
 
 \section{\cite{1}:14.247~~~~~$\displaystyle
@@ -269,7 +923,7 @@ $$
 <<*>>=
 )clear all
 
---S 11 of 28
+--S 64
 aa:=integrate(x^3*sqrt(a^2-x^2),x)
 --R 
 --R
@@ -283,6 +937,27 @@ aa:=integrate(x^3*sqrt(a^2-x^2),x)
 --R         (15x  - 180a x  + 240a )\|- x  + a   - 75a x  + 300a x  - 240a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 65
+bb:=(a^2-x^2)^(5/2)/5-(a^2*(a^2-x^2)^(3/2))/3
+--R
+--R                           +---------+
+--R           4    2 2     4  |   2    2
+--R        (3x  - a x  - 2a )\|- x  + a
+--R   (2)  ------------------------------
+--R                      15
+--R                                                     Type: Expression Integer
+--E 
+
+--S 66     14:247 Schaums and Axiom differ by a constant
+cc:=aa-bb
+--R
+--R            5
+--R          2a
+--R   (3)  - ---
+--R           15
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.248~~~~~$\displaystyle
@@ -293,7 +968,7 @@ $$
 <<*>>=
 )clear all
 
---S 12 of 28
+--S 67
 aa:=integrate(sqrt(a^2-x^2)/x,x)
 --R 
 --R
@@ -308,6 +983,56 @@ aa:=integrate(sqrt(a^2-x^2)/x,x)
 --R                       \|- x  + a   - a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 68
+bb:=sqrt(a^2-x^2)-a*log((a+sqrt(a^2-x^2))/x)
+--R
+--R                 +---------+
+--R                 |   2    2          +---------+
+--R                \|- x  + a   + a     |   2    2
+--R   (2)  - a log(----------------) + \|- x  + a
+--R                        x
+--R                                                     Type: Expression Integer
+--E
+
+--S 69
+cc:=aa-bb
+--R
+--R               +---------+               +---------+
+--R               |   2    2                |   2    2
+--R              \|- x  + a   + a          \|- x  + a   - a
+--R   (3)  a log(----------------) + a log(----------------) + a
+--R                      x                         x
+--R                                                     Type: Expression Integer
+--E
+
+--S 70
+dd:=expandLog cc
+--R
+--R               +---------+               +---------+
+--R               |   2    2                |   2    2
+--R   (4)  a log(\|- x  + a   + a) + a log(\|- x  + a   - a) - 2a log(x) + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 71
+ee:=complexNormalize dd
+--R
+--R                    x
+--R   (5)  - 2a log(-------) + a
+--R                  +----+
+--R                  |   2
+--R                 \|- x
+--R                                                     Type: Expression Integer
+--E
+
+--S 72     14:248 Schaums and Axiom differ by a constant
+ff:=rootSimp ee
+--R
+--R                +---+
+--R   (6)  2a log(\|- 1 ) + a
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.249~~~~~$\displaystyle
@@ -318,7 +1043,7 @@ $$
 <<*>>=
 )clear all
 
---S 13 of 28
+--S 73
 aa:=integrate(sqrt(a^2-x^2)/x^2,x)
 --R 
 --R
@@ -334,6 +1059,117 @@ aa:=integrate(sqrt(a^2-x^2)/x^2,x)
 --R                             x\|- x  + a   - a x
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 74
+bb:=-sqrt(a^2-x^2)/x-asin(x/a)
+--R
+--R           +---------+
+--R           |   2    2           x
+--R        - \|- x  + a   - x asin(-)
+--R                                a
+--R   (2)  --------------------------
+--R                     x
+--R                                                     Type: Expression Integer
+--E
+
+--S 75
+cc:=aa-bb
+--R
+--R               +---------+
+--R               |   2    2
+--R              \|- x  + a   - a         x
+--R   (3)  2atan(----------------) + asin(-)
+--R                      x                a
+--R                                                     Type: Expression Integer
+--E
+
+--S 76
+asinrule:=rule(asin(x) == %i*log(-%i*x+sqrt(1-x^2)))
+--R
+--R                           +--------+
+--R                           |   2
+--R   (4)  asin(x) == %i log(\|- x  + 1  - %i x)
+--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
+--E
+
+--S 77
+dd:=asinrule cc
+--R
+--R                 +---------+
+--R                 |   2    2
+--R                 |- x  + a
+--R               a |---------  - %i x           +---------+
+--R                 |     2                      |   2    2
+--R                \|    a                      \|- x  + a   - a
+--R   (5)  %i log(--------------------) + 2atan(----------------)
+--R                         a                           x
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 78
+atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
+--R
+--R                            - x + %i
+--R                     %i log(--------)
+--R                             x + %i
+--R   (6)  atan(x) == - ----------------
+--R                             2
+--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
+--E
+
+--S 79
+ee:=atanrule dd
+--R
+--R                 +---------+
+--R                 |   2    2
+--R                 |- x  + a
+--R               a |---------  - %i x              +---------+
+--R                 |     2                         |   2    2
+--R                \|    a                       - \|- x  + a   + %i x + a
+--R   (7)  %i log(--------------------) - %i log(-------------------------)
+--R                         a                      +---------+
+--R                                                |   2    2
+--R                                               \|- x  + a   + %i x - a
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 80
+ff:=expandLog ee
+--R
+--R   (8)
+--R              +---------+
+--R              |   2    2                    +---------+
+--R              |- x  + a                     |   2    2
+--R     %i log(a |---------  - %i x) + %i log(\|- x  + a   + %i x - a)
+--R              |     2
+--R             \|    a
+--R   + 
+--R               +---------+
+--R               |   2    2
+--R     - %i log(\|- x  + a   - %i x - a) - %i log(a) - %i log(- 1)
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 81
+gg:=rootSimp ff
+--R
+--R   (9)
+--R               +-------+                         +-------+
+--R               | 2    2                          | 2    2
+--R     %i log(%i\|x  - a   + %i x - a) + %i log(%i\|x  - a   - %i x)
+--R   + 
+--R                 +-------+
+--R                 | 2    2
+--R     - %i log(%i\|x  - a   - %i x - a) - %i log(a) - %i log(- 1)
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 82     14:249 Schaums and Axiom agree
+hh:=complexNormalize gg
+--R
+--R   (10)  0
+--R                                             Type: Expression Complex Integer
+--E
 @
 
 \section{\cite{1}:14.250~~~~~$\displaystyle
@@ -345,7 +1181,7 @@ $$
 <<*>>=
 )clear all
 
---S 14 of 28
+--S 83
 aa:=integrate(sqrt(a^2-x^2)/x^3,x)
 --R 
 --R
@@ -365,6 +1201,67 @@ aa:=integrate(sqrt(a^2-x^2)/x^3,x)
 --R     4a x \|- x  + a   + 2a x  - 4a x
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 84
+bb:=-sqrt(a^2-x^2)/(2*x^2)+1/(2*a)*log((a+sqrt(a^2-x^2))/x)
+--R
+--R               +---------+
+--R               |   2    2           +---------+
+--R         2    \|- x  + a   + a      |   2    2
+--R        x log(----------------) - a\|- x  + a
+--R                      x
+--R   (2)  ---------------------------------------
+--R                             2
+--R                         2a x
+--R                                                     Type: Expression Integer
+--E
+
+--S 85
+cc:=aa-bb
+--R
+--R               +---------+             +---------+
+--R               |   2    2              |   2    2
+--R              \|- x  + a   + a        \|- x  + a   - a
+--R        - log(----------------) - log(----------------)
+--R                      x                       x
+--R   (3)  -----------------------------------------------
+--R                               2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 86
+dd:=expandLog cc
+--R
+--R               +---------+             +---------+
+--R               |   2    2              |   2    2
+--R        - log(\|- x  + a   + a) - log(\|- x  + a   - a) + 2log(x)
+--R   (4)  ---------------------------------------------------------
+--R                                    2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 87
+ee:=complexNormalize dd
+--R
+--R               x
+--R        log(-------)
+--R             +----+
+--R             |   2
+--R            \|- x
+--R   (5)  ------------
+--R              a
+--R                                                     Type: Expression Integer
+--E
+
+--S 88     14:250 Schaums and Axiom differ by a constant
+ff:=rootSimp ee
+--R
+--R               +---+
+--R          log(\|- 1 )
+--R   (6)  - -----------
+--R               a
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.251~~~~~$\displaystyle\int{\frac{dx}{(a^2-x^2)^{3/2}}}$}
@@ -374,7 +1271,7 @@ $$
 <<*>>=
 )clear all
 
---S 15 of 28
+--S 89
 aa:=integrate(1/(a^2-x^2)^(3/2),x)
 --R 
 --R
@@ -387,6 +1284,24 @@ aa:=integrate(1/(a^2-x^2)^(3/2),x)
 --R        a \|- x  + a   + a x  - a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 90
+bb:=x/(a^2*sqrt(a^2-x^2))
+--R
+--R               x
+--R   (2)  --------------
+--R           +---------+
+--R         2 |   2    2
+--R        a \|- x  + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 91     14:251 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.252~~~~~$\displaystyle
@@ -397,7 +1312,7 @@ $$
 <<*>>=
 )clear all
 
---S 16 of 28
+--S 92
 aa:=integrate(x/(a^2-x^2)^(3/2),x)
 --R 
 --R
@@ -409,6 +1324,26 @@ aa:=integrate(x/(a^2-x^2)^(3/2),x)
 --R        a \|- x  + a   + a x  - a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 93
+bb:=1/sqrt(a^2-x^2)
+--R
+--R              1
+--R   (2)  ------------
+--R         +---------+
+--R         |   2    2
+--R        \|- x  + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 94     14:252 Schaums and Axiom differ by a constant
+cc:=aa-bb
+--R
+--R        1
+--R   (3)  -
+--R        a
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.253~~~~~$\displaystyle
@@ -419,7 +1354,7 @@ $$
 <<*>>=
 )clear all
 
---S 17 of 28
+--S 95
 aa:=integrate(x^2/(a^2-x^2)^(3/2),x)
 --R 
 --R
@@ -435,6 +1370,118 @@ aa:=integrate(x^2/(a^2-x^2)^(3/2),x)
 --R                            a\|- x  + a   + x  - a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 96
+bb:=x/sqrt(a^2-x^2)-asin(x/a)
+--R
+--R                  +---------+
+--R               x  |   2    2
+--R        - asin(-)\|- x  + a   + x
+--R               a
+--R   (2)  -------------------------
+--R                +---------+
+--R                |   2    2
+--R               \|- x  + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 97
+cc:=aa-bb
+--R
+--R               +---------+
+--R               |   2    2
+--R              \|- x  + a   - a         x
+--R   (3)  2atan(----------------) + asin(-)
+--R                      x                a
+--R                                                     Type: Expression Integer
+--E
+
+--S 98
+atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
+--R
+--R                            - x + %i
+--R                     %i log(--------)
+--R                             x + %i
+--R   (4)  atan(x) == - ----------------
+--R                             2
+--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
+--E
+
+--S 99
+dd:=atanrule cc
+--R
+--R                    +---------+
+--R                    |   2    2
+--R                 - \|- x  + a   + %i x + a         x
+--R   (5)  - %i log(-------------------------) + asin(-)
+--R                   +---------+                     a
+--R                   |   2    2
+--R                  \|- x  + a   + %i x - a
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 100
+asinrule:=rule(asin(x) == %i*log(-%i*x+sqrt(1-x^2)))
+--R
+--R                           +--------+
+--R                           |   2
+--R   (6)  asin(x) == %i log(\|- x  + 1  - %i x)
+--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
+--E
+
+--S 101
+ee:=asinrule dd
+--R
+--R                 +---------+
+--R                 |   2    2
+--R                 |- x  + a
+--R               a |---------  - %i x              +---------+
+--R                 |     2                         |   2    2
+--R                \|    a                       - \|- x  + a   + %i x + a
+--R   (7)  %i log(--------------------) - %i log(-------------------------)
+--R                         a                      +---------+
+--R                                                |   2    2
+--R                                               \|- x  + a   + %i x - a
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 102
+ff:=expandLog ee
+--R
+--R   (8)
+--R              +---------+
+--R              |   2    2                    +---------+
+--R              |- x  + a                     |   2    2
+--R     %i log(a |---------  - %i x) + %i log(\|- x  + a   + %i x - a)
+--R              |     2
+--R             \|    a
+--R   + 
+--R               +---------+
+--R               |   2    2
+--R     - %i log(\|- x  + a   - %i x - a) - %i log(a) - %i log(- 1)
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 103
+gg:=rootSimp ff
+--R
+--R   (9)
+--R               +-------+                         +-------+
+--R               | 2    2                          | 2    2
+--R     %i log(%i\|x  - a   + %i x - a) + %i log(%i\|x  - a   - %i x)
+--R   + 
+--R                 +-------+
+--R                 | 2    2
+--R     - %i log(%i\|x  - a   - %i x - a) - %i log(a) - %i log(- 1)
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 104    14:253 Schaums and Axiom agree
+hh:=complexNormalize gg
+--R
+--R   (10)  0
+--R                                             Type: Expression Complex Integer
+--E
 @
 
 \section{\cite{1}:14.254~~~~~$\displaystyle
@@ -445,7 +1492,7 @@ $$
 <<*>>=
 )clear all
 
---S 18 of 28
+--S 105
 aa:=integrate(x^3/(a^2-x^2)^(3/2),x)
 --R 
 --R
@@ -457,6 +1504,25 @@ aa:=integrate(x^3/(a^2-x^2)^(3/2),x)
 --R          (x  - 2a )\|- x  + a   - 2a x  + 2a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 106
+bb:=sqrt(a^2-x^2)+a^2/sqrt(a^2-x^2)
+--R
+--R            2     2
+--R         - x  + 2a
+--R   (2)  ------------
+--R         +---------+
+--R         |   2    2
+--R        \|- x  + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 107    14:254 Schaums and Axiom differ by a constant
+cc:=aa-bb
+--R
+--R   (3)  2a
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.255~~~~~$\displaystyle
@@ -468,7 +1534,7 @@ $$
 <<*>>=
 )clear all
 
---S 19 of 28
+--S 108
 aa:=integrate(1/(x*(a^2-x^2)^(3/2)),x)
 --R 
 --R
@@ -483,6 +1549,72 @@ aa:=integrate(1/(x*(a^2-x^2)^(3/2)),x)
 --R                     a \|- x  + a   + a x  - a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 109
+bb:=1/(a^2*sqrt(a^2-x^2))-1/a^3*log((a+sqrt(a^2-x^2))/x)
+--R
+--R                           +---------+
+--R           +---------+     |   2    2
+--R           |   2    2     \|- x  + a   + a
+--R        - \|- x  + a  log(----------------) + a
+--R                                  x
+--R   (2)  ---------------------------------------
+--R                        +---------+
+--R                      3 |   2    2
+--R                     a \|- x  + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 110
+cc:=aa-bb
+--R
+--R             +---------+             +---------+
+--R             |   2    2              |   2    2
+--R            \|- x  + a   + a        \|- x  + a   - a
+--R        log(----------------) + log(----------------) + 1
+--R                    x                       x
+--R   (3)  -------------------------------------------------
+--R                                 3
+--R                                a
+--R                                                     Type: Expression Integer
+--E
+
+--S 111
+dd:=expandLog cc
+--R
+--R             +---------+             +---------+
+--R             |   2    2              |   2    2
+--R        log(\|- x  + a   + a) + log(\|- x  + a   - a) - 2log(x) + 1
+--R   (4)  -----------------------------------------------------------
+--R                                      3
+--R                                     a
+--R                                                     Type: Expression Integer
+--E
+
+--S 112
+ee:=complexNormalize dd
+--R
+--R                  x
+--R        - 2log(-------) + 1
+--R                +----+
+--R                |   2
+--R               \|- x
+--R   (5)  -------------------
+--R                  3
+--R                 a
+--R                                                     Type: Expression Integer
+--E
+
+--S 113    14:255 Schaums and Axiom differ by a constant
+ff:=rootSimp ee
+--R
+--R              +---+
+--R        2log(\|- 1 ) + 1
+--R   (6)  ----------------
+--R                3
+--R               a
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.256~~~~~$\displaystyle
@@ -493,7 +1625,7 @@ $$
 <<*>>=
 )clear all
 
---S 20 of 28
+--S 114
 aa:=integrate(1/(x^2*(a^2-x^2)^(3/2)),x)
 --R 
 --R
@@ -506,6 +1638,25 @@ aa:=integrate(1/(x^2*(a^2-x^2)^(3/2)),x)
 --R           (a x  - 2a x)\|- x  + a   - 2a x  + 2a x
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 115
+bb:=-sqrt(a^2-x^2)/(a^4*x)+x/(a^4*sqrt(a^2-x^2))
+--R
+--R              2    2
+--R            2x  - a
+--R   (2)  ---------------
+--R            +---------+
+--R         4  |   2    2
+--R        a x\|- x  + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 116    14:256 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.257~~~~~$\displaystyle
@@ -518,7 +1669,7 @@ $$
 <<*>>=
 )clear all
 
---S 21 of 28
+--S 117
 aa:=integrate(1/(x^3*(a^2-x^2)^(3/2)),x)
 --R 
 --R
@@ -542,6 +1693,72 @@ aa:=integrate(1/(x^3*(a^2-x^2)^(3/2)),x)
 --R     (6a x  - 8a x )\|- x  + a   + 2a x  - 10a x  + 8a x
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 118
+bb:=-1/(2*a^2*x^2*sqrt(a^2-x^2))+3/(2*a^4*sqrt(a^2-x^2))-3/(2*a^5)*log((a+sqrt(a^2-x^2))/x)
+--R
+--R                              +---------+
+--R              +---------+     |   2    2
+--R            2 |   2    2     \|- x  + a   + a        2    3
+--R        - 3x \|- x  + a  log(----------------) + 3a x  - a
+--R                                     x
+--R   (2)  ---------------------------------------------------
+--R                               +---------+
+--R                           5 2 |   2    2
+--R                         2a x \|- x  + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 119
+cc:=aa-bb
+--R
+--R              +---------+              +---------+
+--R              |   2    2               |   2    2
+--R             \|- x  + a   + a         \|- x  + a   - a
+--R        3log(----------------) + 3log(----------------) + 2
+--R                     x                        x
+--R   (3)  ---------------------------------------------------
+--R                                  5
+--R                                2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 120
+dd:=expandLog cc
+--R
+--R              +---------+              +---------+
+--R              |   2    2               |   2    2
+--R        3log(\|- x  + a   + a) + 3log(\|- x  + a   - a) - 6log(x) + 2
+--R   (4)  -------------------------------------------------------------
+--R                                       5
+--R                                     2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 121
+ee:=complexNormalize dd
+--R
+--R                  x
+--R        - 3log(-------) + 1
+--R                +----+
+--R                |   2
+--R               \|- x
+--R   (5)  -------------------
+--R                  5
+--R                 a
+--R                                                     Type: Expression Integer
+--E
+
+--S 122    14:257 Schaums and Axiom differ by a constant
+ff:=rootSimp ee
+--R
+--R              +---+
+--R        3log(\|- 1 ) + 1
+--R   (6)  ----------------
+--R                5
+--R               a
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.258~~~~~$\displaystyle\int{(a^2-x^2)^{3/2}}~dx$}
@@ -552,7 +1769,7 @@ $$
 <<*>>=
 )clear all
 
---S 22 of 28
+--S 123
 aa:=integrate((a^2-x^2)^(3/2),x)
 --R 
 --R
@@ -579,6 +1796,128 @@ aa:=integrate((a^2-x^2)^(3/2),x)
 --R     (32a x  - 64a )\|- x  + a   + 8x  - 64a x  + 64a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 124
+bb:=(x*(a^2-x^2)^(3/2))/4+(3*a^2*x*sqrt(a^2-x^2))/8+3/8*a^4*asin(x/a)
+--R
+--R                       +---------+
+--R             3     2   |   2    2      4     x
+--R        (- 2x  + 5a x)\|- x  + a   + 3a asin(-)
+--R                                             a
+--R   (2)  ---------------------------------------
+--R                           8
+--R                                                     Type: Expression Integer
+--E
+
+--S 125
+cc:=aa-bb
+--R
+--R                   +---------+
+--R                   |   2    2
+--R            4     \|- x  + a   - a      4     x
+--R        - 6a atan(----------------) - 3a asin(-)
+--R                          x                   a
+--R   (3)  ----------------------------------------
+--R                            8
+--R                                                     Type: Expression Integer
+--E
+
+--S 126
+asinrule:=rule(asin(x) == %i*log(-%i*x+sqrt(1-x^2)))
+--R
+--R                           +--------+
+--R                           |   2
+--R   (4)  asin(x) == %i log(\|- x  + 1  - %i x)
+--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
+--E 
+
+--S 127
+ee:=asinrule cc
+--R
+--R                      +---------+
+--R                      |   2    2
+--R                      |- x  + a
+--R                    a |---------  - %i x             +---------+
+--R                      |     2                        |   2    2
+--R               4     \|    a                  4     \|- x  + a   - a
+--R        - 3%i a log(--------------------) - 6a atan(----------------)
+--R                              a                             x
+--R   (5)  -------------------------------------------------------------
+--R                                      8
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 128
+atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
+--R
+--R                            - x + %i
+--R                     %i log(--------)
+--R                             x + %i
+--R   (6)  atan(x) == - ----------------
+--R                             2
+--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
+--E
+
+--S 129
+ff:=atanrule ee
+--R
+--R   (7)
+--R                 +---------+
+--R                 |   2    2
+--R                 |- x  + a
+--R               a |---------  - %i x                 +---------+
+--R                 |     2                            |   2    2
+--R          4     \|    a                     4    - \|- x  + a   + %i x + a
+--R   - 3%i a log(--------------------) + 3%i a log(-------------------------)
+--R                         a                         +---------+
+--R                                                   |   2    2
+--R                                                  \|- x  + a   + %i x - a
+--R   ------------------------------------------------------------------------
+--R                                       8
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 130
+gg:=expandLog ff
+--R
+--R   (8)
+--R                     +---------+
+--R                     |   2    2                       +---------+
+--R              4      |- x  + a                  4     |   2    2
+--R       - 3%i a log(a |---------  - %i x) - 3%i a log(\|- x  + a   + %i x - a)
+--R                     |     2
+--R                    \|    a
+--R     + 
+--R                  +---------+
+--R            4     |   2    2                     4              4
+--R       3%i a log(\|- x  + a   - %i x - a) + 3%i a log(a) + 3%i a log(- 1)
+--R  /
+--R     8
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 131
+hh:=rootSimp gg
+--R
+--R   (9)
+--R                      +-------+                            +-------+
+--R              4       | 2    2                     4       | 2    2
+--R       - 3%i a log(%i\|x  - a   + %i x - a) - 3%i a log(%i\|x  - a   - %i x)
+--R     + 
+--R                    +-------+
+--R            4       | 2    2                     4              4
+--R       3%i a log(%i\|x  - a   - %i x - a) + 3%i a log(a) + 3%i a log(- 1)
+--R  /
+--R     8
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 132    14:258 Schaums and Axiom agree
+ii:=complexNormalize hh
+--R
+--R   (10)  0
+--R                                             Type: Expression Complex Integer
+--E
 @
 
 \section{\cite{1}:14.259~~~~~$\displaystyle\int{x(a^2-x^2)^{3/2}}~dx$}
@@ -586,7 +1925,7 @@ $$\int{x(a^2-x^2)^{3/2}}=\frac{(a^2-x^2)^{5/2}}{5}$$
 <<*>>=
 )clear all
 
---S 23 of 28
+--S 133
 aa:=integrate(x*(a^2-x^2)^(3/2),x)
 --R 
 --R
@@ -603,6 +1942,27 @@ aa:=integrate(x*(a^2-x^2)^(3/2),x)
 --R     (5x  - 60a x  + 80a )\|- x  + a   - 25a x  + 100a x  - 80a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 134
+bb:=-(a^2-x^2)^(5/2)/5
+--R
+--R                            +---------+
+--R            4     2 2    4  |   2    2
+--R        (- x  + 2a x  - a )\|- x  + a
+--R   (2)  -------------------------------
+--R                       5
+--R                                                     Type: Expression Integer
+--E
+
+--S 135    14:259 Schaums and Axiom differ by a constant
+cc:=aa-bb
+--R
+--R           5
+--R          a
+--R   (3)  - --
+--R           5
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.260~~~~~$\displaystyle\int{x^2(a^2-x^2)^{3/2}}~dx$}
@@ -614,7 +1974,7 @@ $$
 <<*>>=
 )clear all
 
---S 24 of 28
+--S 136
 aa:=integrate(x^2*(a^2-x^2)^(3/2),x)
 --R 
 --R
@@ -647,6 +2007,126 @@ aa:=integrate(x^2*(a^2-x^2)^(3/2),x)
 --R       - 1536a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 137
+bb:=-(x*(a^2-x^2)^(5/2))/6+(a^2*x*(a^2-x^2)^(3/2))/24+(a^4*x*sqrt(a^2-x^2))/16+a^6/16*asin(x/a)
+--R
+--R                                +---------+
+--R             5      2 3     4   |   2    2      6     x
+--R        (- 8x  + 14a x  - 3a x)\|- x  + a   + 3a asin(-)
+--R                                                      a
+--R   (2)  ------------------------------------------------
+--R                               48
+--R                                                     Type: Expression Integer
+--E
+
+--S 138
+cc:=aa-bb
+--R
+--R                   +---------+
+--R                   |   2    2
+--R            6     \|- x  + a   - a     6     x
+--R        - 2a atan(----------------) - a asin(-)
+--R                          x                  a
+--R   (3)  ---------------------------------------
+--R                           16
+--R                                                     Type: Expression Integer
+--E 
+
+--S 139
+atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
+--R
+--R                            - x + %i
+--R                     %i log(--------)
+--R                             x + %i
+--R   (4)  atan(x) == - ----------------
+--R                             2
+--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
+--E
+
+--S 140
+dd:=atanrule cc
+--R
+--R                    +---------+
+--R                    |   2    2
+--R            6    - \|- x  + a   + %i x + a     6     x
+--R        %i a log(-------------------------) - a asin(-)
+--R                   +---------+                       a
+--R                   |   2    2
+--R                  \|- x  + a   + %i x - a
+--R   (5)  -----------------------------------------------
+--R                               16
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 141
+asinrule:=rule(asin(x) == %i*log(-%i*x+sqrt(1-x^2)))
+--R
+--R                           +--------+
+--R                           |   2
+--R   (6)  asin(x) == %i log(\|- x  + 1  - %i x)
+--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
+--E
+
+--S 142
+ee:=asinrule dd
+--R
+--R                     +---------+
+--R                     |   2    2
+--R                     |- x  + a
+--R                   a |---------  - %i x                +---------+
+--R                     |     2                           |   2    2
+--R              6     \|    a                    6    - \|- x  + a   + %i x + a
+--R        - %i a log(--------------------) + %i a log(-------------------------)
+--R                             a                        +---------+
+--R                                                      |   2    2
+--R                                                     \|- x  + a   + %i x - a
+--R   (7)  ----------------------------------------------------------------------
+--R                                          16
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 143
+ff:=expandLog ee
+--R
+--R   (8)
+--R                    +---------+
+--R                    |   2    2                      +---------+
+--R             6      |- x  + a                 6     |   2    2
+--R       - %i a log(a |---------  - %i x) - %i a log(\|- x  + a   + %i x - a)
+--R                    |     2
+--R                   \|    a
+--R     + 
+--R                 +---------+
+--R           6     |   2    2                    6             6
+--R       %i a log(\|- x  + a   - %i x - a) + %i a log(a) + %i a log(- 1)
+--R  /
+--R     16
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 144
+gg:=rootSimp ff
+--R
+--R   (9)
+--R                     +-------+                           +-------+
+--R             6       | 2    2                    6       | 2    2
+--R       - %i a log(%i\|x  - a   + %i x - a) - %i a log(%i\|x  - a   - %i x)
+--R     + 
+--R                   +-------+
+--R           6       | 2    2                    6             6
+--R       %i a log(%i\|x  - a   - %i x - a) + %i a log(a) + %i a log(- 1)
+--R  /
+--R     16
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 145    14:260 Schaums and Axiom agree
+hh:=complexNormalize gg
+--R
+--R   (10)  0
+--R                                             Type: Expression Complex Integer
+--E
 @
 
 \section{\cite{1}:14.261~~~~~$\displaystyle\int{x^3(a^2-x^2)^{3/2}}~dx$}
@@ -656,7 +2136,7 @@ $$
 <<*>>=
 )clear all
 
---S 25 of 28
+--S 146
 aa:=integrate(x^3*(a^2-x^2)^(3/2),x)
 --R 
 --R
@@ -676,6 +2156,27 @@ aa:=integrate(x^3*(a^2-x^2)^(3/2),x)
 --R       - 3920a x  + 2240a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 147
+bb:=(a^2-x^2)^(7/2)/7-(a^2*(a^2-x^2)^(5/2))/5
+--R
+--R                                     +---------+
+--R             6     2 4    4 2     6  |   2    2
+--R        (- 5x  + 8a x  - a x  - 2a )\|- x  + a
+--R   (2)  ----------------------------------------
+--R                           35
+--R                                                     Type: Expression Integer
+--E
+
+--S 148    14:261 Schaums and Axiom differ by a constant
+cc:=aa-bb
+--R
+--R            7
+--R          2a
+--R   (3)  - ---
+--R           35
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.262~~~~~$\displaystyle
@@ -687,7 +2188,7 @@ $$
 <<*>>=
 )clear all
 
---S 26 of 28
+--S 149
 aa:=integrate((a^2-x^2)^(3/2)/x,x)
 --R 
 --R
@@ -707,6 +2208,66 @@ aa:=integrate((a^2-x^2)^(3/2)/x,x)
 --R     (3x  - 12a )\|- x  + a   - 9a x  + 12a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 150
+bb:=(a^2-x^2)^(3/2)/3+a^2*sqrt(a^2-x^2)-a^3*log((a+sqrt(a^2-x^2))/x)
+--R
+--R                  +---------+
+--R                  |   2    2                      +---------+
+--R            3    \|- x  + a   + a        2     2  |   2    2
+--R        - 3a log(----------------) + (- x  + 4a )\|- x  + a
+--R                         x
+--R   (2)  -----------------------------------------------------
+--R                                  3
+--R                                                     Type: Expression Integer
+--E
+
+--S 151
+cc:=aa-bb
+--R
+--R                +---------+                +---------+
+--R                |   2    2                 |   2    2
+--R          3    \|- x  + a   + a      3    \|- x  + a   - a      3
+--R        3a log(----------------) + 3a log(----------------) + 4a
+--R                       x                          x
+--R   (3)  ---------------------------------------------------------
+--R                                    3
+--R                                                     Type: Expression Integer
+--E
+
+--S 152
+dd:=expandLog cc
+--R
+--R                +---------+                +---------+
+--R          3     |   2    2           3     |   2    2           3           3
+--R        3a log(\|- x  + a   + a) + 3a log(\|- x  + a   - a) - 6a log(x) + 4a
+--R   (4)  ---------------------------------------------------------------------
+--R                                          3
+--R                                                     Type: Expression Integer
+--E
+
+--S 153
+ee:=complexNormalize dd
+--R
+--R            3       x         3
+--R        - 6a log(-------) + 4a
+--R                  +----+
+--R                  |   2
+--R                 \|- x
+--R   (5)  -----------------------
+--R                   3
+--R                                                     Type: Expression Integer
+--E
+
+--S 154    14:262 Schaums and Axiom differ by a constant
+ff:=rootSimp ee
+--R
+--R          3     +---+      3
+--R        6a log(\|- 1 ) + 4a
+--R   (6)  --------------------
+--R                  3
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.263~~~~~$\displaystyle
@@ -718,7 +2279,7 @@ $$
 <<*>>=
 )clear all
 
---S 27 of 28
+--S 155
 aa:=integrate((a^2-x^2)^{3/2}/x^2,x)
 --R 
 --R
@@ -738,6 +2299,127 @@ aa:=integrate((a^2-x^2)^{3/2}/x^2,x)
 --R     (2x  - 8a x)\|- x  + a   - 6a x  + 8a x
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 156
+bb:=-(a^2-x^2)^(3/2)/x-(3*x*sqrt(a^2-x^2))/2-3/2*a^2*asin(x/a)
+--R
+--R                     +---------+
+--R            2     2  |   2    2      2       x
+--R        (- x  - 2a )\|- x  + a   - 3a x asin(-)
+--R                                             a
+--R   (2)  ---------------------------------------
+--R                           2x
+--R                                                     Type: Expression Integer
+--E
+
+--S 157
+cc:=aa-bb
+--R
+--R                 +---------+
+--R                 |   2    2
+--R          2     \|- x  + a   - a      2     x
+--R        6a atan(----------------) + 3a asin(-)
+--R                        x                   a
+--R   (3)  --------------------------------------
+--R                           2
+--R                                                     Type: Expression Integer
+--E
+
+--S 158
+asinrule:=rule(asin(x) == %i*log(-%i*x+sqrt(1-x^2)))
+--R
+--R                           +--------+
+--R                           |   2
+--R   (4)  asin(x) == %i log(\|- x  + 1  - %i x)
+--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
+--E
+
+--S 159
+dd:=asinrule cc
+--R
+--R                    +---------+
+--R                    |   2    2
+--R                    |- x  + a
+--R                  a |---------  - %i x             +---------+
+--R                    |     2                        |   2    2
+--R             2     \|    a                  2     \|- x  + a   - a
+--R        3%i a log(--------------------) + 6a atan(----------------)
+--R                            a                             x
+--R   (5)  -----------------------------------------------------------
+--R                                     2
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 160
+atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
+--R
+--R                            - x + %i
+--R                     %i log(--------)
+--R                             x + %i
+--R   (6)  atan(x) == - ----------------
+--R                             2
+--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
+--E
+
+--S 161
+ee:=atanrule dd
+--R
+--R                    +---------+
+--R                    |   2    2
+--R                    |- x  + a
+--R                  a |---------  - %i x                 +---------+
+--R                    |     2                            |   2    2
+--R             2     \|    a                     2    - \|- x  + a   + %i x + a
+--R        3%i a log(--------------------) - 3%i a log(-------------------------)
+--R                            a                         +---------+
+--R                                                      |   2    2
+--R                                                     \|- x  + a   + %i x - a
+--R   (7)  ----------------------------------------------------------------------
+--R                                           2
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 162
+ff:=expandLog ee
+--R
+--R   (8)
+--R                   +---------+
+--R                   |   2    2                       +---------+
+--R            2      |- x  + a                  2     |   2    2
+--R       3%i a log(a |---------  - %i x) + 3%i a log(\|- x  + a   + %i x - a)
+--R                   |     2
+--R                  \|    a
+--R     + 
+--R                    +---------+
+--R              2     |   2    2                     2              2
+--R       - 3%i a log(\|- x  + a   - %i x - a) - 3%i a log(a) - 3%i a log(- 1)
+--R  /
+--R     2
+--R                                             Type: Expression Complex Integer
+--E 
+
+--S 163
+gg:=rootSimp ff
+--R
+--R   (9)
+--R                    +-------+                            +-------+
+--R            2       | 2    2                     2       | 2    2
+--R       3%i a log(%i\|x  - a   + %i x - a) + 3%i a log(%i\|x  - a   - %i x)
+--R     + 
+--R                      +-------+
+--R              2       | 2    2                     2              2
+--R       - 3%i a log(%i\|x  - a   - %i x - a) - 3%i a log(a) - 3%i a log(- 1)
+--R  /
+--R     2
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 164    14:263 Schaums and Axiom agree
+hh:=complexNormalize gg
+--R
+--R   (10)  0
+--R                                             Type: Expression Complex Integer
+--E
 @
 
 \section{\cite{1}:14.264~~~~~$\displaystyle
@@ -749,7 +2431,7 @@ $$
 <<*>>=
 )clear all
 
---S 28 of 28
+--S 165
 aa:=integrate((a^2-x^2)^(3/2)/x^3,x)
 --R 
 --R
@@ -770,6 +2452,63 @@ aa:=integrate((a^2-x^2)^(3/2)/x^3,x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
 
+--S 166
+bb:=-(a^2-x^2)^(3/2)/(2*x^2)-(3*sqrt(a^2-x^2))/2+3/2*a*log((a+sqrt(a^2-x^2))/x)
+--R
+--R                  +---------+
+--R                  |   2    2                      +---------+
+--R            2    \|- x  + a   + a         2    2  |   2    2
+--R        3a x log(----------------) + (- 2x  - a )\|- x  + a
+--R                         x
+--R   (2)  -----------------------------------------------------
+--R                                   2
+--R                                 2x
+--R                                                     Type: Expression Integer
+--E
+
+--S 167
+cc:=aa-bb
+--R
+--R                  +---------+                +---------+
+--R                  |   2    2                 |   2    2
+--R                 \|- x  + a   + a           \|- x  + a   - a
+--R        - 3a log(----------------) - 3a log(----------------) - 2a
+--R                         x                          x
+--R   (3)  ----------------------------------------------------------
+--R                                     2
+--R                                                     Type: Expression Integer
+--E
+
+--S 168
+dd:=expandLog cc
+--R
+--R                  +---------+                +---------+
+--R                  |   2    2                 |   2    2
+--R        - 3a log(\|- x  + a   + a) - 3a log(\|- x  + a   - a) + 6a log(x) - 2a
+--R   (4)  ----------------------------------------------------------------------
+--R                                           2
+--R                                                     Type: Expression Integer
+--E
+
+--S 169
+ee:=complexNormalize dd
+--R
+--R                  x
+--R   (5)  3a log(-------) - a
+--R                +----+
+--R                |   2
+--R               \|- x
+--R                                                     Type: Expression Integer
+--E
+
+--S 170    14:264 Schaums and Axiom differ by a constant
+ff:=rootSimp ee
+--R
+--R                  +---+
+--R   (6)  - 3a log(\|- 1 ) - a
+--R                                                     Type: Expression Integer
+--E
+
 )spool
 )lisp (bye)
 @
diff --git a/src/input/schaum2.input.pamphlet b/src/input/schaum2.input.pamphlet
index 184122e..dfbaf88 100644
--- a/src/input/schaum2.input.pamphlet
+++ b/src/input/schaum2.input.pamphlet
@@ -742,58 +742,11 @@ cc:=aa-bb
 --R     15a
 --R                                                     Type: Expression Integer
 --E
-@
-If we had the terms
-<<*>>=
---S 52
-t1:=(3*a*x-2*b)
---R
---R   (4)  3a x - 2b
---R                                                     Type: Polynomial Integer
---E
 
---S 53
-t2:=(a*x+b)
---R
---R   (5)  a x + b
---R                                                     Type: Polynomial Integer
---E
-@
-We can construct the Axiom result 
-<<*>>=
---S 54
-2*t1*t2*sqrt(t2)/(15*a^2)
---R
---R           2 2              2  +-------+
---R        (6a x  + 2a b x - 4b )\|a x + b
---R   (6)  --------------------------------
---R                         2
---R                      15a
---R                                                     Type: Expression Integer
---E
-@
-and we can construct the Spiegel result
-<<*>>=
---S 55
-2*t1*sqrt(t2^3)/(15*a^2)
+--S 52     14:90 Schaums and Axiom agree
+dd:=rootSimp cc
 --R
---R                    +----------------------------+
---R                    | 3 3     2   2       2     3
---R        (6a x - 4b)\|a x  + 3a b x  + 3a b x + b
---R   (7)  ------------------------------------------
---R                              2
---R                           15a
---R                                                     Type: Expression Integer
---E
-@
-the difference of these two depends on
-<<*>>=
---S 56     14:90 Axiom cannot simplify this expression
-t2*sqrt(t2)-sqrt(t2^3)
---R
---R           +----------------------------+
---R           | 3 3     2   2       2     3              +-------+
---R   (8)  - \|a x  + 3a b x  + 3a b x + b   + (a x + b)\|a x + b
+--R   (4)  0
 --R                                                     Type: Expression Integer
 --E
 @
@@ -807,7 +760,7 @@ Note: the sqrt term is almost certainly $\sqrt{(ax+b)}$
 <<*>>=
 )clear all
 
---S 57
+--S 53
 aa:=integrate(x^2*sqrt(a*x+b),x)
 --R 
 --R
@@ -819,27 +772,26 @@ aa:=integrate(x^2*sqrt(a*x+b),x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
 
---S 58
-bb:=(2*(15*a^2*x^2-12*a*b*x+8*b^2))/(105*a^2)*sqrt((a*x+b)^3)
+--S 54
+bb:=(2*(15*a^2*x^2-12*a*b*x+8*b^2))/(105*a^3)*sqrt((a+b*x)^3)
 --R 
 --R
 --R                                  +----------------------------+
---R            2 2                2  | 3 3     2   2       2     3
---R        (30a x  - 24a b x + 16b )\|a x  + 3a b x  + 3a b x + b
+--R            2 2                2  | 3 3       2 2     2       3
+--R        (30a x  - 24a b x + 16b )\|b x  + 3a b x  + 3a b x + a
 --R   (2)  --------------------------------------------------------
---R                                      2
+--R                                      3
 --R                                  105a
 --R                                                     Type: Expression Integer
 --E
 
---S 59     14:91 Axiom cannot simplify this expression
+--S 55     14:91 Axiom cannot simplify this expression. Schaums typo?
 cc:=aa-bb
---R 
 --R
 --R   (3)
---R                                     +----------------------------+
---R             3 2      2           2  | 3 3     2   2       2     3
---R       (- 30a x  + 24a b x - 16a b )\|a x  + 3a b x  + 3a b x + b
+--R                                   +----------------------------+
+--R             2 2                2  | 3 3       2 2     2       3
+--R       (- 30a x  + 24a b x - 16b )\|b x  + 3a b x  + 3a b x + a
 --R     + 
 --R           3 3     2   2       2       3  +-------+
 --R       (30a x  + 6a b x  - 8a b x + 16b )\|a x + b
@@ -848,6 +800,20 @@ cc:=aa-bb
 --R     105a
 --R                                                     Type: Expression Integer
 --E
+
+@
+Notice that if we factor the numerator of 'aa' we get an expression that
+differs from schaums on by the order of the variables in the square root.
+(We can square the term (a*x+b) and drag it under the square root to get
+the cubic term). It appears that Schaums has a typo.
+<<*>>=
+--S 56
+factor numer aa
+--R
+--R                      2 2               2  +-------+
+--R   (4)  2(a x + b)(15a x  - 12a b x + 8b )\|a x + b
+--RType: Factored SparseMultivariatePolynomial(Integer,Kernel Expression Integer)
+--E
 @
 
 \section{\cite{1}:14.92~~~~~$\displaystyle
@@ -858,7 +824,7 @@ $$
 <<*>>=
 )clear all
 
---S 60
+--S 57
 aa:=integrate(sqrt(a*x+b)/x,x)
 --R 
 --R
@@ -875,7 +841,7 @@ aa:=integrate(sqrt(a*x+b)/x,x)
 --R                                     Type: Union(List Expression Integer,...)
 --E 
 
---S 61
+--S 58
 dd:=integrate(1/(x*sqrt(a*x+b)),x)
 --R 
 --R
@@ -889,7 +855,7 @@ dd:=integrate(1/(x*sqrt(a*x+b)),x)
 --R                                     Type: Union(List Expression Integer,...)
 --E
 
---S 62
+--S 59
 bb1:=2*sqrt(a*x+b)+b*dd.1
 --R 
 --R
@@ -903,7 +869,7 @@ bb1:=2*sqrt(a*x+b)+b*dd.1
 --R                                                     Type: Expression Integer
 --E
 
---S 63
+--S 60
 bb2:=2*sqrt(a*x+b)+b*dd.2
 --R 
 --R
@@ -917,7 +883,7 @@ bb2:=2*sqrt(a*x+b)+b*dd.2
 --R                                                     Type: Expression Integer
 --E
 
---S 64
+--S 61
 cc11:=bb1-aa.1
 --R 
 --R
@@ -932,7 +898,7 @@ cc11:=bb1-aa.1
 --R                                                     Type: Expression Integer
 --E
 
---S 65
+--S 62
 cc12:=bb1-aa.2
 --R 
 --R
@@ -947,7 +913,7 @@ cc12:=bb1-aa.2
 --R                                                     Type: Expression Integer
 --E
 
---S 66
+--S 63
 cc21:=bb2-aa.1
 --R 
 --R
@@ -962,7 +928,7 @@ cc21:=bb2-aa.1
 --R                                                     Type: Expression Integer
 --E
 
---S 67     14:92 Axiom cannot simplify this expression
+--S 64     14:92 Axiom cannot simplify this expression
 cc22:=bb2-aa.2
 --R 
 --R
@@ -986,7 +952,7 @@ $$
 <<*>>=
 )clear all
 
---S 68
+--S 65
 aa:=integrate(sqrt(a*x+b)/x^2,x)
 --R 
 --R
@@ -1008,7 +974,7 @@ aa:=integrate(sqrt(a*x+b)/x^2,x)
 --R                                     Type: Union(List Expression Integer,...)
 --E 
 
---S 69
+--S 66
 dd:=integrate(1/(x*sqrt(a*x+b)),x)
 --R 
 --R
@@ -1022,7 +988,7 @@ dd:=integrate(1/(x*sqrt(a*x+b)),x)
 --R                                     Type: Union(List Expression Integer,...)
 --E
 
---S 70
+--S 67
 bb1:=-sqrt(a*x+b)/x+a/2*dd.1
 --R 
 --R
@@ -1036,7 +1002,7 @@ bb1:=-sqrt(a*x+b)/x+a/2*dd.1
 --R                                                     Type: Expression Integer
 --E
 
---S 71
+--S 68
 bb2:=-sqrt(a*x+b)/x+a/2*dd.2
 --R 
 --R
@@ -1050,7 +1016,7 @@ bb2:=-sqrt(a*x+b)/x+a/2*dd.2
 --R                                                     Type: Expression Integer
 --E
 
---S 72
+--S 69
 cc11:=bb1-aa.1
 --R 
 --R
@@ -1058,7 +1024,7 @@ cc11:=bb1-aa.1
 --R                                                     Type: Expression Integer
 --E
 
---S 73
+--S 70
 cc21:=bb-aa.1
 --R 
 --R
@@ -1073,7 +1039,7 @@ cc21:=bb-aa.1
 --R                                                     Type: Expression Integer
 --E
 
---S 74
+--S 71
 cc12:=bb1-aa.2
 --R 
 --R
@@ -1088,7 +1054,7 @@ cc12:=bb1-aa.2
 --R                                                     Type: Expression Integer
 --E
 
---S 75     14:93 Schaums and Axiom agree
+--S 72     14:93 Schaums and Axiom agree
 cc22:=bb2-aa.2
 --R 
 --R
@@ -1106,7 +1072,7 @@ $$
 <<*>>=
 )clear all
 
---S 76     14:94 Axiom cannot do this integral
+--S 73     14:94 Axiom cannot do this integral
 aa:=integrate(x^m/sqrt(a*x+b),x)
 --R 
 --R
@@ -1128,7 +1094,7 @@ $$
 <<*>>=
 )clear all
 
---S 77     14:95 Axiom cannot do this integral
+--S 74     14:95 Axiom cannot do this integral
 aa:=integrate(1/(x^m*sqrt(a*x+b)),x)
 --R 
 --R
@@ -1150,7 +1116,7 @@ $$
 <<*>>=
 )clear all
 
---S 78     14:96 Axiom cannot do this integral
+--S 75     14:96 Axiom cannot do this integral
 aa:=integrate(x^m*sqrt(a*x+b),x)
 --R 
 --R
@@ -1171,7 +1137,7 @@ $$
 <<*>>=
 )clear all
 
---S 79     14:97 Axiom cannot do this integral
+--S 76     14:97 Axiom cannot do this integral
 aa:=integrate(sqrt(a*x+b)/x^m,x)
 --R 
 --R
@@ -1194,7 +1160,7 @@ Note: 14.98 is the same as 14.97
 <<*>>=
 )clear all
 
---S 80     14:98 Axiom cannot do this integral
+--S 77     14:98 Axiom cannot do this integral
 aa:=integrate(sqrt(a*x+b)/x^m,x)
 --R 
 --R
@@ -1215,7 +1181,7 @@ $$
 <<*>>=
 )clear all
 
---S 81
+--S 78
 aa:=integrate((a*x+b)^(m/2),x)
 --R 
 --R
@@ -1228,7 +1194,7 @@ aa:=integrate((a*x+b)^(m/2),x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
 
---S 82
+--S 79
 bb:=(2*(a*x+b)^((m+2)/2))/(a*(m+2))
 --R 
 --R
@@ -1241,7 +1207,7 @@ bb:=(2*(a*x+b)^((m+2)/2))/(a*(m+2))
 --R                                                     Type: Expression Integer
 --E
 
---S 83     14:99 Axiom cannot simplify this expression
+--S 80
 cc:=aa-bb
 --R 
 --R
@@ -1253,6 +1219,33 @@ cc:=aa-bb
 --R                           a m + 2a
 --R                                                     Type: Expression Integer
 --E
+
+--S 81
+explog:=rule(%e^(n*log(x)) == x^n)
+--R
+--R          n log(x)     n
+--R   (4)  %e         == x
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 82
+dd:=explog cc
+--R
+--R                    m + 2                       m
+--R                    -----                       -
+--R                      2                         2
+--R        - 2(a x + b)      + (2a x + 2b)(a x + b)
+--R   (5)  -----------------------------------------
+--R                         a m + 2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 83     14:99 Schaums and Axiom agree
+ee:=complexNormalize dd
+--R
+--R   (6)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.100~~~~~$\displaystyle
@@ -1292,7 +1285,7 @@ bb:=(2*(a*x+b)^((m+4)/2))/(a^2*(m+4))-(2*b*(a*x+b)^((m+2)/2))/(a^2*(m+2))
 --R                                                     Type: Expression Integer
 --E
 
---S 86     14:100 Axiom cannot simplify this expression
+--S 86
 cc:=aa-bb
 --R 
 --R
@@ -1311,6 +1304,40 @@ cc:=aa-bb
 --R     a m  + 6a m + 8a
 --R                                                     Type: Expression Integer
 --E
+
+--S 87
+explog:=rule(%e^(n*log(x)) == x^n)
+--R
+--R          n log(x)     n
+--R   (4)  %e         == x
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 88
+dd:=explog cc
+--R
+--R   (5)
+--R                          m + 4                       m + 2
+--R                          -----                       -----
+--R                            2                           2
+--R       (- 2m - 4)(a x + b)      + (2b m + 8b)(a x + b)
+--R     + 
+--R                                                 m
+--R                                                 -
+--R           2      2  2                2          2
+--R       ((2a m + 4a )x  + 2a b m x - 4b )(a x + b)
+--R  /
+--R      2 2     2      2
+--R     a m  + 6a m + 8a
+--R                                                     Type: Expression Integer
+--E
+
+--S 89     14:100 Schaums and Axiom agree
+ee:=complexNormalize dd
+--R
+--R   (6)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.101~~~~~$\displaystyle
@@ -1323,7 +1350,7 @@ $$
 <<*>>=
 )clear all
 
---S 87
+--S 90
 aa:=integrate(x^2*(a*x+b)^(m/2),x)
 --R 
 --R
@@ -1341,7 +1368,7 @@ aa:=integrate(x^2*(a*x+b)^(m/2),x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
 
---S 88
+--S 91
 bb:=(2*(a*x+b)^((m+6)/2))/(a^3*(m+6))-_
       (4*b*(a*x+b)^((m+4)/2))/(a^3*(m+4))+_
         (2*b^2*(a*x+b)^((m+2)/2))/(a^3*(m+2))
@@ -1363,7 +1390,7 @@ bb:=(2*(a*x+b)^((m+6)/2))/(a^3*(m+6))-_
 --R                                                     Type: Expression Integer
 --E
 
---S 89     14:101 Axiom cannot simplify this expression
+--S 92
 cc:=aa-bb
 --R 
 --R
@@ -1390,6 +1417,48 @@ cc:=aa-bb
 --R     a m  + 12a m  + 44a m + 48a
 --R                                                     Type: Expression Integer
 --E
+
+--S 93
+explog:=rule(%e^(n*log(x)) == x^n)
+--R
+--R          n log(x)     n
+--R   (4)  %e         == x
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 94
+dd:=explog cc
+--R
+--R   (5)
+--R                                  m + 6                                 m + 4
+--R                                  -----                                 -----
+--R            2                       2          2                          2
+--R       (- 2m  - 12m - 16)(a x + b)      + (4b m  + 32b m + 48b)(a x + b)
+--R     + 
+--R                                        m + 2
+--R                                        -----
+--R            2 2      2       2            2
+--R       (- 2b m  - 20b m - 48b )(a x + b)
+--R     + 
+--R             3 2      3       3  3      2   2     2     2       2         3
+--R         ((2a m  + 12a m + 16a )x  + (2a b m  + 4a b m)x  - 8a b m x + 16b )
+--R      *
+--R                  m
+--R                  -
+--R                  2
+--R         (a x + b)
+--R  /
+--R      3 3      3 2      3       3
+--R     a m  + 12a m  + 44a m + 48a
+--R                                                     Type: Expression Integer
+--E
+
+--S 95     14:101 Schaums and Axiom agree
+ee:=complexNormalize dd
+--R
+--R   (6)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.102~~~~~$\displaystyle
@@ -1401,7 +1470,7 @@ $$
 <<*>>=
 )clear all
 
---S 90     14:102 Axiom cannot do this integral
+--S 96     14:102 Axiom cannot do this integral
 aa:=integrate((a*x+b)^(m/2)/x,x)
 --R 
 --R
@@ -1423,7 +1492,7 @@ $$
 <<*>>=
 )clear all
 
---S 91     14:103 Axiom cannot do this integral
+--S 97     14:103 Axiom cannot do this integral
 aa:=integrate((a*x+b)^(m/2)/x^2,x)
 --R 
 --R
@@ -1446,7 +1515,7 @@ $$
 <<*>>=
 )clear all
 
---S 92     14:104 Axiom cannot do this integral
+--S 98     14:104 Axiom cannot do this integral
 aa:=integrate(1/(x*(a*x+b)^(m/2)),x)
 --R 
 --R
diff --git a/src/input/schaum6.input.pamphlet b/src/input/schaum6.input.pamphlet
index 9b6f4f0..854e780 100644
--- a/src/input/schaum6.input.pamphlet
+++ b/src/input/schaum6.input.pamphlet
@@ -792,7 +792,7 @@ explog:=rule(%e^(n*log(x)) == x^n)
 --R                        Type: RewriteRule(Integer,Integer,Expression Integer)
 --E
 
---S 64     14:140 Schaums and Axiom cannot simplify this expression
+--S 64
 dd:=explog cc
 --R
 --R          2    2 n       2    2   2    2 n - 1
@@ -802,6 +802,13 @@ dd:=explog cc
 --R           (2n - 2)(x  + a )     (x  + a )
 --R                                                     Type: Expression Integer
 --E
+
+--S 65     14:140 Schaums and Axiom agree
+ee:=complexNormalize dd
+--R
+--R   (6)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.141~~~~~$\displaystyle\int{\frac{dx}{x(x^2+a^2)^n}}$}
@@ -812,7 +819,7 @@ $$
 <<*>>=
 )clear all
 
---S 65     14:141 Axiom cannot do this integral
+--S 66     14:141 Axiom cannot do this integral
 aa:=integrate(1/(x*(x^2+a^2)^n),x)
 --R 
 --R
@@ -833,7 +840,7 @@ $$
 <<*>>=
 )clear all
 
---S 66     14:142 Axiom cannot do this integral
+--S 67     14:142 Axiom cannot do this integral
 aa:=integrate(x^m/((x^2+a^2)^n),x)
 --R 
 --R
@@ -854,7 +861,7 @@ $$
 <<*>>=
 )clear all
 
---S 67     14:143 Axiom cannot do this integral
+--S 68     14:143 Axiom cannot do this integral
 aa:=integrate(1/(x^m*(x^2+a^2)^n),x)
 --R 
 --R
diff --git a/src/input/schaum7.input.pamphlet b/src/input/schaum7.input.pamphlet
index ce37f19..fcdd71c 100644
--- a/src/input/schaum7.input.pamphlet
+++ b/src/input/schaum7.input.pamphlet
@@ -915,7 +915,7 @@ explog:=rule(%e^(n*log(x)) == x^n)
 --R                        Type: RewriteRule(Integer,Integer,Expression Integer)
 --E
 
---S 76     14:159 Axiom cannot simplify this expression
+--S 76
 dd:=explog cc
 --R
 --R          2    2 n       2    2   2    2 n - 1
@@ -926,6 +926,12 @@ dd:=explog cc
 --R                                                     Type: Expression Integer
 --E
 
+--S 77     14:159 Schaums and Axiom agree
+ee:=complexNormalize dd
+--R
+--R   (6)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.160~~~~~$\displaystyle\int{\frac{dx}{x(x^2-a^2)^n}}$}
@@ -936,7 +942,7 @@ $$
 <<*>>=
 )clear all
 
---S 77     14:160 Axiom cannot compute this integral
+--S 78     14:160 Axiom cannot compute this integral
 aa:=integrate(1/(x*(x^2-a^2)^n),x)
 --R 
 --R
@@ -957,7 +963,7 @@ $$
 <<*>>=
 )clear all
 
---S 78     14:161 Axiom cannot compute this integral
+--S 79     14:161 Axiom cannot compute this integral
 aa:=integrate(x^m/((x^2-a^2)^n),x)
 --R 
 --R
@@ -978,7 +984,7 @@ $$
 <<*>>=
 )clear all
 
---S 79     14:162 Axiom cannot compute this integral
+--S 80     14:162 Axiom cannot compute this integral
 aa:=integrate(1/(x^m*(x^2-a^2)^n),x)
 --R 
 --R
diff --git a/src/input/schaum8.input.pamphlet b/src/input/schaum8.input.pamphlet
index 778d135..10d9ef5 100644
--- a/src/input/schaum8.input.pamphlet
+++ b/src/input/schaum8.input.pamphlet
@@ -1103,7 +1103,7 @@ explog:=rule(%e^(n*log(x)) == x^n)
 --R                        Type: RewriteRule(Integer,Integer,Expression Integer)
 --E
 
---S 95     14:178 Axiom cannot simplify this expression
+--S 95
 dd:=explog cc
 --R
 --R              2    2 n       2    2     2    2 n - 1
@@ -1114,6 +1114,13 @@ dd:=explog cc
 --R                                                     Type: Expression Integer
 --E
 
+--S 96     14:178 Schaums and Axiom agree
+ee:=complexNormalize dd
+--R
+--R   (6)  0
+--R                                                     Type: Expression Integer
+--E
+
 @
 
 \section{\cite{1}:14.179~~~~~$\displaystyle\int{\frac{dx}{x(a^2-x^2)^n}}$}
@@ -1124,7 +1131,7 @@ $$
 <<*>>=
 )clear all
 
---S 96     14:179 Axiom cannot integrate this expression
+--S 97     14:179 Axiom cannot integrate this expression
 aa:=integrate(1/(x*(a^2-x^2)^n),x)
 --R 
 --R
@@ -1145,7 +1152,7 @@ $$
 <<*>>=
 )clear all
 
---S 97     14:180 Axiom cannot integrate this expression
+--S 98     14:180 Axiom cannot integrate this expression
 aa:=integrate(x^m/((a^2-x^2)^n),x)
 --R 
 --R
@@ -1166,7 +1173,7 @@ $$
 <<*>>=
 )clear all
 
---S 98     14:181 Axiom cannot integrate this expression
+--S 99     14:181 Axiom cannot integrate this expression
 aa:=integrate(1/(x^m*(a^2-x^2)^n),x)
 --R 
 --R
diff --git a/src/input/schaum9.input.pamphlet b/src/input/schaum9.input.pamphlet
index fceb094..d632de7 100644
--- a/src/input/schaum9.input.pamphlet
+++ b/src/input/schaum9.input.pamphlet
@@ -35,7 +35,7 @@ bb:=log(x+sqrt(x^2+a^2))
 --R                                                     Type: Expression Integer
 --E
 
---S 3      14:182 Axiom cannot simplify this expression
+--S 3
 cc:=aa-bb
 --R
 --R               +-------+             +-------+
@@ -43,6 +43,15 @@ cc:=aa-bb
 --R   (3)  - log(\|x  + a   + x) - log(\|x  + a   - x)
 --R                                                     Type: Expression Integer
 --E
+
+--S 4      14:182 Schaums and Axiom differ by a constant
+dd:=complexNormalize cc
+--R
+--R               2
+--R   (4)  - log(a )
+--R                                                     Type: Expression Integer
+--E
+
 @
 This is equal to $-\log(a^2)$ but Axiom cannot prove it.
 
@@ -51,7 +60,7 @@ $$\int{\frac{x}{\sqrt{x^2+a^2}}}=\sqrt{x^2+a^2}$$
 <<*>>=
 )clear all
 
---S 4
+--S 5
 aa:=integrate(x/(sqrt(x^2+a^2)),x)
 --R 
 --R
@@ -65,7 +74,7 @@ aa:=integrate(x/(sqrt(x^2+a^2)),x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
 
---S 5
+--S 6
 bb:=sqrt(x^2+a^2)
 --R
 --R         +-------+
@@ -74,7 +83,7 @@ bb:=sqrt(x^2+a^2)
 --R                                                     Type: Expression Integer
 --E
 
---S 6      14:183 Schaums and Axiom agree
+--S 7      14:183 Schaums and Axiom agree
 cc:=aa-bb
 --R
 --R   (3)  0
@@ -90,7 +99,7 @@ $$
 <<*>>=
 )clear all
 
---S 7
+--S 8
 aa:=integrate(x^2/sqrt(x^2+a^2),x)
 --R 
 --R
@@ -109,7 +118,7 @@ aa:=integrate(x^2/sqrt(x^2+a^2),x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
 
---S 8
+--S 9
 bb:=(x*sqrt(x^2+a^2))/2-a^2/2*log(x+sqrt(x^2+a^2))
 --R
 --R                 +-------+          +-------+
@@ -120,7 +129,7 @@ bb:=(x*sqrt(x^2+a^2))/2-a^2/2*log(x+sqrt(x^2+a^2))
 --R                                                     Type: Expression Integer
 --E
 
---S 9
+--S 10
 cc:=aa-bb
 --R
 --R               +-------+               +-------+
@@ -131,14 +140,14 @@ cc:=aa-bb
 --R                                                     Type: Expression Integer
 --E
 
---S 10
+--S 11
 logmul1:=rule(c*log(a)+c*log(b) == c*log(a*b))
 --R
 --I   (4)  c log(b) + c log(a) + %K == c log(a b) + %K
 --R                        Type: RewriteRule(Integer,Integer,Expression Integer)
 --E
 
---S 11     14:184 Schaums and Axiom differ by a constant
+--S 12     14:184 Schaums and Axiom differ by a constant
 dd:=logmul1 cc
 --R
 --R         2     2
@@ -158,7 +167,7 @@ $$
 <<*>>=
 )clear all
 
---S 12
+--S 13
 aa:=integrate(x^3/sqrt(x^2+a^2),x)
 --R 
 --R
@@ -172,7 +181,7 @@ aa:=integrate(x^3/sqrt(x^2+a^2),x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
 
---S 13
+--S 14
 bb:=(x^2+a^2)^(3/2)/3-a^2*sqrt(x^2+a^2)
 --R
 --R                   +-------+
@@ -183,7 +192,7 @@ bb:=(x^2+a^2)^(3/2)/3-a^2*sqrt(x^2+a^2)
 --R                                                     Type: Expression Integer
 --E
 
---S 14     14:185 Schaums and Axiom agree
+--S 15     14:185 Schaums and Axiom agree
 cc:=aa-bb
 --R
 --R   (3)  0
@@ -198,7 +207,7 @@ $$
 <<*>>=
 )clear all
 
---S 15
+--S 16
 aa:=integrate(1/(x*sqrt(x^2+a^2)),x)
 --R 
 --R
@@ -210,7 +219,7 @@ aa:=integrate(1/(x*sqrt(x^2+a^2)),x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
 
---S 16
+--S 17
 bb:=-1/a*log((a+sqrt(x^2+a^2))/x)
 --R
 --R               +-------+
@@ -223,7 +232,7 @@ bb:=-1/a*log((a+sqrt(x^2+a^2))/x)
 --R                                                     Type: Expression Integer
 --E
 
---S 17
+--S 18
 cc:=aa-bb
 --R
 --R   (3)
@@ -237,19 +246,10 @@ cc:=aa-bb
 --R                                                     Type: Expression Integer
 --E
 
---S 18
-divlog:=rule(log(a/b) == log(a) - log(b))
---R
---R            a
---R   (4)  log(-) == - log(b) + log(a)
---R            b
---R                        Type: RewriteRule(Integer,Integer,Expression Integer)
---E
-
---S 19     14:186 Axiom cannot simplify this expression
-dd:=divlog cc
+--S 19
+dd:=expandLog cc
 --R
---R   (5)
+--R   (4)
 --R            +-------+             +-------+                 +-------+
 --R            | 2    2              | 2    2                  | 2    2
 --R       log(\|x  + a   + a) - log(\|x  + a   - x + a) + log(\|x  + a   - x - a)
@@ -260,6 +260,15 @@ dd:=divlog cc
 --R                                                     Type: Expression Integer
 --E
 
+--S 20     14:186 Schaums and Axiom differ by a constant
+ee:=complexNormalize dd
+--R
+--R          log(- 1)
+--R   (5)  - --------
+--R              a
+--R                                                     Type: Expression Integer
+--E
+
 @
 
 \section{\cite{1}:14.187~~~~~$\displaystyle
@@ -270,7 +279,7 @@ $$
 <<*>>=
 )clear all
 
---S 20
+--S 21
 aa:=integrate(1/(x^2*sqrt(x^2+a^2)),x)
 --R 
 --R
@@ -282,7 +291,7 @@ aa:=integrate(1/(x^2*sqrt(x^2+a^2)),x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
 
---S 21
+--S 22
 bb:=-sqrt(x^2+a^2)/(a^2*x)
 --R
 --R           +-------+
@@ -294,7 +303,7 @@ bb:=-sqrt(x^2+a^2)/(a^2*x)
 --R                                                     Type: Expression Integer
 --E
 
---S 22     14:187 Schaums and Axiom differ by a constant
+--S 23     14:187 Schaums and Axiom differ by a constant
 cc:=aa-bb
 --R
 --R           1
@@ -314,7 +323,7 @@ $$
 <<*>>=
 )clear all
 
---S 23
+--S 24
 aa:=integrate(1/(x^3*sqrt(x^2+a^2)),x)
 --R 
 --R
@@ -337,7 +346,7 @@ aa:=integrate(1/(x^3*sqrt(x^2+a^2)),x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
 
---S 24
+--S 25
 bb:=-sqrt(x^2+a^2)/(2*a^2*x^2)+1/(2*a^3)*log((a+sqrt(x^2+a^2))/x)
 --R
 --R               +-------+
@@ -351,7 +360,7 @@ bb:=-sqrt(x^2+a^2)/(2*a^2*x^2)+1/(2*a^3)*log((a+sqrt(x^2+a^2))/x)
 --R                                                     Type: Expression Integer
 --E
 
---S 25
+--S 26
 cc:=aa-bb
 --R
 --R   (3)
@@ -366,19 +375,10 @@ cc:=aa-bb
 --R                                                     Type: Expression Integer
 --E
 
---S 26
-divlog:=rule(log(a/b) == log(a) - log(b))
+--S 27
+dd:=expandLog cc
 --R
---R            a
---R   (4)  log(-) == - log(b) + log(a)
---R            b
---R                        Type: RewriteRule(Integer,Integer,Expression Integer)
---E
-
---S 27     14:188 Axiom cannot simplify this expression
-dd:=divlog cc
---R
---R   (5)
+--R   (4)
 --R              +-------+             +-------+                 +-------+
 --R              | 2    2              | 2    2                  | 2    2
 --R       - log(\|x  + a   + a) + log(\|x  + a   - x + a) - log(\|x  + a   - x - a)
@@ -389,6 +389,17 @@ dd:=divlog cc
 --R     2a
 --R                                                     Type: Expression Integer
 --E
+
+--S 28     14:188 Schaums and Axiom differ by a constant
+ee:=complexNormalize dd
+
+        log(- 1)
+   (5)  --------
+             3
+           2a
+                                                     Type: Expression Integer
+--E
+
 @
 
 \section{\cite{1}:14.189~~~~~$\displaystyle\int{\sqrt{x^2+a^2}}~dx$}
@@ -398,7 +409,7 @@ $$
 <<*>>=
 )clear all
 
---S 28
+--S 29
 aa:=integrate(sqrt(x^2+a^2),x)
 --R 
 --R
@@ -417,7 +428,7 @@ aa:=integrate(sqrt(x^2+a^2),x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
 
---S 29
+--S 30
 bb:=(x*sqrt(x^2+a^2))/2+a^2/2*log(x+sqrt(x^2+a^2))
 --R
 --R               +-------+          +-------+
@@ -428,7 +439,7 @@ bb:=(x*sqrt(x^2+a^2))/2+a^2/2*log(x+sqrt(x^2+a^2))
 --R                                                     Type: Expression Integer
 --E
 
---S 30     14:189 Axiom cannot simplify this expression
+--S 31
 cc:=aa-bb
 --R
 --R                 +-------+               +-------+
@@ -438,6 +449,17 @@ cc:=aa-bb
 --R                               2
 --R                                                     Type: Expression Integer
 --E
+
+--S 32     14:189 Schaums and Axiom differ by a constant
+dd:=complexNormalize cc
+--R
+--R           2     2
+--R          a log(a )
+--R   (4)  - ---------
+--R              2
+--R                                                     Type: Expression Integer
+--E
+
 @
 
 \section{\cite{1}:14.190~~~~~$\displaystyle\int{x\sqrt{x^2+a^2}}~dx$}
@@ -447,7 +469,7 @@ $$
 <<*>>=
 )clear all
 
---S 31
+--S 33
 aa:=integrate(x*sqrt(x^2+a^2),x)
 --R 
 --R
@@ -461,7 +483,7 @@ aa:=integrate(x*sqrt(x^2+a^2),x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
 
---S 32
+--S 34
 bb:=(x^2+a^2)^(3/2)/3
 --R
 --R                  +-------+
@@ -472,7 +494,7 @@ bb:=(x^2+a^2)^(3/2)/3
 --R                                                     Type: Expression Integer
 --E
 
---S 33     14:190 Schaums and Axiom agree
+--S 35     14:190 Schaums and Axiom agree
 cc:=aa-bb
 --R
 --R   (3)  0
@@ -489,7 +511,7 @@ $$
 <<*>>=
 )clear all
 
---S 34
+--S 36
 aa:=integrate(x^2*sqrt(x^2+a^2),x)
 --R 
 --R
@@ -508,7 +530,7 @@ aa:=integrate(x^2*sqrt(x^2+a^2),x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
 
---S 35
+--S 37
 bb:=(x*(x^2+a^2)^(3/2))/4-(a^2*x*sqrt(x^2+a^2))/8-a^4/8*log(x+sqrt(x^2+a^2))
 --R
 --R                 +-------+                    +-------+
@@ -519,7 +541,7 @@ bb:=(x*(x^2+a^2)^(3/2))/4-(a^2*x*sqrt(x^2+a^2))/8-a^4/8*log(x+sqrt(x^2+a^2))
 --R                                                     Type: Expression Integer
 --E
 
---S 36     14:191 Axiom cannot simplify this expression
+--S 38
 cc:=aa-bb
 --R
 --R               +-------+               +-------+
@@ -529,6 +551,16 @@ cc:=aa-bb
 --R                              8
 --R                                                     Type: Expression Integer
 --E
+
+--S 39     14:191 Schaums and Axiom differ by a constant
+dd:=complexNormalize cc
+--R
+--R         4     2
+--R        a log(a )
+--R   (4)  ---------
+--R            8
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.192~~~~~$\displaystyle
@@ -539,7 +571,7 @@ $$
 <<*>>=
 )clear all
 
---S 37
+--S 40
 aa:=integrate(x^3*sqrt(x^2+a^2),x)
 --R 
 --R
@@ -557,7 +589,7 @@ aa:=integrate(x^3*sqrt(x^2+a^2),x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
 
---S 38
+--S 41
 bb:=(x^2+a^2)^(5/2)/5-(a^2*(x^2+a^2)^(3/2))/3
 --R
 --R                           +-------+
@@ -568,7 +600,7 @@ bb:=(x^2+a^2)^(5/2)/5-(a^2*(x^2+a^2)^(3/2))/3
 --R                                                     Type: Expression Integer
 --E
 
---S 39     14:192 Schaums and Axiom agree
+--S 42     14:192 Schaums and Axiom agree
 cc:=aa-bb
 --R
 --R   (3)  0
@@ -584,7 +616,7 @@ $$
 <<*>>=
 )clear all
 
---S 40
+--S 43
 aa:=integrate(sqrt(x^2+a^2)/x,x)
 --R 
 --R
@@ -603,7 +635,7 @@ aa:=integrate(sqrt(x^2+a^2)/x,x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
 
---S 41
+--S 44
 bb:=sqrt(x^2+a^2)-a*log((a+sqrt(x^2+a^2))/x)
 --R
 --R                 +-------+
@@ -614,7 +646,7 @@ bb:=sqrt(x^2+a^2)-a*log((a+sqrt(x^2+a^2))/x)
 --R                                                     Type: Expression Integer
 --E
 
---S 42     14:193 Axiom cannot simplify this expression
+--S 45
 cc:=aa-bb
 --R
 --R   (3)
@@ -629,6 +661,27 @@ cc:=aa-bb
 --R                  x
 --R                                                     Type: Expression Integer
 --E
+
+--S 46
+dd:=expandLog cc
+--R
+--R   (4)
+--R            +-------+               +-------+
+--R            | 2    2                | 2    2
+--R     a log(\|x  + a   + a) - a log(\|x  + a   - x + a)
+--R   + 
+--R            +-------+
+--R            | 2    2
+--R     a log(\|x  + a   - x - a) - a log(x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 47     14:193 Schaums and Axiom differ by a constant
+ee:=complexNormalize dd
+--R
+--R   (5)  - a log(- 1)
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.194~~~~~$\displaystyle
@@ -639,7 +692,7 @@ $$
 <<*>>=
 )clear all
 
---S 43
+--S 48
 aa:=integrate(sqrt(x^2+a^2)/x^2,x)
 --R 
 --R
@@ -653,7 +706,7 @@ aa:=integrate(sqrt(x^2+a^2)/x^2,x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
 
---S 44
+--S 49
 bb:=-sqrt(x^2+a^2)/x+log(x+sqrt(x^2+a^2))
 --R
 --R               +-------+         +-------+
@@ -664,7 +717,7 @@ bb:=-sqrt(x^2+a^2)/x+log(x+sqrt(x^2+a^2))
 --R                                                     Type: Expression Integer
 --E
 
---S 45     14:194 Axiom cannot simplify this expression
+--S 50
 cc:=aa-bb
 --R
 --R               +-------+             +-------+
@@ -672,6 +725,15 @@ cc:=aa-bb
 --R   (3)  - log(\|x  + a   + x) - log(\|x  + a   - x) - 1
 --R                                                     Type: Expression Integer
 --E
+
+--S 51     14:194 Schaums and Axiom differ by a constant
+dd:=complexNormalize cc
+--R
+--R               2
+--R   (4)  - log(a ) - 1
+--R                                                     Type: Expression Integer
+--E
+
 @
 
 \section{\cite{1}:14.195~~~~~$\displaystyle
@@ -683,7 +745,7 @@ $$
 <<*>>=
 )clear all
 
---S 46
+--S 52
 aa:=integrate(sqrt(x^2+a^2)/x^3,x)
 --R 
 --R
@@ -706,7 +768,7 @@ aa:=integrate(sqrt(x^2+a^2)/x^3,x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
 
---S 47
+--S 53
 bb:=-sqrt(x^2+a^2)/(2*x^2)-1/(2*a)*log((a+sqrt(x^2+a^2))/x)
 --R
 --R                 +-------+
@@ -720,7 +782,7 @@ bb:=-sqrt(x^2+a^2)/(2*x^2)-1/(2*a)*log((a+sqrt(x^2+a^2))/x)
 --R                                                     Type: Expression Integer
 --E
 
---S 48
+--S 54
 cc:=aa-bb
 --R
 --R   (3)
@@ -734,19 +796,10 @@ cc:=aa-bb
 --R                                                     Type: Expression Integer
 --E
 
---S 49
-divlog:=rule(log(a/b) == log(a) - log(b))
---R
---R            a
---R   (4)  log(-) == - log(b) + log(a)
---R            b
---R                        Type: RewriteRule(Integer,Integer,Expression Integer)
---E
-
---S 50     14:195 Axiom cannot simplify this expression
-dd:=divlog cc
+--S 55
+dd:=expandLog cc
 --R
---R   (5)
+--R   (4)
 --R            +-------+             +-------+                 +-------+
 --R            | 2    2              | 2    2                  | 2    2
 --R       log(\|x  + a   + a) - log(\|x  + a   - x + a) + log(\|x  + a   - x - a)
@@ -756,6 +809,15 @@ dd:=divlog cc
 --R     2a
 --R                                                     Type: Expression Integer
 --E
+
+--S 56     14:195 Schaums and Axiom differ by a constant
+ee:=complexNormalize dd
+--R
+--R          log(- 1)
+--R   (5)  - --------
+--R             2a
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.196~~~~~$\displaystyle\int{\frac{dx}{(x^2+a^2)^{3/2}}}$}
@@ -765,7 +827,7 @@ $$
 <<*>>=
 )clear all
 
---S 51
+--S 57
 aa:=integrate(1/(x^2+a^2)^(3/2),x)
 --R 
 --R
@@ -777,7 +839,7 @@ aa:=integrate(1/(x^2+a^2)^(3/2),x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
 
---S 52
+--S 58
 bb:=x/(a^2*sqrt(x^2+a^2))
 --R
 --R              x
@@ -788,7 +850,7 @@ bb:=x/(a^2*sqrt(x^2+a^2))
 --R                                                     Type: Expression Integer
 --E
 
---S 53     14:196 Schaums and Axiom differ by a constant
+--S 59     14:196 Schaums and Axiom differ by a constant
 cc:=aa-bb
 --R
 --R         1
@@ -807,7 +869,7 @@ $$
 <<*>>=
 )clear all
 
---S 54
+--S 60
 aa:=integrate(x/(x^2+a^2)^(3/2),x)
 --R 
 --R
@@ -821,7 +883,7 @@ aa:=integrate(x/(x^2+a^2)^(3/2),x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
 
---S 55
+--S 61
 bb:=-1/sqrt(x^2+a^2)
 --R
 --R               1
@@ -832,7 +894,7 @@ bb:=-1/sqrt(x^2+a^2)
 --R                                                     Type: Expression Integer
 --E
 
---S 56     14:197 Schaums and Axiom agree
+--S 62     14:197 Schaums and Axiom agree
 cc:=aa-bb
 --R
 --R   (3)  0
@@ -849,7 +911,7 @@ $$
 <<*>>=
 )clear all
 
---S 57
+--S 63
 aa:=integrate(x^2/(x^2+a^2)^(3/2),x)
 --R 
 --R
@@ -863,7 +925,7 @@ aa:=integrate(x^2/(x^2+a^2)^(3/2),x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
 
---S 58
+--S 64
 bb:=-x/sqrt(x^2+a^2)+log(x+sqrt(x^2+a^2))
 --R
 --R         +-------+     +-------+
@@ -876,7 +938,7 @@ bb:=-x/sqrt(x^2+a^2)+log(x+sqrt(x^2+a^2))
 --R                                                     Type: Expression Integer
 --E
 
---S 59     14:198 Axiom cannot simplify this expression
+--S 65
 cc:=aa-bb
 --R
 --R               +-------+             +-------+
@@ -884,6 +946,14 @@ cc:=aa-bb
 --R   (3)  - log(\|x  + a   + x) - log(\|x  + a   - x) - 1
 --R                                                     Type: Expression Integer
 --E
+
+--S 66     14:198 Schaums and Axiom differ by a constant
+dd:=complexNormalize cc
+--R
+--R               2
+--R   (4)  - log(a ) - 1
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.199~~~~~$\displaystyle
@@ -894,7 +964,7 @@ $$
 <<*>>=
 )clear all
 
---S 60
+--S 67
 aa:=integrate(x^3/(x^2+a^2)^(3/2),x)
 --R 
 --R
@@ -908,7 +978,7 @@ aa:=integrate(x^3/(x^2+a^2)^(3/2),x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
 
---S 61
+--S 68
 bb:=sqrt(x^2+a^2)+a^2/sqrt(x^2+a^2)
 --R
 --R          2     2
@@ -920,7 +990,7 @@ bb:=sqrt(x^2+a^2)+a^2/sqrt(x^2+a^2)
 --R                                                     Type: Expression Integer
 --E
 
---S 62     14:199 Schaums and Axiom agree
+--S 69     14:199 Schaums and Axiom agree
 cc:=aa-bb
 --R
 --R   (3)  0
@@ -937,7 +1007,7 @@ $$
 <<*>>=
 )clear all
 
---S 63
+--S 70
 aa:=integrate(1/(x*(x^2+a^2)^(3/2)),x)
 --R 
 --R
@@ -956,7 +1026,7 @@ aa:=integrate(1/(x*(x^2+a^2)^(3/2)),x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
 
---S 64
+--S 71
 bb:=1/(a^2*sqrt(x^2+a^2))-1/a^3*log((a+sqrt(x^2+a^2))/x)
 --R
 --R                         +-------+
@@ -971,7 +1041,7 @@ bb:=1/(a^2*sqrt(x^2+a^2))-1/a^3*log((a+sqrt(x^2+a^2))/x)
 --R                                                     Type: Expression Integer
 --E
 
---S 65
+--S 72
 cc:=aa-bb
 --R
 --R   (3)
@@ -986,19 +1056,10 @@ cc:=aa-bb
 --R                                                     Type: Expression Integer
 --E
 
---S 66
-divlog:=rule(log(a/b) == log(a) - log(b))
---R
---R            a
---R   (4)  log(-) == - log(b) + log(a)
---R            b
---R                        Type: RewriteRule(Integer,Integer,Expression Integer)
---E
-
---S 67     14:200 Axiom cannot simplify this expression
-dd:=divlog cc
+--S 73
+dd:=expandLog cc
 --R
---R   (5)
+--R   (4)
 --R            +-------+             +-------+                 +-------+
 --R            | 2    2              | 2    2                  | 2    2
 --R       log(\|x  + a   + a) - log(\|x  + a   - x + a) + log(\|x  + a   - x - a)
@@ -1009,6 +1070,17 @@ dd:=divlog cc
 --R     a
 --R                                                     Type: Expression Integer
 --E
+
+--S 74     14:200 Schaums and Axiom differ by a constant
+ee:=complexNormalize dd
+--R
+--R          log(- 1)
+--R   (5)  - --------
+--R              3
+--R             a
+--R                                                     Type: Expression Integer
+--E
+
 @
 
 \section{\cite{1}:14.201~~~~~$\displaystyle
@@ -1019,7 +1091,7 @@ $$
 <<*>>=
 )clear all
 
---S 68
+--S 75
 aa:=integrate(1/(x^2*(x^2+a^2)^(3/2)),x)
 --R 
 --R
@@ -1031,7 +1103,7 @@ aa:=integrate(1/(x^2*(x^2+a^2)^(3/2)),x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
 
---S 69
+--S 76
 bb:=-sqrt(x^2+a^2)/(a^4*x)-x/(a^4*sqrt(x^2+a^2))
 --R
 --R              2    2
@@ -1043,7 +1115,7 @@ bb:=-sqrt(x^2+a^2)/(a^4*x)-x/(a^4*sqrt(x^2+a^2))
 --R                                                     Type: Expression Integer
 --E
 
---S 70     14:201 Schaums and Axiom differ by a constant
+--S 77     14:201 Schaums and Axiom differ by a constant
 cc:=aa-bb
 --R
 --R           2
@@ -1064,7 +1136,7 @@ $$
 <<*>>=
 )clear all
 
---S 71
+--S 78
 aa:=integrate(1/(x^3*(x^2+a^2)^(3/2)),x)
 --R 
 --R
@@ -1091,7 +1163,7 @@ aa:=integrate(1/(x^3*(x^2+a^2)^(3/2)),x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
 
---S 72
+--S 79
 bb:=-1/(2*a^2*x^2*sqrt(x^2+a^2))-3/(2*a^4*sqrt(x^2+a^2))+3/(2*a^5)*log((a+sqrt(x^2+a^2))/x)
 --R
 --R                          +-------+
@@ -1106,7 +1178,7 @@ bb:=-1/(2*a^2*x^2*sqrt(x^2+a^2))-3/(2*a^4*sqrt(x^2+a^2))+3/(2*a^5)*log((a+sqrt(x
 --R                                                     Type: Expression Integer
 --E
 
---S 73
+--S 80
 cc:=aa-bb
 --R
 --R   (3)
@@ -1121,19 +1193,10 @@ cc:=aa-bb
 --R                                                     Type: Expression Integer
 --E
 
---S 74
-divlog:=rule(log(a/b) == log(a) - log(b))
---R
---R            a
---R   (4)  log(-) == - log(b) + log(a)
---R            b
---R                        Type: RewriteRule(Integer,Integer,Expression Integer)
---E
-
---S 75     14:202 Axiom cannot simplify this expression
-dd:=divlog cc
+--S 81
+dd:=expandLog cc
 --R
---R   (5)
+--R   (4)
 --R               +-------+              +-------+
 --R               | 2    2               | 2    2
 --R       - 3log(\|x  + a   + a) + 3log(\|x  + a   - x + a)
@@ -1146,6 +1209,16 @@ dd:=divlog cc
 --R     2a
 --R                                                     Type: Expression Integer
 --E
+
+--S 82     14:202 Schaums and Axiom differ by a constant
+ee:=complexNormalize dd
+--R
+--R        3log(- 1)
+--R   (5)  ---------
+--R             5
+--R           2a
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.203~~~~~$\displaystyle\int{(x^2+a^2)^{3/2}}~dx$}
@@ -1156,7 +1229,7 @@ $$
 <<*>>=
 )clear all
 
---S 76
+--S 83
 aa:=integrate((x^2+a^2)^(3/2),x)
 --R
 --R   (1)
@@ -1177,7 +1250,7 @@ aa:=integrate((x^2+a^2)^(3/2),x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
 
---S 77
+--S 84
 bb:=(x*(x^2+a^2)^(3/2))/4+(3*a^2*x*sqrt(x^2+a^2))/8+3/8*a^4*log(x+sqrt(x^2+a^2))
 --R
 --R                +-------+                     +-------+
@@ -1188,7 +1261,7 @@ bb:=(x*(x^2+a^2)^(3/2))/4+(3*a^2*x*sqrt(x^2+a^2))/8+3/8*a^4*log(x+sqrt(x^2+a^2))
 --R                                                     Type: Expression Integer
 --E
 
---S 78     14:203 Axiom cannot simplify this expression
+--S 85
 cc:=aa-bb
 --R
 --R                  +-------+                +-------+
@@ -1198,6 +1271,16 @@ cc:=aa-bb
 --R                                8
 --R                                                     Type: Expression Integer
 --E
+
+--S 86     14:203 Schaums and Axiom differ by a constant
+dd:=complexNormalize cc
+--R
+--R            4     2
+--R          3a log(a )
+--R   (4)  - ----------
+--R               8
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.204~~~~~$\displaystyle\int{x(x^2+a^2)^{3/2}}~dx$}
@@ -1205,7 +1288,7 @@ $$\int{x(x^2+a^2)^{3/2}}=\frac{(x^2+a^2)^{5/2}}{5}$$
 <<*>>=
 )clear all
 
---S 79
+--S 87
 aa:=integrate(x*(x^2+a^2)^(3/2),x)
 --R 
 --R
@@ -1223,7 +1306,7 @@ aa:=integrate(x*(x^2+a^2)^(3/2),x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
 
---S 80
+--S 88
 bb:=(x^2+a^2)^(5/2)/5
 --R
 --R                          +-------+
@@ -1234,7 +1317,7 @@ bb:=(x^2+a^2)^(5/2)/5
 --R                                                     Type: Expression Integer
 --E
 
---S 81     14:204 Schaums and Axiom agree
+--S 89     14:204 Schaums and Axiom agree
 cc:=aa-bb
 --R
 --R   (3)  0
@@ -1251,7 +1334,7 @@ $$
 <<*>>=
 )clear all
 
---S 82
+--S 90
 aa:=integrate(x^2*(x^2+a^2)^(3/2),x)
 --R 
 --R
@@ -1280,7 +1363,7 @@ aa:=integrate(x^2*(x^2+a^2)^(3/2),x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
 
---S 83
+--S 91
 bb:=(x*(x^2+a^2)^(5/2))/6-(a^2*x*(x^2+a^2)^(3/2))/24-(a^4*x*sqrt(x^2+a^2))/16-a^6/16*log(x+sqrt(x^2+a^2))
 --R
 --R                  +-------+                              +-------+
@@ -1291,7 +1374,7 @@ bb:=(x*(x^2+a^2)^(5/2))/6-(a^2*x*(x^2+a^2)^(3/2))/24-(a^4*x*sqrt(x^2+a^2))/16-a^
 --R                                                     Type: Expression Integer
 --E
 
---S 84     14:205 Axiom cannot simplify this expression
+--S 92
 cc:=aa-bb
 --R
 --R               +-------+               +-------+
@@ -1301,6 +1384,16 @@ cc:=aa-bb
 --R                              16
 --R                                                     Type: Expression Integer
 --E
+
+--S 93     14:205 Schaums and Axiom differ by a constant
+dd:=complexNormalize cc
+--R
+--R         6     2
+--R        a log(a )
+--R   (4)  ---------
+--R            16
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.206~~~~~$\displaystyle\int{x^3(x^2+a^2)^{3/2}}~dx$}
@@ -1310,7 +1403,7 @@ $$
 <<*>>=
 )clear all
 
---S 85
+--S 94
 aa:=integrate(x^3*(x^2+a^2)^(3/2),x)
 --R 
 --R
@@ -1340,7 +1433,7 @@ aa:=integrate(x^3*(x^2+a^2)^(3/2),x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
 
---S 86
+--S 95
 bb:=(x^2+a^2)^(7/2)/7-(a^2*(x^2+a^2)^(5/2))/5
 --R
 --R                                   +-------+
@@ -1351,7 +1444,7 @@ bb:=(x^2+a^2)^(7/2)/7-(a^2*(x^2+a^2)^(5/2))/5
 --R                                                     Type: Expression Integer
 --E
 
---S 87     14:206 Schaums and Axiom agree
+--S 96     14:206 Schaums and Axiom agree
 cc:=aa-bb
 --R
 --R   (3)  0
@@ -1368,7 +1461,7 @@ $$
 <<*>>=
 )clear all
 
---S 88
+--S 97
 aa:=integrate((x^2+a^2)^(3/2)/x,x)
 --R 
 --R
@@ -1391,7 +1484,7 @@ aa:=integrate((x^2+a^2)^(3/2)/x,x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
 
---S 89
+--S 98
 bb:=(x^2+a^2)^(3/2)/3+a^2*sqrt(x^2+a^2)-a^3*log((a+sqrt(x^2+a^2))/x)
 --R
 --R                  +-------+
@@ -1404,7 +1497,7 @@ bb:=(x^2+a^2)^(3/2)/3+a^2*sqrt(x^2+a^2)-a^3*log((a+sqrt(x^2+a^2))/x)
 --R                                                     Type: Expression Integer
 --E
 
---S 90
+--S 99
 cc:=aa-bb
 --R
 --R   (3)
@@ -1420,19 +1513,10 @@ cc:=aa-bb
 --R                                                     Type: Expression Integer
 --E
 
---S 91
-divlog:=rule(log(a/b) == log(a) - log(b))
+--S 100
+dd:=expandLog cc
 --R
---R            a
---R   (4)  log(-) == - log(b) + log(a)
---R            b
---R                        Type: RewriteRule(Integer,Integer,Expression Integer)
---E
-
---S 92     14:207 Axiom cannot simplify this expression
-dd:=divlog cc
---R
---R   (5)
+--R   (4)
 --R            +-------+               +-------+
 --R      3     | 2    2          3     | 2    2
 --R     a log(\|x  + a   + a) - a log(\|x  + a   - x + a)
@@ -1442,6 +1526,14 @@ dd:=divlog cc
 --R     a log(\|x  + a   - x - a) - a log(x)
 --R                                                     Type: Expression Integer
 --E
+
+--S 101    14:207 Schaums and Axiom differ by a constant
+ee:=complexNormalize dd
+--R
+--R           3
+--R   (5)  - a log(- 1)
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.208~~~~~$\displaystyle
@@ -1453,7 +1545,7 @@ $$
 <<*>>=
 )clear all
 
---S 93
+--S 102
 aa:=integrate((x^2+a^2)^{3/2}/x^2,x)
 --R 
 --R
@@ -1472,7 +1564,7 @@ aa:=integrate((x^2+a^2)^{3/2}/x^2,x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
 
---S 94
+--S 103
 bb:=-(x^2+a^2)^(3/2)/x+(3*x*sqrt(x^2+a^2))/2+3/2*a^2*log(x+sqrt(x^2+a^2))
 --R
 --R                  +-------+                   +-------+
@@ -1483,7 +1575,7 @@ bb:=-(x^2+a^2)^(3/2)/x+(3*x*sqrt(x^2+a^2))/2+3/2*a^2*log(x+sqrt(x^2+a^2))
 --R                                                     Type: Expression Integer
 --E
 
---S 95     14:208 Axiom cannot simplify this expression
+--S 104
 cc:=aa-bb
 --R
 --R                  +-------+                +-------+
@@ -1493,6 +1585,17 @@ cc:=aa-bb
 --R                                   2
 --R                                                     Type: Expression Integer
 --E
+
+--S 105    14:208 Schaums and Axiom differ by a constant
+dd:=complexNormalize cc
+--R
+--R            2     2      2
+--R        - 3a log(a ) - 2a
+--R   (4)  ------------------
+--R                 2
+--R                                                     Type: Expression Integer
+--E
+
 @
 
 \section{\cite{1}:14.209~~~~~$\displaystyle
@@ -1504,7 +1607,7 @@ $$
 <<*>>=
 )clear all
 
---S 96
+--S 106
 aa:=integrate((x^2+a^2)^(3/2)/x^3,x)
 --R 
 --R
@@ -1527,48 +1630,60 @@ aa:=integrate((x^2+a^2)^(3/2)/x^3,x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
 
---S 97
-bb:=-(x^2+a^2)^(3/2)/(2*x^3)+3/2*sqrt(x^2+a^2)-3/2*a*log((a+sqrt(x^2+a^2))/x)
+--S 107
+bb:=-(x^2+a^2)^(3/2)/(2*x^2)+3/2*sqrt(x^2+a^2)-3/2*a*log((a+sqrt(x^2+a^2))/x)
 --R
 --R                    +-------+
---R                    | 2    2                         +-------+
---R              3    \|x  + a   + a       3    2    2  | 2    2
---R        - 3a x log(--------------) + (3x  - x  - a )\|x  + a
+--R                    | 2    2                    +-------+
+--R              2    \|x  + a   + a       2    2  | 2    2
+--R        - 3a x log(--------------) + (2x  - a )\|x  + a
 --R                          x
---R   (2)  ------------------------------------------------------
---R                                    3
---R                                  2x
+--R   (2)  -------------------------------------------------
+--R                                 2
+--R                               2x
 --R                                                     Type: Expression Integer
 --E
 
---S 98     14:209 Axiom cannot simplify this expression
+--S 108
 cc:=aa-bb
 --R
 --R   (3)
---R                           +-------+                       +-------+
---R                5     3 3  | 2    2         6     3 4      | 2    2
---R       ((- 12a x  - 3a x )\|x  + a   + 12a x  + 9a x )log(\|x  + a   - x + a)
---R     + 
---R                         +-------+                       +-------+
---R              5     3 3  | 2    2         6     3 4      | 2    2
---R       ((12a x  + 3a x )\|x  + a   - 12a x  - 9a x )log(\|x  + a   - x - a)
---R     + 
---R                                                         +-------+
---R                         +-------+                       | 2    2
---R              5     3 3  | 2    2         6     3 4     \|x  + a   + a
---R       ((12a x  + 3a x )\|x  + a   - 12a x  - 9a x )log(--------------)
---R                                                               x
+--R                 +-------+                    +-------+
+--R                 | 2    2                     | 2    2
+--R       - 3a log(\|x  + a   - x + a) + 3a log(\|x  + a   - x - a)
 --R     + 
---R                                                  +-------+
---R          6     5     2 4     2 3     4 2     4   | 2    2      7     6     2 5
---R       (4x  - 4x  + 7a x  - 7a x  + 3a x  - 3a x)\|x  + a   - 4x  + 4x  - 9a x
+--R               +-------+
+--R               | 2    2
+--R              \|x  + a   + a
+--R       3a log(--------------)
+--R                     x
+--R  /
+--R     2
+--R                                                     Type: Expression Integer
+--E
+
+--S 109
+dd:=expandLog cc
+--R
+--R   (4)
+--R               +-------+                +-------+
+--R               | 2    2                 | 2    2
+--R       3a log(\|x  + a   + a) - 3a log(\|x  + a   - x + a)
 --R     + 
---R         2 4     4 3     4 2    6     6
---R       9a x  - 6a x  + 6a x  - a x + a
+--R               +-------+
+--R               | 2    2
+--R       3a log(\|x  + a   - x - a) - 3a log(x)
 --R  /
---R                   +-------+
---R        5     2 3  | 2    2      6     2 4
---R     (8x  + 2a x )\|x  + a   - 8x  - 6a x
+--R     2
+--R                                                     Type: Expression Integer
+--E
+
+--S 110    14:209 Schaums and Axiom differ by a constant
+ee:=complexNormalize dd
+--R
+--R          3a log(- 1)
+--R   (5)  - -----------
+--R               2
 --R                                                     Type: Expression Integer
 --E
 



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schaum12.input.pamphlet
  14:265 Axiom cannot simplify these expressions
  14:266 Axiom cannot simplify these expressions
  14:267 Schaums and Axiom differ by a constant
  14:268 Axiom cannot compute this integral
  14:269 Schaums and Axiom differ by a constant
  14:270 Schaums and Axiom differ by a constant
  14:271 Axiom cannot compute this integral
  14:272 Axiom cannot simplify these expressions
  14:273 Schaums and Axiom differ by a constant
  14:274 Schaums and Axiom agree
  14:275 Axiom cannot compute this integral
  14:276 Axiom cannot compute this integral
  14:277 Schaums and Axiom differ by a constant
  14:278 Schaums and Axiom differ by a constant
  14:279 Axiom cannot compute this integral

=========================================================================
diff --git a/changelog b/changelog
index c10550c..d61af40 100644
--- a/changelog
+++ b/changelog
@@ -1,3 +1,4 @@
+20080419 tpd src/input/schaum12.input show Schaums-Axiom equivalence
 20080418 tpd src/input/schaum11.input show Schaums-Axiom equivalence
 20080418 tpd src/input/schaum10.input fix Schaums-Axiom equivalence
 20080418 tpd src/input/schaum9.input fix Schaums-Axiom equivalence
diff --git a/src/input/schaum12.input.pamphlet b/src/input/schaum12.input.pamphlet
index 644ebed..1c0d0b2 100644
--- a/src/input/schaum12.input.pamphlet
+++ b/src/input/schaum12.input.pamphlet
@@ -24,7 +24,7 @@ $$
 )set message auto off
 )clear all
 
---S 1 of 15
+--S 1
 aa:=integrate(1/sqrt(a*x^2+b*x+c),x)
 --R 
 --R
@@ -55,6 +55,152 @@ aa:=integrate(1/sqrt(a*x^2+b*x+c),x)
 --R                       \|- a
 --R                                     Type: Union(List Expression Integer,...)
 --E 
+
+--S 2
+bb1:=2/sqrt(4*a*c-b^2)*atan((2*a*x+b)/sqrt(4*a*c-b^2))
+--R 
+--R
+--R                2a x + b
+--R        2atan(------------)
+--R               +---------+
+--R               |        2
+--R              \|4a c - b
+--R   (2)  -------------------
+--R             +---------+
+--R             |        2
+--R            \|4a c - b
+--R                                                     Type: Expression Integer
+--E
+
+--S 3
+bb2:=1/sqrt(b^2-4*a*c)*log((2*a*x+b-sqrt(b^2-4*a*c))/(2*a*x+b+sqrt(b^2-4*a*c)))
+--R 
+--R
+--R               +-----------+
+--R               |          2
+--R            - \|- 4a c + b   + 2a x + b
+--R        log(---------------------------)
+--R              +-----------+
+--R              |          2
+--R             \|- 4a c + b   + 2a x + b
+--R   (3)  --------------------------------
+--R                  +-----------+
+--R                  |          2
+--R                 \|- 4a c + b
+--R                                                     Type: Expression Integer
+--E
+
+--S 4
+cc1:=aa.1-bb1
+--R
+--R   (4)
+--R          +---------+
+--R          |        2
+--R         \|4a c - b
+--R      *
+--R         log
+--R                                   +--------------+
+--R                   +-+ +-+         |   2                   +-+
+--R                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
+--R              + 
+--R                       2             +-+
+--R                (- 2a x  - b x - 2c)\|a
+--R           /
+--R                    +--------------+
+--R                +-+ |   2
+--R              2\|c \|a x  + b x + c  - b x - 2c
+--R     + 
+--R           +-+       2a x + b
+--R       - 2\|a atan(------------)
+--R                    +---------+
+--R                    |        2
+--R                   \|4a c - b
+--R  /
+--R          +---------+
+--R      +-+ |        2
+--R     \|a \|4a c - b
+--R                                                     Type: Expression Integer
+--E
+
+--S 5
+cc2:=aa.1-bb2
+--R
+--R   (5)
+--R          +-----------+
+--R          |          2
+--R         \|- 4a c + b
+--R      *
+--R         log
+--R                                   +--------------+
+--R                   +-+ +-+         |   2                   +-+
+--R                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
+--R              + 
+--R                       2             +-+
+--R                (- 2a x  - b x - 2c)\|a
+--R           /
+--R                    +--------------+
+--R                +-+ |   2
+--R              2\|c \|a x  + b x + c  - b x - 2c
+--R     + 
+--R                    +-----------+
+--R                    |          2
+--R          +-+    - \|- 4a c + b   + 2a x + b
+--R       - \|a log(---------------------------)
+--R                   +-----------+
+--R                   |          2
+--R                  \|- 4a c + b   + 2a x + b
+--R  /
+--R      +-----------+
+--R      |          2  +-+
+--R     \|- 4a c + b  \|a
+--R                                                     Type: Expression Integer
+--E
+
+--S 6
+cc3:=aa.2-bb1
+--R
+--R   (6)
+--R                                +--------------+
+--R         +---------+      +---+ |   2               +---+ +-+
+--R         |        2      \|- a \|a x  + b x + c  - \|- a \|c
+--R       2\|4a c - b  atan(------------------------------------)
+--R                                          a x
+--R     + 
+--R           +---+       2a x + b
+--R       - 2\|- a atan(------------)
+--R                      +---------+
+--R                      |        2
+--R                     \|4a c - b
+--R  /
+--R            +---------+
+--R      +---+ |        2
+--R     \|- a \|4a c - b
+--R                                                     Type: Expression Integer
+--E
+
+--S 7      14:265 Axiom cannot simplify these expressions
+cc4:=aa.2-bb2
+--R
+--R   (7)
+--R                      +-----------+
+--R                      |          2
+--R          +---+    - \|- 4a c + b   + 2a x + b
+--R       - \|- a log(---------------------------)
+--R                     +-----------+
+--R                     |          2
+--R                    \|- 4a c + b   + 2a x + b
+--R     + 
+--R                                  +--------------+
+--R         +-----------+      +---+ |   2               +---+ +-+
+--R         |          2      \|- a \|a x  + b x + c  - \|- a \|c
+--R       2\|- 4a c + b  atan(------------------------------------)
+--R                                            a x
+--R  /
+--R      +-----------+
+--R      |          2  +---+
+--R     \|- 4a c + b  \|- a
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.266~~~~~$\displaystyle
@@ -65,7 +211,7 @@ $$
 <<*>>=
 )clear all
 
---S 2 of 15
+--S 8
 aa:=integrate(x/sqrt(a*x^2+b*x+c),x)
 --R 
 --R
@@ -116,6 +262,316 @@ aa:=integrate(x/sqrt(a*x^2+b*x+c),x)
 --R     ]
 --R                                     Type: Union(List Expression Integer,...)
 --E 
+
+--S 9
+t1:=integrate(1/(a*x^2+b*x+c),x)
+--R 
+--R
+--R   (2)
+--R   [
+--R       log
+--R                                           +-----------+
+--R                 2 2                    2  |          2       2        2
+--R              (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
+--R            + 
+--R                        3
+--R              4a b c - b
+--R         /
+--R               2
+--R            a x  + b x + c
+--R    /
+--R        +-----------+
+--R        |          2
+--R       \|- 4a c + b
+--R     ,
+--R                     +---------+
+--R                     |        2
+--R          (2a x + b)\|4a c - b
+--R    2atan(----------------------)
+--R                         2
+--R                 4a c - b
+--R    -----------------------------]
+--R              +---------+
+--R              |        2
+--R             \|4a c - b
+--R                                     Type: Union(List Expression Integer,...)
+--E
+
+--S 10
+bb1:=1/(2*a)*log(a*x^2+b*x+c)-b/(2*a)*t1.1
+--R 
+--R
+--R   (3)
+--R       -
+--R            b
+--R         *
+--R            log
+--R                                                +-----------+
+--R                      2 2                    2  |          2       2        2
+--R                   (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
+--R                 + 
+--R                             3
+--R                   4a b c - b
+--R              /
+--R                    2
+--R                 a x  + b x + c
+--R     + 
+--R                           +-----------+
+--R              2            |          2
+--R       log(a x  + b x + c)\|- 4a c + b
+--R  /
+--R        +-----------+
+--R        |          2
+--R     2a\|- 4a c + b
+--R                                                     Type: Expression Integer
+--E
+
+--S 11
+bb2:=1/(2*a)*log(a*x^2+b*x+c)-b/(2*a)*t1.2
+--R 
+--R
+--R                             +---------+
+--R                             |        2                         +---------+
+--R                  (2a x + b)\|4a c - b             2            |        2
+--R        - 2b atan(----------------------) + log(a x  + b x + c)\|4a c - b
+--R                                 2
+--R                         4a c - b
+--R   (4)  -------------------------------------------------------------------
+--R                                      +---------+
+--R                                      |        2
+--R                                   2a\|4a c - b
+--R                                                     Type: Expression Integer
+--E
+
+--S 12
+cc1:=aa.1-bb1
+--R
+--R   (5)
+--R             +-----------+     +--------------+                  +-----------+
+--R             |          2  +-+ |   2                  2          |          2
+--R         (2b\|- 4a c + b  \|c \|a x  + b x + c  + (- b x - 2b c)\|- 4a c + b  )
+--R      *
+--R         log
+--R                                   +--------------+
+--R                   +-+ +-+         |   2                   +-+
+--R                (2\|a \|c  + 2a x)\|a x  + b x + c  - 2a x\|c
+--R              + 
+--R                       2             +-+
+--R                (- 2a x  - b x - 2c)\|a
+--R           /
+--R                    +--------------+
+--R                +-+ |   2
+--R              2\|c \|a x  + b x + c  - b x - 2c
+--R     + 
+--R                     +--------------+
+--R             +-+ +-+ |   2                  2          +-+
+--R         (2b\|a \|c \|a x  + b x + c  + (- b x - 2b c)\|a )
+--R      *
+--R         log
+--R                                             +-----------+
+--R                   2 2                    2  |          2       2        2
+--R                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
+--R              + 
+--R                          3
+--R                4a b c - b
+--R           /
+--R                 2
+--R              a x  + b x + c
+--R     + 
+--R                                 +-----------+                +-----------+
+--R                    2            |          2  +-+ +-+        |          2  +-+
+--R         (- 2log(a x  + b x + c)\|- 4a c + b  \|a \|c  - 2b x\|- 4a c + b  \|a )
+--R      *
+--R          +--------------+
+--R          |   2
+--R         \|a x  + b x + c
+--R     + 
+--R                      +-----------+
+--R            2         |          2  +-+ +-+
+--R       (4a x  + 2b x)\|- 4a c + b  \|a \|c
+--R     + 
+--R                                     +-----------+
+--R                        2            |          2  +-+
+--R       (b x + 2c)log(a x  + b x + c)\|- 4a c + b  \|a
+--R  /
+--R          +-----------+         +--------------+
+--R          |          2  +-+ +-+ |   2
+--R       4a\|- 4a c + b  \|a \|c \|a x  + b x + c
+--R     + 
+--R                         +-----------+
+--R                         |          2  +-+
+--R       (- 2a b x - 4a c)\|- 4a c + b  \|a
+--R                                                     Type: Expression Integer
+--E
+
+--S 13
+cc2:=aa.2-bb1
+--R
+--R   (6)
+--R                       +--------------+
+--R             +---+ +-+ |   2                  2          +---+
+--R         (2b\|- a \|c \|a x  + b x + c  + (- b x - 2b c)\|- a )
+--R      *
+--R         log
+--R                                             +-----------+
+--R                   2 2                    2  |          2       2        2
+--R                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
+--R              + 
+--R                          3
+--R                4a b c - b
+--R           /
+--R                 2
+--R              a x  + b x + c
+--R     + 
+--R               +-----------+     +--------------+                 +-----------+
+--R               |          2  +-+ |   2                 2          |          2
+--R         (- 4b\|- 4a c + b  \|c \|a x  + b x + c  + (2b x + 4b c)\|- 4a c + b  )
+--R      *
+--R                     +--------------+
+--R               +---+ |   2               +---+ +-+
+--R              \|- a \|a x  + b x + c  - \|- a \|c
+--R         atan(------------------------------------)
+--R                               a x
+--R     + 
+--R                                  +-----------+
+--R                     2            |          2  +---+ +-+
+--R           - 2log(a x  + b x + c)\|- 4a c + b  \|- a \|c
+--R         + 
+--R                  +-----------+
+--R                  |          2  +---+
+--R           - 2b x\|- 4a c + b  \|- a
+--R      *
+--R          +--------------+
+--R          |   2
+--R         \|a x  + b x + c
+--R     + 
+--R                      +-----------+
+--R            2         |          2  +---+ +-+
+--R       (4a x  + 2b x)\|- 4a c + b  \|- a \|c
+--R     + 
+--R                                     +-----------+
+--R                        2            |          2  +---+
+--R       (b x + 2c)log(a x  + b x + c)\|- 4a c + b  \|- a
+--R  /
+--R          +-----------+           +--------------+
+--R          |          2  +---+ +-+ |   2
+--R       4a\|- 4a c + b  \|- a \|c \|a x  + b x + c
+--R     + 
+--R                         +-----------+
+--R                         |          2  +---+
+--R       (- 2a b x - 4a c)\|- 4a c + b  \|- a
+--R                                                     Type: Expression Integer
+--E
+
+--S 14
+cc3:=aa.2-bb1
+--R
+--R   (7)
+--R                       +--------------+
+--R             +---+ +-+ |   2                  2          +---+
+--R         (2b\|- a \|c \|a x  + b x + c  + (- b x - 2b c)\|- a )
+--R      *
+--R         log
+--R                                             +-----------+
+--R                   2 2                    2  |          2       2        2
+--R                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
+--R              + 
+--R                          3
+--R                4a b c - b
+--R           /
+--R                 2
+--R              a x  + b x + c
+--R     + 
+--R               +-----------+     +--------------+                 +-----------+
+--R               |          2  +-+ |   2                 2          |          2
+--R         (- 4b\|- 4a c + b  \|c \|a x  + b x + c  + (2b x + 4b c)\|- 4a c + b  )
+--R      *
+--R                     +--------------+
+--R               +---+ |   2               +---+ +-+
+--R              \|- a \|a x  + b x + c  - \|- a \|c
+--R         atan(------------------------------------)
+--R                               a x
+--R     + 
+--R                                  +-----------+
+--R                     2            |          2  +---+ +-+
+--R           - 2log(a x  + b x + c)\|- 4a c + b  \|- a \|c
+--R         + 
+--R                  +-----------+
+--R                  |          2  +---+
+--R           - 2b x\|- 4a c + b  \|- a
+--R      *
+--R          +--------------+
+--R          |   2
+--R         \|a x  + b x + c
+--R     + 
+--R                      +-----------+
+--R            2         |          2  +---+ +-+
+--R       (4a x  + 2b x)\|- 4a c + b  \|- a \|c
+--R     + 
+--R                                     +-----------+
+--R                        2            |          2  +---+
+--R       (b x + 2c)log(a x  + b x + c)\|- 4a c + b  \|- a
+--R  /
+--R          +-----------+           +--------------+
+--R          |          2  +---+ +-+ |   2
+--R       4a\|- 4a c + b  \|- a \|c \|a x  + b x + c
+--R     + 
+--R                         +-----------+
+--R                         |          2  +---+
+--R       (- 2a b x - 4a c)\|- 4a c + b  \|- a
+--R                                                     Type: Expression Integer
+--E
+
+--S 15     14:266 Axiom cannot simplify these expressions
+cc4:=aa.2-bb2
+--R
+--R   (8)
+--R                   +---------+ +--------------+                 +---------+
+--R               +-+ |        2  |   2                 2          |        2
+--R         (- 4b\|c \|4a c - b  \|a x  + b x + c  + (2b x + 4b c)\|4a c - b  )
+--R      *
+--R                     +--------------+
+--R               +---+ |   2               +---+ +-+
+--R              \|- a \|a x  + b x + c  - \|- a \|c
+--R         atan(------------------------------------)
+--R                               a x
+--R     + 
+--R                       +--------------+
+--R             +---+ +-+ |   2                   2          +---+
+--R         (4b\|- a \|c \|a x  + b x + c  + (- 2b x - 4b c)\|- a )
+--R      *
+--R                         +---------+
+--R                         |        2
+--R              (2a x + b)\|4a c - b
+--R         atan(----------------------)
+--R                             2
+--R                     4a c - b
+--R     + 
+--R                                                         +---------+
+--R                    2            +---+ +-+        +---+  |        2
+--R         (- 2log(a x  + b x + c)\|- a \|c  - 2b x\|- a )\|4a c - b
+--R      *
+--R          +--------------+
+--R          |   2
+--R         \|a x  + b x + c
+--R     + 
+--R               2         +---+ +-+                    2            +---+
+--R         ((4a x  + 2b x)\|- a \|c  + (b x + 2c)log(a x  + b x + c)\|- a )
+--R      *
+--R          +---------+
+--R          |        2
+--R         \|4a c - b
+--R  /
+--R                    +---------+ +--------------+
+--R          +---+ +-+ |        2  |   2
+--R       4a\|- a \|c \|4a c - b  \|a x  + b x + c
+--R     + 
+--R                               +---------+
+--R                         +---+ |        2
+--R       (- 2a b x - 4a c)\|- a \|4a c - b
+--R                                                     Type: Expression Integer
+--E
+
 @
 
 \section{\cite{1}:14.267~~~~~$\displaystyle
@@ -127,7 +583,7 @@ $$
 <<*>>=
 )clear all
 
---S 3 of 15
+--S 16
 aa:=integrate(x^2/(a*x^2+b*x+c),x)
 --R 
 --R
@@ -173,6 +629,141 @@ aa:=integrate(x^2/(a*x^2+b*x+c),x)
 --R     ]
 --R                                     Type: Union(List Expression Integer,...)
 --E 
+
+--S 17
+t1:=integrate(1/(a*x^2+b*x+c),x)
+--R 
+--R
+--R   (2)
+--R   [
+--R       log
+--R                                           +-----------+
+--R                 2 2                    2  |          2       2        2
+--R              (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
+--R            + 
+--R                        3
+--R              4a b c - b
+--R         /
+--R               2
+--R            a x  + b x + c
+--R    /
+--R        +-----------+
+--R        |          2
+--R       \|- 4a c + b
+--R     ,
+--R                     +---------+
+--R                     |        2
+--R          (2a x + b)\|4a c - b
+--R    2atan(----------------------)
+--R                         2
+--R                 4a c - b
+--R    -----------------------------]
+--R              +---------+
+--R              |        2
+--R             \|4a c - b
+--R                                     Type: Union(List Expression Integer,...)
+--E
+
+--S 18
+bb1:=x/a-b/(2*a^2)*log(a*x^2+b*x+c)+(b^2-2*a*c)/(2*a^2)*t1.1
+--R 
+--R
+--R   (3)
+--R                    2
+--R         (- 2a c + b )
+--R      *
+--R         log
+--R                                             +-----------+
+--R                   2 2                    2  |          2       2        2
+--R                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
+--R              + 
+--R                          3
+--R                4a b c - b
+--R           /
+--R                 2
+--R              a x  + b x + c
+--R     + 
+--R                                        +-----------+
+--R                   2                    |          2
+--R       (- b log(a x  + b x + c) + 2a x)\|- 4a c + b
+--R  /
+--R         +-----------+
+--R       2 |          2
+--R     2a \|- 4a c + b
+--R                                                     Type: Expression Integer
+--E
+
+--S 19
+bb2:=x/a-b/(2*a^2)*log(a*x^2+b*x+c)+(b^2-2*a*c)/(2*a^2)*t1.2
+--R 
+--R
+--R   (4)
+--R                                     +---------+
+--R                                     |        2
+--R                   2      (2a x + b)\|4a c - b
+--R       (- 4a c + 2b )atan(----------------------)
+--R                                         2
+--R                                 4a c - b
+--R     + 
+--R                                        +---------+
+--R                   2                    |        2
+--R       (- b log(a x  + b x + c) + 2a x)\|4a c - b
+--R  /
+--R         +---------+
+--R       2 |        2
+--R     2a \|4a c - b
+--R                                                     Type: Expression Integer
+--E
+
+--S 20
+cc1:=bb1-aa.1
+--R
+--R   (5)
+--R                    2
+--R         (- 2a c + b )
+--R      *
+--R         log
+--R                                             +-----------+
+--R                   2 2                    2  |          2       2        2
+--R                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
+--R              + 
+--R                          3
+--R                4a b c - b
+--R           /
+--R                 2
+--R              a x  + b x + c
+--R     + 
+--R                    2
+--R         (- 2a c + b )
+--R      *
+--R         log
+--R                                             +-----------+
+--R                   2 2                    2  |          2         2        2
+--R                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
+--R              + 
+--R                            3
+--R                - 4a b c + b
+--R           /
+--R                 2
+--R              a x  + b x + c
+--R  /
+--R         +-----------+
+--R       2 |          2
+--R     2a \|- 4a c + b
+--R                                                     Type: Expression Integer
+--E
+
+--S 21     14:267 Schaums and Axiom differ by a constant
+dd1:=complexNormalize cc1
+--R
+--R                   2          3      2 2
+--R        (- 2a c + b )log(- 16a c + 4a b )
+--R   (6)  ---------------------------------
+--R                    +-----------+
+--R                  2 |          2
+--R                2a \|- 4a c + b
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.268~~~~~$\displaystyle
@@ -184,7 +775,7 @@ $$
 <<*>>=
 )clear all
 
---S 4 of 15
+--S 22     14:268 Axiom cannot compute this integral
 aa:=integrate(x^m/(a*x^2+b*x+c),x)
 --R 
 --R
@@ -195,6 +786,7 @@ aa:=integrate(x^m/(a*x^2+b*x+c),x)
 --I             c + %N b + %N a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
 @
 
 \section{\cite{1}:14.269~~~~~$\displaystyle
@@ -206,7 +798,7 @@ $$
 <<*>>=
 )clear all
 
---S 5 of 15
+--S 23
 aa:=integrate(1/(x*(a*x^2+b*x+c)),x)
 --R 
 --R
@@ -251,6 +843,179 @@ aa:=integrate(1/(x*(a*x^2+b*x+c)),x)
 --R     ]
 --R                                     Type: Union(List Expression Integer,...)
 --E 
+
+--S 24
+t1:=integrate(1/(a*x^2+b*x+c),x)
+--R 
+--R
+--R   (2)
+--R   [
+--R       log
+--R                                           +-----------+
+--R                 2 2                    2  |          2       2        2
+--R              (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
+--R            + 
+--R                        3
+--R              4a b c - b
+--R         /
+--R               2
+--R            a x  + b x + c
+--R    /
+--R        +-----------+
+--R        |          2
+--R       \|- 4a c + b
+--R     ,
+--R                     +---------+
+--R                     |        2
+--R          (2a x + b)\|4a c - b
+--R    2atan(----------------------)
+--R                         2
+--R                 4a c - b
+--R    -----------------------------]
+--R              +---------+
+--R              |        2
+--R             \|4a c - b
+--R                                     Type: Union(List Expression Integer,...)
+--E
+
+--S 25
+bb1:=1/(2*c)*log(x^2/(a*x^2+b*x+c))-b/(2*c)*t1.1
+--R 
+--R
+--R   (3)
+--R       -
+--R            b
+--R         *
+--R            log
+--R                                                +-----------+
+--R                      2 2                    2  |          2       2        2
+--R                   (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
+--R                 + 
+--R                             3
+--R                   4a b c - b
+--R              /
+--R                    2
+--R                 a x  + b x + c
+--R     + 
+--R                  2        +-----------+
+--R                 x         |          2
+--R       log(--------------)\|- 4a c + b
+--R              2
+--R           a x  + b x + c
+--R  /
+--R        +-----------+
+--R        |          2
+--R     2c\|- 4a c + b
+--R                                                     Type: Expression Integer
+--E
+
+--S 26
+bb2:=1/(2*c)*log(x^2/(a*x^2+b*x+c))-b/(2*c)*t1.2
+--R 
+--R
+--R                             +---------+
+--R                             |        2                2        +---------+
+--R                  (2a x + b)\|4a c - b                x         |        2
+--R        - 2b atan(----------------------) + log(--------------)\|4a c - b
+--R                                 2                 2
+--R                         4a c - b               a x  + b x + c
+--R   (4)  -------------------------------------------------------------------
+--R                                      +---------+
+--R                                      |        2
+--R                                   2c\|4a c - b
+--R                                                     Type: Expression Integer
+--E
+
+--S 27
+cc1:=bb1-aa.1
+--R
+--R   (5)
+--R       -
+--R            b
+--R         *
+--R            log
+--R                                                +-----------+
+--R                      2 2                    2  |          2       2        2
+--R                   (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
+--R                 + 
+--R                             3
+--R                   4a b c - b
+--R              /
+--R                    2
+--R                 a x  + b x + c
+--R     + 
+--R       -
+--R            b
+--R         *
+--R            log
+--R                                                +-----------+
+--R                      2 2                    2  |          2
+--R                   (2a x  + 2a b x - 2a c + b )\|- 4a c + b
+--R                 + 
+--R                        2        2               3
+--R                   (- 8a c + 2a b )x - 4a b c + b
+--R              /
+--R                    2
+--R                 a x  + b x + c
+--R     + 
+--R                                                   2         +-----------+
+--R               2                                  x          |          2
+--R       (log(a x  + b x + c) - 2log(x) + log(--------------))\|- 4a c + b
+--R                                               2
+--R                                            a x  + b x + c
+--R  /
+--R        +-----------+
+--R        |          2
+--R     2c\|- 4a c + b
+--R                                                     Type: Expression Integer
+--E
+
+--S 28
+dd1:=expandLog cc1
+--R
+--R   (6)
+--R       -
+--R            b
+--R         *
+--R            log
+--R                                              +-----------+
+--R                    2 2                    2  |          2       2        2
+--R                 (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
+--R               + 
+--R                           3
+--R                 4a b c - b
+--R     + 
+--R       -
+--R            b
+--R         *
+--R            log
+--R                                              +-----------+
+--R                    2 2                    2  |          2         2        2
+--R                 (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
+--R               + 
+--R                             3
+--R                 - 4a b c + b
+--R     + 
+--R                 2
+--R       2b log(a x  + b x + c)
+--R  /
+--R        +-----------+
+--R        |          2
+--R     2c\|- 4a c + b
+--R                                                     Type: Expression Integer
+--E
+
+--S 29     14:269 Schaums and Axiom differ by a constant
+ee1:=complexNormalize dd1
+--R
+--R                     3      2 2
+--R          b log(- 16a c + 4a b )
+--R   (7)  - ----------------------
+--R                +-----------+
+--R                |          2
+--R             2c\|- 4a c + b
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.270~~~~~$\displaystyle
@@ -262,7 +1027,7 @@ $$
 <<*>>=
 )clear all
 
---S 6 of 15
+--S 30
 aa:=integrate(1/(x^2*(a*x^2+b*x+c)),x)
 --R 
 --R
@@ -308,6 +1073,186 @@ aa:=integrate(1/(x^2*(a*x^2+b*x+c)),x)
 --R     ]
 --R                                     Type: Union(List Expression Integer,...)
 --E 
+
+--S 31
+t1:=integrate(1/(a*x^2+b*x+c),x)
+--R 
+--R
+--R   (2)
+--R   [
+--R       log
+--R                                           +-----------+
+--R                 2 2                    2  |          2       2        2
+--R              (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
+--R            + 
+--R                        3
+--R              4a b c - b
+--R         /
+--R               2
+--R            a x  + b x + c
+--R    /
+--R        +-----------+
+--R        |          2
+--R       \|- 4a c + b
+--R     ,
+--R                     +---------+
+--R                     |        2
+--R          (2a x + b)\|4a c - b
+--R    2atan(----------------------)
+--R                         2
+--R                 4a c - b
+--R    -----------------------------]
+--R              +---------+
+--R              |        2
+--R             \|4a c - b
+--R                                     Type: Union(List Expression Integer,...)
+--E
+
+--S 32
+bb1:=b/(2*c^2)*log((a*x^2+b*x+c)/x^2)-1/(c*x)+(b^2-2*a*c)/(2*c^2)*t1.1
+--R 
+--R
+--R   (3)
+--R                    2
+--R         (- 2a c + b )x
+--R      *
+--R         log
+--R                                             +-----------+
+--R                   2 2                    2  |          2       2        2
+--R                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
+--R              + 
+--R                          3
+--R                4a b c - b
+--R           /
+--R                 2
+--R              a x  + b x + c
+--R     + 
+--R                   2                  +-----------+
+--R                a x  + b x + c        |          2
+--R       (b x log(--------------) - 2c)\|- 4a c + b
+--R                       2
+--R                      x
+--R  /
+--R          +-----------+
+--R       2  |          2
+--R     2c x\|- 4a c + b
+--R                                                     Type: Expression Integer
+--E
+
+--S 33
+bb2:=b/(2*c^2)*log((a*x^2+b*x+c)/x^2)-1/(c*x)+(b^2-2*a*c)/(2*c^2)*t1.2
+--R 
+--R
+--R   (4)
+--R                                       +---------+
+--R                                       |        2
+--R                   2        (2a x + b)\|4a c - b
+--R       (- 4a c + 2b )x atan(----------------------)
+--R                                           2
+--R                                   4a c - b
+--R     + 
+--R                   2                  +---------+
+--R                a x  + b x + c        |        2
+--R       (b x log(--------------) - 2c)\|4a c - b
+--R                       2
+--R                      x
+--R  /
+--R          +---------+
+--R       2  |        2
+--R     2c x\|4a c - b
+--R                                                     Type: Expression Integer
+--E
+
+--S 34
+cc1:=bb1-aa.1
+--R
+--R   (5)
+--R                    2
+--R         (- 2a c + b )
+--R      *
+--R         log
+--R                                             +-----------+
+--R                   2 2                    2  |          2       2        2
+--R                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
+--R              + 
+--R                          3
+--R                4a b c - b
+--R           /
+--R                 2
+--R              a x  + b x + c
+--R     + 
+--R                    2
+--R         (- 2a c + b )
+--R      *
+--R         log
+--R                                             +-----------+
+--R                   2 2                    2  |          2         2        2
+--R                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
+--R              + 
+--R                            3
+--R                - 4a b c + b
+--R           /
+--R                 2
+--R              a x  + b x + c
+--R     + 
+--R                                                     2             +-----------+
+--R                 2                                a x  + b x + c   |          2
+--R     (- b log(a x  + b x + c) + 2b log(x) + b log(--------------))\|- 4a c + b
+--R                                                         2
+--R                                                        x
+--R  /
+--R         +-----------+
+--R       2 |          2
+--R     2c \|- 4a c + b
+--R                                                     Type: Expression Integer
+--E
+
+--S 35
+dd1:=expandLog cc1
+--R
+--R   (6)
+--R                    2
+--R         (- 2a c + b )
+--R      *
+--R         log
+--R                                           +-----------+
+--R                 2 2                    2  |          2       2        2
+--R              (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
+--R            + 
+--R                        3
+--R              4a b c - b
+--R     + 
+--R                    2
+--R         (- 2a c + b )
+--R      *
+--R         log
+--R                                           +-----------+
+--R                 2 2                    2  |          2         2        2
+--R              (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
+--R            + 
+--R                          3
+--R              - 4a b c + b
+--R     + 
+--R                 2        2
+--R       (4a c - 2b )log(a x  + b x + c)
+--R  /
+--R         +-----------+
+--R       2 |          2
+--R     2c \|- 4a c + b
+--R                                                     Type: Expression Integer
+--E
+
+--S 36     14:270 Schaums and Axiom differ by a constant
+ee1:=complexNormalize dd1
+--R
+--R                   2          3      2 2
+--R        (- 2a c + b )log(- 16a c + 4a b )
+--R   (7)  ---------------------------------
+--R                    +-----------+
+--R                  2 |          2
+--R                2c \|- 4a c + b
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.271~~~~~$\displaystyle
@@ -320,7 +1265,7 @@ $$
 <<*>>=
 )clear all
 
---S 7 of 15
+--S 37     14:271 Axiom cannot compute this integral
 aa:=integrate(1/(x^n*(a*x^2+b*x+c)),x)
 --R 
 --R
@@ -331,6 +1276,7 @@ aa:=integrate(1/(x^n*(a*x^2+b*x+c)),x)
 --I             (c + %N b + %N a)%N
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
 @
 
 \section{\cite{1}:14.272~~~~~$\displaystyle
@@ -342,7 +1288,7 @@ $$
 <<*>>=
 )clear all
 
---S 8 of 15
+--S 38
 aa:=integrate(1/(a*x^2+b*x+c)^2,x)
 --R 
 --R
@@ -383,6 +1329,213 @@ aa:=integrate(1/(a*x^2+b*x+c)^2,x)
 --R     ]
 --R                                     Type: Union(List Expression Integer,...)
 --E 
+
+--S 39
+t1:=integrate(1/(a*x^2+b*x+c),x)
+--R 
+--R
+--R   (2)
+--R   [
+--R       log
+--R                                           +-----------+
+--R                 2 2                    2  |          2       2        2
+--R              (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
+--R            + 
+--R                        3
+--R              4a b c - b
+--R         /
+--R               2
+--R            a x  + b x + c
+--R    /
+--R        +-----------+
+--R        |          2
+--R       \|- 4a c + b
+--R     ,
+--R                     +---------+
+--R                     |        2
+--R          (2a x + b)\|4a c - b
+--R    2atan(----------------------)
+--R                         2
+--R                 4a c - b
+--R    -----------------------------]
+--R              +---------+
+--R              |        2
+--R             \|4a c - b
+--R                                     Type: Union(List Expression Integer,...)
+--E
+
+--S 40
+bb1:=(b*x+2*c)/((4*a*c-b^2)*(a*x^2+b*x+c))-b/(4*a*c-b^2)*t1.1
+--R 
+--R
+--R   (3)
+--R                 2    2
+--R         (- a b x  - b x - b c)
+--R      *
+--R         log
+--R                                             +-----------+
+--R                   2 2                    2  |          2       2        2
+--R                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
+--R              + 
+--R                          3
+--R                4a b c - b
+--R           /
+--R                 2
+--R              a x  + b x + c
+--R     + 
+--R                  +-----------+
+--R                  |          2
+--R       (b x + 2c)\|- 4a c + b
+--R  /
+--R                                                      +-----------+
+--R         2       2  2              3         2    2   |          2
+--R     ((4a c - a b )x  + (4a b c - b )x + 4a c  - b c)\|- 4a c + b
+--R                                                     Type: Expression Integer
+--E
+
+--S 41
+bb2:=(b*x+2*c)/((4*a*c-b^2)*(a*x^2+b*x+c))-b/(4*a*c-b^2)*t1.2
+--R 
+--R
+--R   (4)
+--R                                                +---------+
+--R                                                |        2
+--R                2     2              (2a x + b)\|4a c - b
+--R       (- 2a b x  - 2b x - 2b c)atan(----------------------)
+--R                                                    2
+--R                                            4a c - b
+--R     + 
+--R                  +---------+
+--R                  |        2
+--R       (b x + 2c)\|4a c - b
+--R  /
+--R                                                      +---------+
+--R         2       2  2              3         2    2   |        2
+--R     ((4a c - a b )x  + (4a b c - b )x + 4a c  - b c)\|4a c - b
+--R                                                     Type: Expression Integer
+--E
+
+--S 42
+cc1:=aa.1-bb1
+--R
+--R   (5)
+--R                   2  2     2
+--R         ((a b + 2a )x  + (b  + 2a b)x + (b + 2a)c)
+--R      *
+--R         log
+--R                                             +-----------+
+--R                   2 2                    2  |          2       2        2
+--R                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
+--R              + 
+--R                          3
+--R                4a b c - b
+--R           /
+--R                 2
+--R              a x  + b x + c
+--R     + 
+--R                              +-----------+
+--R                              |          2
+--R       ((- b + 2a)x - 2c + b)\|- 4a c + b
+--R  /
+--R                                                      +-----------+
+--R         2       2  2              3         2    2   |          2
+--R     ((4a c - a b )x  + (4a b c - b )x + 4a c  - b c)\|- 4a c + b
+--R                                                     Type: Expression Integer
+--E
+
+--S 43
+cc2:=aa.2-bb1
+--R
+--R   (6)
+--R                              +---------+
+--R               2    2         |        2
+--R         (a b x  + b x + b c)\|4a c - b
+--R      *
+--R         log
+--R                                             +-----------+
+--R                   2 2                    2  |          2       2        2
+--R                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
+--R              + 
+--R                          3
+--R                4a b c - b
+--R           /
+--R                 2
+--R              a x  + b x + c
+--R     + 
+--R                                                            +---------+
+--R                               +-----------+                |        2
+--R          2 2                  |          2      (2a x + b)\|4a c - b
+--R       (4a x  + 4a b x + 4a c)\|- 4a c + b  atan(----------------------)
+--R                                                                2
+--R                                                        4a c - b
+--R     + 
+--R                              +-----------+ +---------+
+--R                              |          2  |        2
+--R       ((- b + 2a)x - 2c + b)\|- 4a c + b  \|4a c - b
+--R  /
+--R                                                      +-----------+ +---------+
+--R         2       2  2              3         2    2   |          2  |        2
+--R     ((4a c - a b )x  + (4a b c - b )x + 4a c  - b c)\|- 4a c + b  \|4a c - b
+--R                                                     Type: Expression Integer
+--E
+
+--S 44
+cc3:=aa.1-bb2
+--R
+--R   (7)
+--R                                 +---------+
+--R            2 2                  |        2
+--R         (2a x  + 2a b x + 2a c)\|4a c - b
+--R      *
+--R         log
+--R                                             +-----------+
+--R                   2 2                    2  |          2       2        2
+--R                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
+--R              + 
+--R                          3
+--R                4a b c - b
+--R           /
+--R                 2
+--R              a x  + b x + c
+--R     + 
+--R                                                            +---------+
+--R                               +-----------+                |        2
+--R              2     2          |          2      (2a x + b)\|4a c - b
+--R       (2a b x  + 2b x + 2b c)\|- 4a c + b  atan(----------------------)
+--R                                                                2
+--R                                                        4a c - b
+--R     + 
+--R                              +-----------+ +---------+
+--R                              |          2  |        2
+--R       ((- b + 2a)x - 2c + b)\|- 4a c + b  \|4a c - b
+--R  /
+--R                                                      +-----------+ +---------+
+--R         2       2  2              3         2    2   |          2  |        2
+--R     ((4a c - a b )x  + (4a b c - b )x + 4a c  - b c)\|- 4a c + b  \|4a c - b
+--R                                                     Type: Expression Integer
+--E
+
+--S 45     14:272 Axiom cannot simplify these expressions
+cc4:=aa.2-bb2
+--R
+--R   (8)
+--R                                                                    +---------+
+--R                                                                    |        2
+--R                  2  2      2                            (2a x + b)\|4a c - b
+--R       ((2a b + 4a )x  + (2b  + 4a b)x + (2b + 4a)c)atan(----------------------)
+--R                                                                        2
+--R                                                                4a c - b
+--R     + 
+--R                              +---------+
+--R                              |        2
+--R       ((- b + 2a)x - 2c + b)\|4a c - b
+--R  /
+--R                                                      +---------+
+--R         2       2  2              3         2    2   |        2
+--R     ((4a c - a b )x  + (4a b c - b )x + 4a c  - b c)\|4a c - b
+--R                                                     Type: Expression Integer
+--E
+
 @
 
 \section{\cite{1}:14.273~~~~~$\displaystyle
@@ -394,7 +1547,7 @@ $$
 <<*>>=
 )clear all
 
---S 9 of 15
+--S 46
 aa:=integrate(x/(a*x^2+b*x+c)^2,x)
 --R 
 --R
@@ -440,6 +1593,177 @@ aa:=integrate(x/(a*x^2+b*x+c)^2,x)
 --R     ]
 --R                                     Type: Union(List Expression Integer,...)
 --E
+
+--S 47
+t1:=integrate(1/(a*x^2+b*x+c),x)
+--R 
+--R
+--R   (2)
+--R   [
+--R       log
+--R                                           +-----------+
+--R                 2 2                    2  |          2       2        2
+--R              (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
+--R            + 
+--R                        3
+--R              4a b c - b
+--R         /
+--R               2
+--R            a x  + b x + c
+--R    /
+--R        +-----------+
+--R        |          2
+--R       \|- 4a c + b
+--R     ,
+--R                     +---------+
+--R                     |        2
+--R          (2a x + b)\|4a c - b
+--R    2atan(----------------------)
+--R                         2
+--R                 4a c - b
+--R    -----------------------------]
+--R              +---------+
+--R              |        2
+--R             \|4a c - b
+--R                                     Type: Union(List Expression Integer,...)
+--E
+
+--S 48
+bb1:=-(b*x+2*c)/((4*a*c-b^2)*(a*x^2+b*x+c))-b/(4*a*c-b^2)*t1.1
+--R 
+--R
+--R   (3)
+--R                 2    2
+--R         (- a b x  - b x - b c)
+--R      *
+--R         log
+--R                                             +-----------+
+--R                   2 2                    2  |          2       2        2
+--R                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
+--R              + 
+--R                          3
+--R                4a b c - b
+--R           /
+--R                 2
+--R              a x  + b x + c
+--R     + 
+--R                    +-----------+
+--R                    |          2
+--R       (- b x - 2c)\|- 4a c + b
+--R  /
+--R                                                      +-----------+
+--R         2       2  2              3         2    2   |          2
+--R     ((4a c - a b )x  + (4a b c - b )x + 4a c  - b c)\|- 4a c + b
+--R                                                     Type: Expression Integer
+--E
+
+--S 49
+bb2:=-(b*x+2*c)/((4*a*c-b^2)*(a*x^2+b*x+c))-b/(4*a*c-b^2)*t1.2
+--R 
+--R
+--R   (4)
+--R                                                +---------+
+--R                                                |        2
+--R                2     2              (2a x + b)\|4a c - b
+--R       (- 2a b x  - 2b x - 2b c)atan(----------------------)
+--R                                                    2
+--R                                            4a c - b
+--R     + 
+--R                    +---------+
+--R                    |        2
+--R       (- b x - 2c)\|4a c - b
+--R  /
+--R                                                      +---------+
+--R         2       2  2              3         2    2   |        2
+--R     ((4a c - a b )x  + (4a b c - b )x + 4a c  - b c)\|4a c - b
+--R                                                     Type: Expression Integer
+--E
+
+--S 50
+cc1:=bb1-aa.1
+--R
+--R   (5)
+--R       -
+--R            b
+--R         *
+--R            log
+--R                                                +-----------+
+--R                      2 2                    2  |          2       2        2
+--R                   (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
+--R                 + 
+--R                             3
+--R                   4a b c - b
+--R              /
+--R                    2
+--R                 a x  + b x + c
+--R     + 
+--R       -
+--R            b
+--R         *
+--R            log
+--R                                                +-----------+
+--R                      2 2                    2  |          2
+--R                   (2a x  + 2a b x - 2a c + b )\|- 4a c + b
+--R                 + 
+--R                        2        2               3
+--R                   (- 8a c + 2a b )x - 4a b c + b
+--R              /
+--R                    2
+--R                 a x  + b x + c
+--R  /
+--R                 +-----------+
+--R              2  |          2
+--R     (4a c - b )\|- 4a c + b
+--R                                                     Type: Expression Integer
+--E
+
+--S 51
+dd1:=expandLog cc1
+--R
+--R   (6)
+--R       -
+--R            b
+--R         *
+--R            log
+--R                                              +-----------+
+--R                    2 2                    2  |          2       2        2
+--R                 (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
+--R               + 
+--R                           3
+--R                 4a b c - b
+--R     + 
+--R       -
+--R            b
+--R         *
+--R            log
+--R                                              +-----------+
+--R                    2 2                    2  |          2         2        2
+--R                 (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
+--R               + 
+--R                             3
+--R                 - 4a b c + b
+--R     + 
+--R                 2
+--R       2b log(a x  + b x + c)
+--R  /
+--R                 +-----------+
+--R              2  |          2
+--R     (4a c - b )\|- 4a c + b
+--R                                                     Type: Expression Integer
+--E
+
+--S 52     14:273 Schaums and Axiom differ by a constant
+ee1:=complexNormalize dd1
+--R
+--R                       3      2 2
+--R            b log(- 16a c + 4a b )
+--R   (7)  - -------------------------
+--R                      +-----------+
+--R                   2  |          2
+--R          (4a c - b )\|- 4a c + b
+--R                                                     Type: Expression Integer
+--E
+
 @
 
 \section{\cite{1}:14.274~~~~~$\displaystyle
@@ -451,7 +1775,7 @@ $$
 <<*>>=
 )clear all
 
---S 10 of 15
+--S 53
 aa:=integrate(x^2/(a*x^2+b*x+c)^2,x)
 --R 
 --R
@@ -497,6 +1821,96 @@ aa:=integrate(x^2/(a*x^2+b*x+c)^2,x)
 --R     ]
 --R                                     Type: Union(List Expression Integer,...)
 --E 
+
+--S 54
+t1:=integrate(1/(a*x^2+b*x+c),x)
+--R 
+--R
+--R   (2)
+--R   [
+--R       log
+--R                                           +-----------+
+--R                 2 2                    2  |          2       2        2
+--R              (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
+--R            + 
+--R                        3
+--R              4a b c - b
+--R         /
+--R               2
+--R            a x  + b x + c
+--R    /
+--R        +-----------+
+--R        |          2
+--R       \|- 4a c + b
+--R     ,
+--R                     +---------+
+--R                     |        2
+--R          (2a x + b)\|4a c - b
+--R    2atan(----------------------)
+--R                         2
+--R                 4a c - b
+--R    -----------------------------]
+--R              +---------+
+--R              |        2
+--R             \|4a c - b
+--R                                     Type: Union(List Expression Integer,...)
+--E
+
+--S 55
+bb1:=((b^2-2*a*c)*x+b*c)/(a*(4*a*c-b^2)*(a*x^2+b*x+c))+(2*c)/(4*a*c-b^2)*t1.1
+--R
+--R   (3)
+--R            2   2                  2
+--R         (2a c x  + 2a b c x + 2a c )
+--R      *
+--R         log
+--R                                             +-----------+
+--R                   2 2                    2  |          2       2        2
+--R                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
+--R              + 
+--R                          3
+--R                4a b c - b
+--R           /
+--R                 2
+--R              a x  + b x + c
+--R     + 
+--R                              +-----------+
+--R                   2          |          2
+--R       ((- 2a c + b )x + b c)\|- 4a c + b
+--R  /
+--R                                                          +-----------+
+--R         3     2 2  2      2         3       2 2      2   |          2
+--R     ((4a c - a b )x  + (4a b c - a b )x + 4a c  - a b c)\|- 4a c + b
+--R                                                     Type: Expression Integer
+--E
+
+--S 56
+bb2:=((b^2-2*a*c)*x+b*c)/(a*(4*a*c-b^2)*(a*x^2+b*x+c))+(2*c)/(4*a*c-b^2)*t1.2
+--R
+--R   (4)
+--R                                                   +---------+
+--R                                                   |        2
+--R          2   2                  2      (2a x + b)\|4a c - b
+--R       (4a c x  + 4a b c x + 4a c )atan(----------------------)
+--R                                                       2
+--R                                               4a c - b
+--R     + 
+--R                              +---------+
+--R                   2          |        2
+--R       ((- 2a c + b )x + b c)\|4a c - b
+--R  /
+--R                                                          +---------+
+--R         3     2 2  2      2         3       2 2      2   |        2
+--R     ((4a c - a b )x  + (4a b c - a b )x + 4a c  - a b c)\|4a c - b
+--R                                                     Type: Expression Integer
+--E
+
+--S 57     14:274 Schaums and Axiom agree
+cc1:=aa.1-bb1
+--R
+--R   (5)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.275~~~~~$\displaystyle
@@ -514,7 +1928,7 @@ $$
 <<*>>=
 )clear all
 
---S 11 of 15
+--S 58     14:275 Axiom cannot compute this integral
 aa:=integrate(x^m/(a*x^2+b*x+c)^n,x)
 --R 
 --R
@@ -525,6 +1939,7 @@ aa:=integrate(x^m/(a*x^2+b*x+c)^n,x)
 --I             (c + %N b + %N a)
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
 @
 
 \section{\cite{1}:14.276~~~~~$\displaystyle
@@ -541,7 +1956,7 @@ $$
 <<*>>=
 )clear all
 
---S 12 of 15
+--S 59     14:276 Axiom cannot compute this integral
 aa:=integrate(x^(2*n-1)/(a*x^2+b*x+c)^n,x)
 --R 
 --R
@@ -552,6 +1967,7 @@ aa:=integrate(x^(2*n-1)/(a*x^2+b*x+c)^n,x)
 --I             (c + %N b + %N a)
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
 @
 
 \section{\cite{1}:14.277~~~~~$\displaystyle
@@ -568,7 +1984,7 @@ $$
 <<*>>=
 )clear all
 
---S 13 of 15
+--S 60
 aa:=integrate(1/(x*(a*x^2+b*x+c)^2),x)
 --R 
 --R
@@ -641,6 +2057,380 @@ aa:=integrate(1/(x*(a*x^2+b*x+c)^2),x)
 --R     ]
 --R                                     Type: Union(List Expression Integer,...)
 --E 
+
+--S 61
+t1:=integrate(1/(a*x^2+b*x+c)^2,x)
+--R 
+--R
+--R   (2)
+--R   [
+--R              2 2
+--R           (2a x  + 2a b x + 2a c)
+--R        *
+--R           log
+--R                                               +-----------+
+--R                     2 2                    2  |          2       2        2
+--R                  (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
+--R                + 
+--R                            3
+--R                  4a b c - b
+--R             /
+--R                   2
+--R                a x  + b x + c
+--R       + 
+--R                    +-----------+
+--R                    |          2
+--R         (2a x + b)\|- 4a c + b
+--R    /
+--R                                                        +-----------+
+--R           2       2  2              3         2    2   |          2
+--R       ((4a c - a b )x  + (4a b c - b )x + 4a c  - b c)\|- 4a c + b
+--R     ,
+--R                                           +---------+
+--R                                           |        2                +---------+
+--R       2 2                      (2a x + b)\|4a c - b                 |        2
+--R    (4a x  + 4a b x + 4a c)atan(----------------------) + (2a x + b)\|4a c - b
+--R                                               2
+--R                                       4a c - b
+--R    ----------------------------------------------------------------------------
+--R                                                             +---------+
+--R                2       2  2              3         2    2   |        2
+--R            ((4a c - a b )x  + (4a b c - b )x + 4a c  - b c)\|4a c - b
+--R     ]
+--R                                     Type: Union(List Expression Integer,...)
+--E
+
+--S 62
+t2:=integrate(1/(x*(a*x^2+b*x+c)),x)
+--R 
+--R
+--R   (3)
+--R   [
+--R           b
+--R        *
+--R           log
+--R                                               +-----------+
+--R                     2 2                    2  |          2         2        2
+--R                  (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
+--R                + 
+--R                              3
+--R                  - 4a b c + b
+--R             /
+--R                   2
+--R                a x  + b x + c
+--R       + 
+--R                                           +-----------+
+--R                   2                       |          2
+--R         (- log(a x  + b x + c) + 2log(x))\|- 4a c + b
+--R    /
+--R          +-----------+
+--R          |          2
+--R       2c\|- 4a c + b
+--R     ,
+--R
+--R                              +---------+
+--R                              |        2
+--R                   (2a x + b)\|4a c - b
+--R         - 2b atan(----------------------)
+--R                                  2
+--R                          4a c - b
+--R       + 
+--R                                           +---------+
+--R                   2                       |        2
+--R         (- log(a x  + b x + c) + 2log(x))\|4a c - b
+--R    /
+--R          +---------+
+--R          |        2
+--R       2c\|4a c - b
+--R     ]
+--R                                     Type: Union(List Expression Integer,...)
+--E
+
+--S 63
+bb1:=1/(2*c*(a*x^2+b*x+c))-b/(2*c)*t1.1+1/c*t2.1
+--R 
+--R
+--R   (4)
+--R              2     2       2            2
+--R         (- 2a b c x  - 2a b c x - 2a b c )
+--R      *
+--R         log
+--R                                             +-----------+
+--R                   2 2                    2  |          2       2        2
+--R                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
+--R              + 
+--R                          3
+--R                4a b c - b
+--R           /
+--R                 2
+--R              a x  + b x + c
+--R     + 
+--R             2         3  2        2     4           2    3
+--R         ((4a b c - a b )x  + (4a b c - b )x + 4a b c  - b c)
+--R      *
+--R         log
+--R                                             +-----------+
+--R                   2 2                    2  |          2         2        2
+--R                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
+--R              + 
+--R                            3
+--R                - 4a b c + b
+--R           /
+--R                 2
+--R              a x  + b x + c
+--R     + 
+--R                   2       2  2                3         2    2
+--R             ((- 4a c + a b )x  + (- 4a b c + b )x - 4a c  + b c)
+--R          *
+--R                    2
+--R             log(a x  + b x + c)
+--R         + 
+--R               2        2  2               3         2     2
+--R           ((8a c - 2a b )x  + (8a b c - 2b )x + 8a c  - 2b c)log(x) - 2a b c x
+--R         + 
+--R               2     2
+--R           4a c  - 2b c
+--R      *
+--R          +-----------+
+--R          |          2
+--R         \|- 4a c + b
+--R  /
+--R                                                                +-----------+
+--R         2 3       2 2  2          3     3 2         4     2 3  |          2
+--R     ((8a c  - 2a b c )x  + (8a b c  - 2b c )x + 8a c  - 2b c )\|- 4a c + b
+--R                                                     Type: Expression Integer
+--E
+
+--S 64
+bb2:=1/(2*c*(a*x^2+b*x+c))-b/(2*c)*t1.2+1/c*t2.1
+--R 
+--R
+--R   (5)
+--R                                                              +---------+
+--R             2         3  2        2     4           2    3   |        2
+--R         ((4a b c - a b )x  + (4a b c - b )x + 4a b c  - b c)\|4a c - b
+--R      *
+--R         log
+--R                                             +-----------+
+--R                   2 2                    2  |          2         2        2
+--R                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
+--R              + 
+--R                            3
+--R                - 4a b c + b
+--R           /
+--R                 2
+--R              a x  + b x + c
+--R     + 
+--R                                            +-----------+
+--R              2     2       2            2  |          2
+--R         (- 4a b c x  - 4a b c x - 4a b c )\|- 4a c + b
+--R      *
+--R                         +---------+
+--R                         |        2
+--R              (2a x + b)\|4a c - b
+--R         atan(----------------------)
+--R                             2
+--R                     4a c - b
+--R     + 
+--R                   2       2  2                3         2    2
+--R             ((- 4a c + a b )x  + (- 4a b c + b )x - 4a c  + b c)
+--R          *
+--R                    2
+--R             log(a x  + b x + c)
+--R         + 
+--R               2        2  2               3         2     2
+--R           ((8a c - 2a b )x  + (8a b c - 2b )x + 8a c  - 2b c)log(x) - 2a b c x
+--R         + 
+--R               2     2
+--R           4a c  - 2b c
+--R      *
+--R          +-----------+ +---------+
+--R          |          2  |        2
+--R         \|- 4a c + b  \|4a c - b
+--R  /
+--R                                                                  +-----------+
+--R           2 3       2 2  2          3     3 2         4     2 3  |          2
+--R       ((8a c  - 2a b c )x  + (8a b c  - 2b c )x + 8a c  - 2b c )\|- 4a c + b
+--R    *
+--R        +---------+
+--R        |        2
+--R       \|4a c - b
+--R                                                     Type: Expression Integer
+--E
+
+--S 65
+bb3:=1/(2*c*(a*x^2+b*x+c))-b/(2*c)*t1.1+1/c*t2.2
+--R 
+--R
+--R   (6)
+--R                                            +---------+
+--R              2     2       2            2  |        2
+--R         (- 2a b c x  - 2a b c x - 2a b c )\|4a c - b
+--R      *
+--R         log
+--R                                             +-----------+
+--R                   2 2                    2  |          2       2        2
+--R                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
+--R              + 
+--R                          3
+--R                4a b c - b
+--R           /
+--R                 2
+--R              a x  + b x + c
+--R     + 
+--R               2          3  2          2      4           2     3
+--R         ((- 8a b c + 2a b )x  + (- 8a b c + 2b )x - 8a b c  + 2b c)
+--R      *
+--R                                       +---------+
+--R          +-----------+                |        2
+--R          |          2      (2a x + b)\|4a c - b
+--R         \|- 4a c + b  atan(----------------------)
+--R                                           2
+--R                                   4a c - b
+--R     + 
+--R                   2       2  2                3         2    2
+--R             ((- 4a c + a b )x  + (- 4a b c + b )x - 4a c  + b c)
+--R          *
+--R                    2
+--R             log(a x  + b x + c)
+--R         + 
+--R               2        2  2               3         2     2
+--R           ((8a c - 2a b )x  + (8a b c - 2b )x + 8a c  - 2b c)log(x) - 2a b c x
+--R         + 
+--R               2     2
+--R           4a c  - 2b c
+--R      *
+--R          +-----------+ +---------+
+--R          |          2  |        2
+--R         \|- 4a c + b  \|4a c - b
+--R  /
+--R                                                                  +-----------+
+--R           2 3       2 2  2          3     3 2         4     2 3  |          2
+--R       ((8a c  - 2a b c )x  + (8a b c  - 2b c )x + 8a c  - 2b c )\|- 4a c + b
+--R    *
+--R        +---------+
+--R        |        2
+--R       \|4a c - b
+--R                                                     Type: Expression Integer
+--E
+
+--S 66
+bb4:=1/(2*c*(a*x^2+b*x+c))-b/(2*c)*t1.2+1/c*t2.2
+--R 
+--R
+--R   (7)
+--R                2          3  2           2      4            2     3
+--R         ((- 12a b c + 2a b )x  + (- 12a b c + 2b )x - 12a b c  + 2b c)
+--R      *
+--R                         +---------+
+--R                         |        2
+--R              (2a x + b)\|4a c - b
+--R         atan(----------------------)
+--R                             2
+--R                     4a c - b
+--R     + 
+--R                   2       2  2                3         2    2
+--R             ((- 4a c + a b )x  + (- 4a b c + b )x - 4a c  + b c)
+--R          *
+--R                    2
+--R             log(a x  + b x + c)
+--R         + 
+--R               2        2  2               3         2     2
+--R           ((8a c - 2a b )x  + (8a b c - 2b )x + 8a c  - 2b c)log(x) - 2a b c x
+--R         + 
+--R               2     2
+--R           4a c  - 2b c
+--R      *
+--R          +---------+
+--R          |        2
+--R         \|4a c - b
+--R  /
+--R                                                                +---------+
+--R         2 3       2 2  2          3     3 2         4     2 3  |        2
+--R     ((8a c  - 2a b c )x  + (8a b c  - 2b c )x + 8a c  - 2b c )\|4a c - b
+--R                                                     Type: Expression Integer
+--E
+
+--S 67
+cc1:=aa.1-bb1
+--R
+--R   (8)
+--R         a b
+--R      *
+--R         log
+--R                                             +-----------+
+--R                   2 2                    2  |          2       2        2
+--R                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
+--R              + 
+--R                          3
+--R                4a b c - b
+--R           /
+--R                 2
+--R              a x  + b x + c
+--R     + 
+--R         a b
+--R      *
+--R         log
+--R                                             +-----------+
+--R                   2 2                    2  |          2         2        2
+--R                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
+--R              + 
+--R                            3
+--R                - 4a b c + b
+--R           /
+--R                 2
+--R              a x  + b x + c
+--R  /
+--R                   +-----------+
+--R          2    2   |          2
+--R     (4a c  - b c)\|- 4a c + b
+--R                                                     Type: Expression Integer
+--E
+
+--S 68
+dd1:=expandLog cc1
+--R
+--R   (9)
+--R         a b
+--R      *
+--R         log
+--R                                           +-----------+
+--R                 2 2                    2  |          2       2        2
+--R              (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
+--R            + 
+--R                        3
+--R              4a b c - b
+--R     + 
+--R         a b
+--R      *
+--R         log
+--R                                           +-----------+
+--R                 2 2                    2  |          2         2        2
+--R              (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
+--R            + 
+--R                          3
+--R              - 4a b c + b
+--R     + 
+--R                     2
+--R       - 2a b log(a x  + b x + c)
+--R  /
+--R                   +-----------+
+--R          2    2   |          2
+--R     (4a c  - b c)\|- 4a c + b
+--R                                                     Type: Expression Integer
+--E
+
+--S 69     14:277 Schaums and Axiom differ by a constant
+ee1:=complexNormalize dd1
+--R
+--R                        3      2 2
+--R           a b log(- 16a c + 4a b )
+--R   (10)  ---------------------------
+--R                       +-----------+
+--R              2    2   |          2
+--R         (4a c  - b c)\|- 4a c + b
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.278~~~~~$\displaystyle
@@ -657,7 +2447,7 @@ $$
 <<*>>=
 )clear all
 
---S 14 of 15
+--S 70
 aa:=integrate(1/(x^2*(a*x^2+b*x+c)^2),x)
 --R 
 --R
@@ -740,6 +2530,426 @@ aa:=integrate(1/(x^2*(a*x^2+b*x+c)^2),x)
 --R     ]
 --R                                     Type: Union(List Expression Integer,...)
 --E 
+
+--S 71
+t1:=integrate(1/(a*x^2+b*x+c)^2,x)
+--R 
+--R
+--R   (2)
+--R   [
+--R              2 2
+--R           (2a x  + 2a b x + 2a c)
+--R        *
+--R           log
+--R                                               +-----------+
+--R                     2 2                    2  |          2       2        2
+--R                  (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
+--R                + 
+--R                            3
+--R                  4a b c - b
+--R             /
+--R                   2
+--R                a x  + b x + c
+--R       + 
+--R                    +-----------+
+--R                    |          2
+--R         (2a x + b)\|- 4a c + b
+--R    /
+--R                                                        +-----------+
+--R           2       2  2              3         2    2   |          2
+--R       ((4a c - a b )x  + (4a b c - b )x + 4a c  - b c)\|- 4a c + b
+--R     ,
+--R                                           +---------+
+--R                                           |        2                +---------+
+--R       2 2                      (2a x + b)\|4a c - b                 |        2
+--R    (4a x  + 4a b x + 4a c)atan(----------------------) + (2a x + b)\|4a c - b
+--R                                               2
+--R                                       4a c - b
+--R    ----------------------------------------------------------------------------
+--R                                                             +---------+
+--R                2       2  2              3         2    2   |        2
+--R            ((4a c - a b )x  + (4a b c - b )x + 4a c  - b c)\|4a c - b
+--R     ]
+--R                                     Type: Union(List Expression Integer,...)
+--E
+
+--S 72
+t2:=integrate(1/(x*(a*x^2+b*x+c)^2),x)
+--R 
+--R
+--R   (3)
+--R   [
+--R               2         3  2        2     4           2    3
+--R           ((6a b c - a b )x  + (6a b c - b )x + 6a b c  - b c)
+--R        *
+--R           log
+--R                                               +-----------+
+--R                     2 2                    2  |          2         2        2
+--R                  (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
+--R                + 
+--R                              3
+--R                  - 4a b c + b
+--R             /
+--R                   2
+--R                a x  + b x + c
+--R       + 
+--R                     2       2  2                3         2    2
+--R               ((- 4a c + a b )x  + (- 4a b c + b )x - 4a c  + b c)
+--R            *
+--R                      2
+--R               log(a x  + b x + c)
+--R           + 
+--R                 2        2  2               3         2     2
+--R             ((8a c - 2a b )x  + (8a b c - 2b )x + 8a c  - 2b c)log(x)
+--R           + 
+--R                              2     2
+--R             - 2a b c x + 4a c  - 2b c
+--R        *
+--R            +-----------+
+--R            |          2
+--R           \|- 4a c + b
+--R    /
+--R                                                                  +-----------+
+--R           2 3       2 2  2          3     3 2         4     2 3  |          2
+--R       ((8a c  - 2a b c )x  + (8a b c  - 2b c )x + 8a c  - 2b c )\|- 4a c + b
+--R     ,
+--R
+--R                  2          3  2           2      4            2     3
+--R           ((- 12a b c + 2a b )x  + (- 12a b c + 2b )x - 12a b c  + 2b c)
+--R        *
+--R                           +---------+
+--R                           |        2
+--R                (2a x + b)\|4a c - b
+--R           atan(----------------------)
+--R                               2
+--R                       4a c - b
+--R       + 
+--R                     2       2  2                3         2    2
+--R               ((- 4a c + a b )x  + (- 4a b c + b )x - 4a c  + b c)
+--R            *
+--R                      2
+--R               log(a x  + b x + c)
+--R           + 
+--R                 2        2  2               3         2     2
+--R             ((8a c - 2a b )x  + (8a b c - 2b )x + 8a c  - 2b c)log(x)
+--R           + 
+--R                              2     2
+--R             - 2a b c x + 4a c  - 2b c
+--R        *
+--R            +---------+
+--R            |        2
+--R           \|4a c - b
+--R    /
+--R                                                                  +---------+
+--R           2 3       2 2  2          3     3 2         4     2 3  |        2
+--R       ((8a c  - 2a b c )x  + (8a b c  - 2b c )x + 8a c  - 2b c )\|4a c - b
+--R     ]
+--R                                     Type: Union(List Expression Integer,...)
+--E
+
+--S 73
+bb1:=-1/(c*x*(a*x^2+b*x+c))-((3*a)/c)*t1.1-(2*b)/c*t2.1
+--R 
+--R
+--R   (4)
+--R              3 2 3     2   2 2     2 3
+--R         (- 6a c x  - 6a b c x  - 6a c x)
+--R      *
+--R         log
+--R                                             +-----------+
+--R                   2 2                    2  |          2       2        2
+--R                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
+--R              + 
+--R                          3
+--R                4a b c - b
+--R           /
+--R                 2
+--R              a x  + b x + c
+--R     + 
+--R               2 2       4  3          3     5  2          2 2    4
+--R         ((- 6a b c + a b )x  + (- 6a b c + b )x  + (- 6a b c  + b c)x)
+--R      *
+--R         log
+--R                                             +-----------+
+--R                   2 2                    2  |          2         2        2
+--R                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
+--R              + 
+--R                            3
+--R                - 4a b c + b
+--R           /
+--R                 2
+--R              a x  + b x + c
+--R     + 
+--R                 2         3  3        2     4  2          2    3
+--R             ((4a b c - a b )x  + (4a b c - b )x  + (4a b c  - b c)x)
+--R          *
+--R                    2
+--R             log(a x  + b x + c)
+--R         + 
+--R                   2          3  3          2      4  2            2     3
+--R             ((- 8a b c + 2a b )x  + (- 8a b c + 2b )x  + (- 8a b c  + 2b c)x)
+--R          *
+--R             log(x)
+--R         + 
+--R                2 2       2   2            2     3          3    2 2
+--R           (- 6a c  + 2a b c)x  + (- 7a b c  + 2b c)x - 4a c  + b c
+--R      *
+--R          +-----------+
+--R          |          2
+--R         \|- 4a c + b
+--R  /
+--R                                                                 +-----------+
+--R         2 4      2 3  3          4    3 3  2        5    2 4    |          2
+--R     ((4a c  - a b c )x  + (4a b c  - b c )x  + (4a c  - b c )x)\|- 4a c + b
+--R                                                     Type: Expression Integer
+--E
+
+--S 74
+bb2:=-1/(c*x*(a*x^2+b*x+c))-((3*a)/c)*t1.2-(2*b)/c*t2.1
+--R 
+--R
+--R   (5)
+--R               2 2       4  3          3     5  2          2 2    4
+--R         ((- 6a b c + a b )x  + (- 6a b c + b )x  + (- 6a b c  + b c)x)
+--R      *
+--R          +---------+
+--R          |        2
+--R         \|4a c - b
+--R      *
+--R         log
+--R                                             +-----------+
+--R                   2 2                    2  |          2         2        2
+--R                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
+--R              + 
+--R                            3
+--R                - 4a b c + b
+--R           /
+--R                 2
+--R              a x  + b x + c
+--R     + 
+--R                                             +-----------+
+--R               3 2 3      2   2 2      2 3   |          2
+--R         (- 12a c x  - 12a b c x  - 12a c x)\|- 4a c + b
+--R      *
+--R                         +---------+
+--R                         |        2
+--R              (2a x + b)\|4a c - b
+--R         atan(----------------------)
+--R                             2
+--R                     4a c - b
+--R     + 
+--R                 2         3  3        2     4  2          2    3
+--R             ((4a b c - a b )x  + (4a b c - b )x  + (4a b c  - b c)x)
+--R          *
+--R                    2
+--R             log(a x  + b x + c)
+--R         + 
+--R                   2          3  3          2      4  2            2     3
+--R             ((- 8a b c + 2a b )x  + (- 8a b c + 2b )x  + (- 8a b c  + 2b c)x)
+--R          *
+--R             log(x)
+--R         + 
+--R                2 2       2   2            2     3          3    2 2
+--R           (- 6a c  + 2a b c)x  + (- 7a b c  + 2b c)x - 4a c  + b c
+--R      *
+--R          +-----------+ +---------+
+--R          |          2  |        2
+--R         \|- 4a c + b  \|4a c - b
+--R  /
+--R                                                                   +-----------+
+--R           2 4      2 3  3          4    3 3  2        5    2 4    |          2
+--R       ((4a c  - a b c )x  + (4a b c  - b c )x  + (4a c  - b c )x)\|- 4a c + b
+--R    *
+--R        +---------+
+--R        |        2
+--R       \|4a c - b
+--R                                                     Type: Expression Integer
+--E
+
+--S 75
+bb3:=-1/(c*x*(a*x^2+b*x+c))-((3*a)/c)*t1.1-(2*b)/c*t2.2
+--R 
+--R
+--R   (6)
+--R                                          +---------+
+--R              3 2 3     2   2 2     2 3   |        2
+--R         (- 6a c x  - 6a b c x  - 6a c x)\|4a c - b
+--R      *
+--R         log
+--R                                             +-----------+
+--R                   2 2                    2  |          2       2        2
+--R                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
+--R              + 
+--R                          3
+--R                4a b c - b
+--R           /
+--R                 2
+--R              a x  + b x + c
+--R     + 
+--R              2 2        4  3         3      5  2         2 2     4
+--R         ((12a b c - 2a b )x  + (12a b c - 2b )x  + (12a b c  - 2b c)x)
+--R      *
+--R                                       +---------+
+--R          +-----------+                |        2
+--R          |          2      (2a x + b)\|4a c - b
+--R         \|- 4a c + b  atan(----------------------)
+--R                                           2
+--R                                   4a c - b
+--R     + 
+--R                 2         3  3        2     4  2          2    3
+--R             ((4a b c - a b )x  + (4a b c - b )x  + (4a b c  - b c)x)
+--R          *
+--R                    2
+--R             log(a x  + b x + c)
+--R         + 
+--R                   2          3  3          2      4  2            2     3
+--R             ((- 8a b c + 2a b )x  + (- 8a b c + 2b )x  + (- 8a b c  + 2b c)x)
+--R          *
+--R             log(x)
+--R         + 
+--R                2 2       2   2            2     3          3    2 2
+--R           (- 6a c  + 2a b c)x  + (- 7a b c  + 2b c)x - 4a c  + b c
+--R      *
+--R          +-----------+ +---------+
+--R          |          2  |        2
+--R         \|- 4a c + b  \|4a c - b
+--R  /
+--R                                                                   +-----------+
+--R           2 4      2 3  3          4    3 3  2        5    2 4    |          2
+--R       ((4a c  - a b c )x  + (4a b c  - b c )x  + (4a c  - b c )x)\|- 4a c + b
+--R    *
+--R        +---------+
+--R        |        2
+--R       \|4a c - b
+--R                                                     Type: Expression Integer
+--E
+
+--S 76
+bb4:=-1/(c*x*(a*x^2+b*x+c))-((3*a)/c)*t1.2-(2*b)/c*t2.2
+--R 
+--R
+--R   (7)
+--R                 3 2      2 2        4  3         2   2        3      5  2
+--R           (- 12a c  + 12a b c - 2a b )x  + (- 12a b c  + 12a b c - 2b )x
+--R         + 
+--R                 2 3        2 2     4
+--R           (- 12a c  + 12a b c  - 2b c)x
+--R      *
+--R                         +---------+
+--R                         |        2
+--R              (2a x + b)\|4a c - b
+--R         atan(----------------------)
+--R                             2
+--R                     4a c - b
+--R     + 
+--R                 2         3  3        2     4  2          2    3
+--R             ((4a b c - a b )x  + (4a b c - b )x  + (4a b c  - b c)x)
+--R          *
+--R                    2
+--R             log(a x  + b x + c)
+--R         + 
+--R                   2          3  3          2      4  2            2     3
+--R             ((- 8a b c + 2a b )x  + (- 8a b c + 2b )x  + (- 8a b c  + 2b c)x)
+--R          *
+--R             log(x)
+--R         + 
+--R                2 2       2   2            2     3          3    2 2
+--R           (- 6a c  + 2a b c)x  + (- 7a b c  + 2b c)x - 4a c  + b c
+--R      *
+--R          +---------+
+--R          |        2
+--R         \|4a c - b
+--R  /
+--R                                                                 +---------+
+--R         2 4      2 3  3          4    3 3  2        5    2 4    |        2
+--R     ((4a c  - a b c )x  + (4a b c  - b c )x  + (4a c  - b c )x)\|4a c - b
+--R                                                     Type: Expression Integer
+--E
+
+--S 77
+cc1:=aa.1-bb1
+--R
+--R   (8)
+--R           2
+--R         6a
+--R      *
+--R         log
+--R                                             +-----------+
+--R                   2 2                    2  |          2       2        2
+--R                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
+--R              + 
+--R                          3
+--R                4a b c - b
+--R           /
+--R                 2
+--R              a x  + b x + c
+--R     + 
+--R           2
+--R         6a
+--R      *
+--R         log
+--R                                             +-----------+
+--R                   2 2                    2  |          2         2        2
+--R                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
+--R              + 
+--R                            3
+--R                - 4a b c + b
+--R           /
+--R                 2
+--R              a x  + b x + c
+--R  /
+--R                   +-----------+
+--R          2    2   |          2
+--R     (4a c  - b c)\|- 4a c + b
+--R                                                     Type: Expression Integer
+--E
+
+--S 78
+dd1:=expandLog cc1
+--R
+--R   (9)
+--R           2
+--R         6a
+--R      *
+--R         log
+--R                                           +-----------+
+--R                 2 2                    2  |          2       2        2
+--R              (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (8a c - 2a b )x
+--R            + 
+--R                        3
+--R              4a b c - b
+--R     + 
+--R           2
+--R         6a
+--R      *
+--R         log
+--R                                           +-----------+
+--R                 2 2                    2  |          2         2        2
+--R              (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
+--R            + 
+--R                          3
+--R              - 4a b c + b
+--R     + 
+--R            2       2
+--R       - 12a log(a x  + b x + c)
+--R  /
+--R                   +-----------+
+--R          2    2   |          2
+--R     (4a c  - b c)\|- 4a c + b
+--R                                                     Type: Expression Integer
+--E
+
+--S 79     14:278 Schaums and Axiom differ by a constant
+ee1:=complexNormalize dd1
+--R
+--R             2         3      2 2
+--R           6a log(- 16a c + 4a b )
+--R   (10)  ---------------------------
+--R                       +-----------+
+--R              2    2   |          2
+--R         (4a c  - b c)\|- 4a c + b
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.279~~~~~$\displaystyle
@@ -756,7 +2966,7 @@ $$
 <<*>>=
 )clear all
 
---S 15 of 15
+--S 80     14:279 Axiom cannot compute this integral
 aa:=integrate(1/(x^m*(a*x^2+b*x+c)^n),x)
 --R 
 --R



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Martin,

I think discussing things like off the email lists does more damage to
the community then it would if you were to be more public about these
opinions. Are far as I am concerned, you have nothing to fear from
exploring these ideas and other people might benefit greatly by your
experience.

Sage is not going away (It should not go away!) and I think the Axiom
community needs to deal with how it should interact with Sage in the
future.

Regards,
Bill Page.

On Sun, Apr 20, 2008 at 3:10 AM, Martin Rubey <martin.rubey@univie.ac.at> wrote:
> I don't have the guts to send this to a public mailing list.  I probably
>  should.  If you want to, you have my permission.
>
>
>  "Alfredo Portes" <doyenatccny@gmail.com> writes:
>
>  > >  Axiom is so huge, so if Sage would be a part of Axiom that just handles
>  > > the web interface, why not?
>  >
>  > If you think Axiom is huge, then you need to look at Sage. It is ~10x Axiom.
>  > And in the other hand Axiom making a standard package will not happen. There
>  > are discussions on their list to remove lisp and maxima.
>
>  That's bad news, at least for me.  I was hoping a lot that Axiom could be
>  merged into Sage at some point, in some way.  After all, Axiom does have some
>  interesting and huge packages, like the integration stuff.  But maybe I'm
>  mistaken.
>
>  It seems that Sage is going to connect with OLPC.  If all those kids do their
>  math using Sage, I think there is no way around Sage anymore.  Sage can already
>  do many many things better than Axiom, I suppose, so we need really good
>  reasons to continue with Axiom, I think.  Maybe I should just redo the guessing
>  package in Python and be done with it?  Some time ago I said that I'll quit
>  Axiom if there are less than twenty contributors by the end of 2008.  However,
>  it seems to me that the number of algebra contributors actually went down!
>
>  I'd really like to hear some comments on the general plan.  Do you think it's
>  feasible to
>
>  a) attract other people, not working on Sage
>  b) merge our community into the Sage community
>
>  Martin
>
>



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Hi Ralf,

My own perspective in what I'm doing is authoring mathematical web documents
that can be live by connecting to a CAS somewhere on a server.  All 
tools I use
must be completely free and open source, but in addition it is very 
important to
me that somebody should be able to navigate to a URL and get full 
mathematical
content without having to download or install anything. I realized this 
was a
possibility about three years ago when I noticed that Firefox supported both
MathML and SVG.  Axiom/FriCAS/OpenAxiom serve as a backend to make the
document live.  I could use something else as a backend but when I first 
started
and looked around at what was available Axiom looked best.

I checked out Sage when I first heard about it and it didn't seem to be 
what I wanted.
Certainly Sage is an excellent project and with all this discussion I've 
just downloaded
and compiled the latest version so I can take a closer look at it's 
current status.

Arthur

Ralf Hemmecke wrote:
> I simply don't know on which mailing list I should send it. Forward it 
> if you like.
>
>> This is based completely on Arthur's work. First it uses his
>> axserver.spad package
>> which basically opens a TCP port to communicate to Axiom. This is 
>> basically
>> what Tim is using for his replacement of Hyperdoc.
>
>> Also, it uses the MathML package developed by Arthur, to display the 
>> answer
>> in the web browser. Arthur also created the initial worksheet style 
>> interface.
>
>> I have added some functions that allow to browse the databases (based 
>> on some
>> functions by Tim.). I have modified it so it looks like the Sage
>> Notebook. It can be ran from a remote machine also.
> > The Sage notebook is nice, but it depends on
>> having Sage on your system. Plus this can be run in Windows without a 
>> problem.
>> Currently is very simple, but I see a lot of potential in it.
>
> Cannot the Sage-Notebook be tweaked for Axiom? Or is your (and 
> Arthur's) stuff simply better. Or is the sage notebook not easily made 
> appropriate for Axiom?
>
>> Currently I am working with Fricas and Axiom...OpenAxiom is almost 
>> there, we
>> just need the MathML output. The current name is jyperdoc, but this
>> will change in
>> the future. (As soon as Arthur decides on another name :-)
>
>> You can check out the code from here: http://code.google.com/p/jyperdoc/
>>
>> Arthur initial interface is at:
>> http://jyperdoc.googlecode.com/svn/branches/friserver/
>
>> There is a README file that tells you how to run it, but basically is 
>> just start
>> Fricas/Axiom from inside the directory and then )read jyperdoc.input
>
> Good. I did that. With axserver running the fan of my laptop 
> immediately starts spinning. The CPU is at about 60% working. And I am 
> doing nothing. I have not even typed a single command.
>
> I am a bit puzzled. There must be something strange going on here. But 
> all I did was to checkout trunk, start FriCAS' AXIOMsys
>
>                  FriCAS (AXIOM fork) Computer Algebra System
>                          Version: FriCAS 2008-01-18
>                Timestamp: Monday January 21, 2008 at 19:44:19
>
> and then )read jyperdoc.input .
>
>> You can then open the browser to http://
>> localhost:8085/the-path-to-jyperdoc/jyperdoc.xhtml
>> To evaluate a cell, type shift and enter. Hitting enter will create a
>> new line. Multiple
>> lines are allowed.  If you click on the answer you will see more
>> options created by
>> Arthur that allow to change the order of the cells, and even include
>> tex code around
>> the cells (documentation is needed about this).
>
> The window that is poping up has the same color as the background 
> (white). That looks ugly. I also seem to have some problem with 
> firefox 2.0.0.14, since suddenly there were several of these little 
> windows that I had to close one by one.
>
>> I have added an initial type of editor based on codepress, that 
>> allows for SPAD
>> syntax highlighting. Here is where I think we can add noweb and
>> ALLPROSE support.
>
> Ah. Then it should be enough to support noweb. ALLPROSE is a framework 
> to compile Aldor libraries. Syntax is Noweb+Aldor.
>
>> Things that I will like to add in the future is allow graphs 2D/3D
>> (Arthur is working
>> on this) and allow it to display the current ht pages from HyperDoc. 
>> Martin gave
>> me an idea with his code that I may explore.
>
>> If you have any suggestions, please let me know. Anything you think 
>> it should
>> be removed or added, or of interest for ALLPROSE.
>
> When I see the output of Axiom, like "Polynomial(Integer)", both of 
> these should be clickable and point to their documentation. I have not 
> been able to see something like Hyperdoc.
>
> I have erronously typed
>
> http://localhost:8085//home/hemmecke/SVK/jyperdoc
>
> (no jyperdoc.xhtml at the end)
>
> Then fricas said:
>
> axServer(8085, multiServ)$AXSERV
>
> multiServ begin
> request type: GET
> getFile: //home/hemmecke/SVK/jyperdoc
> getContentType begin
>
>    >> Error detected within library code:
>    index out of bound
>
> ----------------------------------------------------------------------------- 
>
>
> Some nasty questions...
>
> What is the reason to develop yet another notebook and not take the 
> one from Sage? Is Sage's webinterface not able to deal with axiom? 
> What are the deficiencies wrt Axiom?
>
> Axiom is so huge, so if Sage would be a part of Axiom that just 
> handles the web interface, why not?
>
> Shouldn't it already be possible to show graphics with the Sage notebook?
>
>
> Ralf
>




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> How does the fricas/axiom source code layout work?
> Is it all written in pamphlets that lisp is generated from?

There is a bit of a philosophical split between Axiom and
Fricas about source code layout and it is fairly fundamental.

Axiom has everything in pamphlet files and is gradually moving
to book-style layout. (As far as I know this is the only project
that is structured this way). One of Axiom's fundamental goals
is to restructure the complete source tree to be literate
programs. See the Lisp in Small Pieces or Tex, The Program books.

Fricas is a project fork and one of its fundamental goals is to
remove the literate programming structure. This is an ongoing
effort (as evidenced by the post in late March, 2008:
<http://groups.google.com/group/fricas-commit/browse_thread/thread/
ba4f3be7d257fef?hl=en>
So I really cannot comment on the non-Axiom processes.

In Axiom all of the source code lives in Knuth-style literate
documents. So the basic process is to extract the source code
from the document and then compile it. This can involve several
steps since the algebra code has its own language (Spad). Thus
algebra goes thru the steps:

extract spad from pamphlet ->
  compile code with spad compiler to lisp ->
    compile lisp code with GCL to C ->
      compile C code to machine code with GCC

> Anyway, I would love if somebody who knows what they
> are talking about regarding axiom (not me!) would
> explain what the human-written/readable code
> parts of the axiom distro are

In the near term every "source code file" is a literate document.
The idea is that you should be able to open (using a div/pdf
viewer) the file and read it like a book.

The rational for this huge change is based on experience. I
was one of the original authors of Axiom. I got my own code
back after 15 years and found it unreadable. This is despite
my best efforts at the time to write dirt-simple, clear code.
(You will encounter the same problem with Sage in the future.)

I spent some time reading and pondering this issue and eventually
discovered that Knuth had already solved it using Web technology
for literate programs. I STRONGLY encourage you to learn about
this technology because Sage is going to have the same fundamental
problems that Axiom encountered.

One problem is that the research is not associated with the source
code. A recent example is the Pollard-Rho algorithm that was part
of the Sage/Fricas discussion. It turns out that Axiom implements
Brent's algorithm which is an extension of Pollard-Rho, despite
the comments to this list. The only way to know that is to read
the code, read the literature, and "discover" what the code does.

Sage is being built by experts who are the primary source for the
material. This is excellent while it lasts but it won't last. At
some point in the future these experts will no longer be available.
If you think long term it becomes clear what this implies.

Code is guaranteed to be opaque because the world's expert in some
area (L-functions?) wrote clever, highly optimized code that does
not correspond to anything in the literature. Thus, the only person
who can properly maintain, modify, and extend the code will no
longer be available and the code will be frozen in time. My
Magnus infinite group theory project has this problem.

New people coming onto the project cannot find the literature
that corresponds to the actual code because it does not exist.
Most published results are 5 page conference papers that just
hint at the non-core, but vitally important, details if they
mention them at all. This problem has 2 parts, both of which
stem from the lack of focus on the new discipline of computational
mathematics. Part 1 is that journals and conferences only want
short papers, which are adequate for math, not the complete
implementation. Part 2 is that there is no place to describe the
actual code-level optimizations that make the implementation
practical and fast.

I believe that the Knuth's literate programming technology will
solve the long term problem and keep the code as a living,
understandable, maintainable, and extensible object. It directly
addresses the problem of bringing the research and the code together.
It gives a place to explain both the algorithm and the current
code optimizations. Further, I've been working with Carlo Traverso
(Univ. of Pisa, Math) to create a journal of these literate
programs so the algorithms and their implementations can be made
widely available for study and improvement.

This is a controversial position and led to a philosophical
split between Axiom and Fricas. Fricas has the stated goal of
competing with Mathematica. Axiom plans to change the game so
Mathematica is irrelevant.

> and roughly how big each is, in some sense.

Ah, size. Here is where Axiom parts company with most of the
other systems. Axiom is highly structured using categories
and domains. It is trivially easy to construct a domain which
overrides the categorical definition of a single function
but uses all of the rest by inheritance. Thus, "line of code"
have nothing to do with "conceptual size".

That said, Axiom is still huge by any measure. It represents
about 30 years and 300 man-years of research. It covers a
wide range of computational mathematics.



> Or just point me to an article or wiki page
> about this.  And who are some of the Axiom original
> authors?  Some files have headers like:
>
> ++ Author: Grabmeier, Gschnitzer, Williamson
> ++ Date Created: 1987
> ++ Date Last Updated: July 1990
>
> I wonder who those guys were...?

Ummm, who these guy *ARE*.

There is a very active community based around the ISSAC
(International Symposium on Scientific and Algebraic
Computation) and ECCAD (East Coast Computer Algebra Days)
which is attended by almost everyone in the computational
mathematics community. It has a long history. There are
a large number of people still active from the early Axiom
days. You can see a list of the some of the people by
starting Axiom and typing )credits. Sage may be new but
we've been at this for a long time :-)

Sage should definitely concentrate on presenting at ISSAC.
You could probably start a Sage paper track. Since I know
most of the people involved I'd be willing to help.




> There are rumblings but *definitely* no specific plans to remove
> lisp or maxima.

Lisp has already solved a lot of the problems Python has yet to
face. But since that discussion is a prelude to a language war
I'll end it here.

>
> That might sound weird, since why would an Axiom guy want to
> help with working on or improving Maxima?

While both are coded in Lisp they are philosophically wildly
different. Axiom algebra is in the spad language, not Lisp.
Thus "fixing maxima" (which works fine, btw) would be like
working in a completely separate language. I know James
(the Maxima Lead) and we're not in any kind of competition.

>    But that's the
> ** Sage WAY ** which is to get all open source software packages
> to work better.  I think any and all competition/fighting between
> open source math software is completely counterproductive.
> The goal we should all have is to provide a viable free open
> source alternative to Maple, Mathematica, Matlab, and Magma.

While I agree with "free" and "open source" (given that I've spent
the last 7 years doing that with Axiom) I have to question the
"viable" point. I think "viable" needs to be discussed within
Sage because it is vital.

If you looked at the list of credits from Axiom mentioned above
you'll notice that, of the 140+ contributors, some of them are dead.
I just attended a funeral for one in January.

Sage is too new to think about this problem but what happens when
your expertise "disappears"? What happens when you are the only
use of an open source program (such as Magnus, an infinite group
theory package)? Suppose the maintainer quits or dies? What will
Sage do (WWSD)? Do you just drop the package? Do you let it rot?
Will I find that my notebooks won't work in the next release?
If Magnus fails to compile under C++0X do you just drop it?
Do you try to recode it in Python? Do you know enough infinite
group theory to recode it? Do you know anyone willing to recode
it? Do you even know what algorithms it has?

I would hope to convince the Sage team that THE most important
contribution they can make is to provide a firm base for future
computational mathematics. Think of the science and the long
term. Insist that people document their code in a literate form
so that others can maintain and extend the code. Your REAL
issue is not the "4Ms". They are going to die because all
companies die and they are going to disappear because dying
companies take their code with them (witness Symbolics and
Macsyma). The REAL issue is the science of computational
mathematics.

Open source suffers from "project rot". Lead developers and
maintainers move on to other things and the projects die.
(Witness "Pinger", which was my open source implementation of
a closed source network management tool for Worldcom, another
company that "couldn't disappear" but did.)


> because Maxima (via pexpect) is too slow and,
> much more importantly, it is too hard for developers to improve
> and change.  This difficulty for developers has stopped dead
> promising Sage development projects related to symbolic
> calculus computation.   This symbolic manipulation rewrite
> is actually well on its way; Gary Furnish has been working on
> it day and night for a few months now, and has been funded
> by the NSF and Google (thanks!) to work on it full time at UW
> all summer.

Gee, wouldn't it be great if Gary could just read the literate
documentation of a system like Maxima and know the details of
how to implement the algorithm? This IS the late 90s and we can
construct real documentation of real computational mathematics
if we want so that the science as a whole benefits. I hope that
Gary generates literate documents so I can re-implement his
algorithms in Axiom.




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Cc: axiom-dev <axiom-developer@nongnu.org>, sage-devel@googlegroups.com,
	open-axiom-devel <open-axiom-devel@lists.sourceforge.net>
Subject: [Axiom-developer] Re: [fricas-devel] Re: [sage-devel] Re:
	[fricas-devel] Re: Project
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Hi William,

On 04/20/2008 05:29 PM, William Stein wrote:
>>  >  On Sun, Apr 20, 2008 at 3:10 AM, Martin Rubey <martin.rubey@univie.ac.at> wrote:
>>  >  > I don't have the guts to send this to a public mailing list.  I probably
>>  >  >  should.  If you want to, you have my permission.
>>  >  >
>>  >  >
>>  >  >  "Alfredo Portes" <doyenatccny@gmail.com> writes:
>>  >  >
>>  >  >  > >  Axiom is so huge, so if Sage would be a part of Axiom that just handles
>>  >  >  > > the web interface, why not?
> 
> The part of Sage that deals with the web interface is written
> in pure Python and depends only on Python, Twisted, and
> Pexpect.   At present it is somewhat tightly integrated into
> the Sage distribution.  But this is only *temporary*, which
> we intend to change in the future, most likely this summer.
> Thus if you just want to have an Axiom GUI and or web notebook
> interface, you could just ship or depend on
> 
>      Python+Twisted+Pexpect+a small part of Sage.

Oh, that looks interesting. The question is, who is going to implement 
that? Are there any volunteers around?

> I don't understand the Axiom distribution enough to understand
> how big it is, but my impression is that it is *also* huge.

Well, one cannot cover a big part of mathematics ant not being huge.

> Looking
> in the src/src/algebra directory there are many hundreds of
> thousands of lines of code (over 300,000 distinct lines just of
> dot-lsp files).  By the way, how do you guys read
> some of this stuff?

Nobody should have need to read LISP. Mathematicians are used to "higher 
level". I would prefer if under src/algebra there would be only spad 
files with nothing but SPAD (or Aldor) and documentation in them.
One can write relatively compact code in SPAD/Aldor and nothing like 
LISP should distract from that.

 > I looked in INTALG.lsp and it is
> pages of code that look like this:
>                                              (PROGN
>                                                (LETT #0# NIL
>                                                 |INTALG;palglogint|)
>                                                (SEQ
>                                                 (LETT |q| NIL
>                                                  |INTALG;palglogint|)
>                                                 (LETT #1#
>                                                  (SPADCALL (QCDR |fc|)
>                                                   |lf| (QREFELT $ 79))
>                                                  |INTALG;palglogint|)
>                                                 G190
>                                                 (COND
>                                                   ((OR (ATOM #1#)
>                                                     (PROGN
>                                                       (LETT |q|
>                                                        (CAR #1#)
>                                                        |INTALG;palglogint|)
>                                                       NIL))
>                                                    (GO G191)))
>                                                 (SEQ
>                                                  (EXIT
>                                                   (LETT #0#
>                                                    (CONS
>                                                     (SPADCALL
>                                                      (SPADCALL
>                                                       (QCAR |q|) 0
>                                                       (QREFELT $ 82))
>                                                      (QREFELT $ 83))
>                                                     #0#)
>                                                    |INTALG;palglogint|)))
> 
> This is from INTALG.lsp.  Surely this is some machine-generated
> code that isn't meant to be human readable, so I'm
> measuring the wrong thing!

Of course. And of course, nobody reads that. Or is there someone?

> How does the fricas/axiom source code layout work?
> Is it all written in pamphlets that lisp is generated from?
> Anyway, I would love if somebody who knows what they
> are talking about regarding axiom (not me!) would
> explain what the human-written/readable code
> parts of the axiom distro are and roughly how big each is,
> in some sense.

William, since you are an invited speaker at ISSAC, why not staying a 
little longer and attending the Aldor & Axiom Workshop right after 
ISSAC? There might be some people around that could explain.

> And who are some of the Axiom original
> authors?  Some files have headers like:

> ++ Author: Grabmeier, Gschnitzer, Williamson
> ++ Date Created: 1987
> ++ Date Last Updated: July 1990
> 
> I wonder who those guys were...?

I agree, nothing is perfect. But as for this particular case, I know Dr. 
Johannes Grabmeier personally, and since he is working near Linz, he 
might be around at the Aldor & Axiom Workshop.

Ralf



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Subject: [sage-devel] Re: [fricas-devel] Re: [sage-devel] Re: [fricas-devel]
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> >  A good unifying graphical interface is extremely important to creating
> >  something that is a viable alternative to
> >  Maple/Mathematica/Magma/Matlab.  In some sense it is perhaps it
> >  is *the* most important thing.

I fully agree that a unifying graphical interface is extremely
important. But I find that Sage is again not thinking "long term".

Another lesson from history.... Axiom has a help system that was
wildly innovative at the time it was created. Hyperdoc did things
like "back buttons", "tear-off pages" (aka open a new window),
"live embedded graphics" (click on an image and get a graph you
can actively manipulate), "client-server interaction" (AJAX),
"network based" (e.g browser/server model).

It WAS wildly innovative at the time but "just barely" matches
what you can do in today's browser for the clever ideas it did
forsee. However, its "age is showing" and Axiom is moving to a
Firefox-based front end, similar in concept to the Sage notebook.

What causes me pause about the Sage notebook is that it is not
very innovative. Throw yourself into the future 30 years from now.
You have infinite CPU, memory, disk, and bandwidth. What will the
researcher use all of this power for? And what interface will they
use to structure their work? And what concepts will be "painfully
obvious" that everyone "should have"?

Axiom is working on a user interface based around a simple idea
called "the crystal". Think of your "problem" as a graph hanging
in space that gets continually updated with information from the
"river of the internet". Wrap a crystal with many facets around
that graph. Each facet of the crystal shows a different (but
consistent) view of the current state of the problem. Each facet
can be a face of many recursive sub-crystals covering smaller
parts of the problem. The crystals maintain the "intensional
stance" (what the user appears to be trying to do) of the user
and the graph is actively updated dynamically in anticipation
of potential requests. Thus, mentioning "L-functions" will kick
off a dynamics search and classification of all known work from
the "internet river" into the graph. Oh, yeah, and clicking for
"help" on a function brings up a LITERATE version of the function
documentation so you can learn how it really works in readable
form along with clickable bibliographic references to yet-other
literate algorithms.

It is not an issue that this cannot be done efficiently with
today's hardware. The issue is that it is a conceptual structure
that allows a consistent growth path. In the language of design
(e.g. Winograd's books) it has new tacits and new affordances
with less breakage. I'd encourage you to read Winograd or other
"design philosophy" books and think about the design of the user
interface further. Norman's design books are especially entertaining:
<http://www.amazon.com/Design-Everyday-Things-Donald-Norman/dp/
0385267746>
Ask the questions: What does a computational mathematician need?
How can we structure the science platform so those needs are
fulfilled? What conceptual structures underlie that solution?

The 4Ms cannot make this kind of leap. The corporate structure won't
allow anything so innovative to set direction. In fact, I doubt you
could get Google, despite its corporate cleverness, to even consider
funding the development of such an interface, despite the fact that
they ARE "the river of the internet". At best, you get funded for
yet-another-notebook. Sigh.

You can continue to copy the 4Ms or by defining the new tacits and
affordances you can make the 4Ms irrelevant. To paraphrase Sun Tzu,
"A great general wins wars by not fighting them"

Think long term. Look toward the 30 year horizon.

Tim

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On Sun, Apr 20, 2008 at 11:13 AM, TimDaly <daly@axiom-developer.org> wrote:
>
>
>  > How does the fricas/axiom source code layout work?
>  > Is it all written in pamphlets that lisp is generated from?
>
>  There is a bit of a philosophical split between Axiom and
>  Fricas about source code layout and it is fairly fundamental.

Thanks for your explanation of this, which I think was very helpful.

>  Axiom has everything in pamphlet files and is gradually moving
>  to book-style layout. (As far as I know this is the only project
>  that is structured this way). One of Axiom's fundamental goals
>  is to restructure the complete source tree to be literate
>  programs. See the Lisp in Small Pieces or Tex, The Program books.
>
>  Fricas is a project fork and one of its fundamental goals is to
>  remove the literate programming structure. This is an ongoing
>  effort (as evidenced by the post in late March, 2008:
>  <http://groups.google.com/group/fricas-commit/browse_thread/thread/
>  ba4f3be7d257fef?hl=en>
>  So I really cannot comment on the non-Axiom processes.
>
>  In Axiom all of the source code lives in Knuth-style literate
>  documents. So the basic process is to extract the source code
>  from the document and then compile it. This can involve several
>  steps since the algebra code has its own language (Spad). Thus
>  algebra goes thru the steps:
>
>  extract spad from pamphlet ->
>   compile code with spad compiler to lisp ->
>     compile lisp code with GCL to C ->
>       compile C code to machine code with GCC

What kind of runtime/build dependencies does the code
generated by GCL have?  It would be cool if Axiom/Maxima/whatever
could be built as a pure C program, with no lisp involved at all,
and GCL were only used say on linux to do the
lisp --> C conversion.  I have no idea if this makes any sense,
but this is what happens with Cython.

>  > Anyway, I would love if somebody who knows what they
>  > are talking about regarding axiom (not me!) would
>  > explain what the human-written/readable code
>  > parts of the axiom distro are
>
>  In the near term every "source code file" is a literate document.
>  The idea is that you should be able to open (using a div/pdf
>  viewer) the file and read it like a book.
>
>  The rational for this huge change is based on experience. I
>  was one of the original authors of Axiom. I got my own code
>  back after 15 years and found it unreadable. This is despite
>  my best efforts at the time to write dirt-simple, clear code.
>  (You will encounter the same problem with Sage in the future.)

Some people are a lot better at jumping into random code
and making sense of it than others.   My thesis adviser -- Hendrik
Lenstra -- didn't code, but he was amazingly good at jumping
into "random mathematics" and making sense of it.  Reading
code is similar.    Actually, this whole problem you'll describing
is a problem also in mathematics research.  When a person
decides to read a serious research paper in mathematics,
they will often allocate weeks (at least) to really understand the
paper (especially if they can't talk to any experts in the area).
I'm not talking about computational math here, but just research
mathematics in general, which is really the culture I was
trained in.

>  I spent some time reading and pondering this issue and eventually
>  discovered that Knuth had already solved it using Web technology
>  for literate programs. I STRONGLY encourage you to learn about
>  this technology because Sage is going to have the same fundamental
>  problems that Axiom encountered.

I'm unconvinced that literate programming is a silver bullet that
solves the problem of making code easier to understand later.   I do
strongly
advocate documenting and writing excellent test suites for code.
All code that goes into Sage has every function tested, documented,
and it is refereed by a different person (who may as well be somebody
reading the code 15 years later...).  I think peer review is a valuable
step in the right direction toward solving the problem you are addressing.
That's what's done in mathematics to increase the chances that
somebody can understand a math paper 15 years after it is written.

>  One problem is that the research is not associated with the source
>  code. A recent example is the Pollard-Rho algorithm that was part
>  of the Sage/Fricas discussion. It turns out that Axiom implements
>  Brent's algorithm which is an extension of Pollard-Rho, despite
>  the comments to this list. The only way to know that is to read
>  the code, read the literature, and "discover" what the code does.
>
>  Sage is being built by experts who are the primary source for the
>  material. This is excellent while it lasts but it won't last.

Why won't it last?  I mean, the experts will change, but I see no
reason that the statement "Sage is being built by experts ..." will
not last.

> At  some point in the future these experts will no longer be available.

I guess that's true.  At some point in the future nobody in particular
will be available.

>  If you think long term it becomes clear what this implies.

How longterm are you thinking?

>  Code is guaranteed to be opaque because the world's expert in some
>  area (L-functions?) wrote clever, highly optimized code that does
>  not correspond to anything in the literature. Thus, the only person
>  who can properly maintain, modify, and extend the code will no
>  longer be available and the code will be frozen in time.

I simply do *NOT* have such a pessimistic view of the capabilities
of the people who work on Sage.

> My Magnus infinite group theory project has this problem.
>
>  New people coming onto the project cannot find the literature
>  that corresponds to the actual code because it does not exist.
>  Most published results are 5 page conference papers that just
>  hint at the non-core, but vitally important, details if they
>  mention them at all. This problem has 2 parts, both of which
>  stem from the lack of focus on the new discipline of computational
>  mathematics. Part 1 is that journals and conferences only want
>  short papers, which are adequate for math, not the complete
>  implementation. Part 2 is that there is no place to describe the
>  actual code-level optimizations that make the implementation
>  practical and fast.

I assume your talking specifically about your project(s) and not
all computational mathematics projects.  Since the above is
not true of all such projects.

>  I believe that the Knuth's literate programming technology will
>  solve the long term problem and keep the code as a living,
>  understandable, maintainable, and extensible object. It directly
>  addresses the problem of bringing the research and the code together.
>  It gives a place to explain both the algorithm and the current
>  code optimizations. Further, I've been working with Carlo Traverso
>  (Univ. of Pisa, Math) to create a journal of these literate
>  programs so the algorithms and their implementations can be made
>  widely available for study and improvement.
>
>  This is a controversial position and led to a philosophical
>  split between Axiom and Fricas. Fricas has the stated goal of
>  competing with Mathematica. Axiom plans to change the game so
>  Mathematica is irrelevant.

I'm surprised by how convinced you are that using a specific
technology/language -- literate programming -- can be a silver
bullet to solve such a difficult problem.  I think peer review,
and many many other things, are steps in the right direction,
but *not* solutions to the problem.  I think it's just a difficult
problem, with no easy solutions.

>  > and roughly how big each is, in some sense.
>
>  Ah, size. Here is where Axiom parts company with most of the
>  other systems. Axiom is highly structured using categories
>  and domains. It is trivially easy to construct a domain which
>  overrides the categorical definition of a single function
>  but uses all of the rest by inheritance.

I think Magma (and Sage) are exactly like that.

>  Thus, "line of code"  have nothing to do with "conceptual size".
>
>  That said, Axiom is still huge by any measure. It represents
>  about 30 years and 300 man-years of research. It covers a
>  wide range of computational mathematics.

Sorry I was mainly interested in how many lines of code, in
some rough sense, are in the Axiom codebase, since this
whole thread started discussing the difficulties involved with
the code size of Axiom (since it's about combining source
code for project).   I'm still really curious how big the Axiom
codebase is.
>
>
>
>  > Or just point me to an article or wiki page
>  > about this.  And who are some of the Axiom original
>  > authors?  Some files have headers like:
>  >
>  > ++ Author: Grabmeier, Gschnitzer, Williamson
>  > ++ Date Created: 1987
>  > ++ Date Last Updated: July 1990
>  >
>  > I wonder who those guys were...?
>
>  Ummm, who these guy *ARE*.
>
>  There is a very active community based around the ISSAC
>  (International Symposium on Scientific and Algebraic
>  Computation) and ECCAD (East Coast Computer Algebra Days)
>  which is attended by almost everyone in the computational
>  mathematics community. It has a long history. There are
>  a large number of people still active from the early Axiom
>  days. You can see a list of the some of the people by
>  starting Axiom and typing )credits. Sage may be new but
>  we've been at this for a long time :-)

So have I.  I've been seriously involved in writing mathematical
software for over 10 years.  I worked as a developer on Magma
for 5 years...

>  Sage should definitely concentrate on presenting at ISSAC.
>  You could probably start a Sage paper track. Since I know
>  most of the people involved I'd be willing to help.

I'm speaking at the next ISSAC...  we'll see how it goes.
If that community likes Sage, then I bet a lot of positive
things will come of it.   I really don't know what to expect.

>  > There are rumblings but *definitely* no specific plans to remove
>  > lisp or maxima.
>
>  Lisp has already solved a lot of the problems Python has yet to
>  face. But since that discussion is a prelude to a language war
>  I'll end it here.

That's where you're a *lot* more fun to discuss mathematical
software with that Richard Fateman!  Thanks for taking the
time to write.

>
>
>  >
>  > That might sound weird, since why would an Axiom guy want to
>  > help with working on or improving Maxima?
>
>  While both are coded in Lisp they are philosophically wildly
>  different. Axiom algebra is in the spad language, not Lisp.
>  Thus "fixing maxima" (which works fine, btw) would be like
>  working in a completely separate language. I know James
>  (the Maxima Lead) and we're not in any kind of competition.

I have the impression that Waldek Habisch is extremely
talented at hacking build systems and building code that
involves lisp.   I wouldn't be surprised if he could make
many positive contributions toward getting Maxima to
run on http://ecls.sourceforge.net/.

>
>  >    But that's the
>  > ** Sage WAY ** which is to get all open source software packages
>  > to work better.  I think any and all competition/fighting between
>  > open source math software is completely counterproductive.
>  > The goal we should all have is to provide a viable free open
>  > source alternative to Maple, Mathematica, Matlab, and Magma.
>
>  While I agree with "free" and "open source" (given that I've spent
>  the last 7 years doing that with Axiom) I have to question the
>  "viable" point. I think "viable" needs to be discussed within
>  Sage because it is vital.

What do you mean?  Do you mean that disagree with making
mathematical software that is viable?  Instead you only want to
make mathematical software that is free and open source, but
isn't viable?

>
>  If you looked at the list of credits from Axiom mentioned above
>  you'll notice that, of the 140+ contributors, some of them are dead.
>  I just attended a funeral for one in January.

Sage also unfortunately has a deceased contributor listed at
        http://lite.sagemath.org/devmap.html

>  Sage is too new to think about this problem but what happens when
>  your expertise "disappears"?

It happens all the time. Iregardless of whether developers die or
not, they do disappear -- e.g., they go into industry instead of
academia and are legally obliged to no longer contribute (or just
not interested) -- or they move onto other things -- or get a job
with an incredibly high teaching load.  It happens all the time.
What happens?  You deal with it.  You realize that it is going to
keep happening, so you constantly build in a wide range of
strategies to protect against it.   This is the way it is with all
large software projects, or indeed all large group enterprises.

> What happens when you are the only
>  use of an open source program (such as Magnus, an infinite group
>  theory package)?

It typically dies.

>  Suppose the maintainer quits or dies?

If there is only one user and that person quits, who cares?

>  What will
>  Sage do (WWSD)?
> Do you just drop the package? Do you let it rot?

We don't like having things in Sage with only 1 users in
the entire world.  In fact, if there is only 1 and they vanish,
who cares?

>  Will I find that my notebooks won't work in the next release?
>  If Magnus fails to compile under C++0X do you just drop it?

We don't include Magnus in Sage.

>  Do you try to recode it in Python? Do you know enough infinite
>  group theory to recode it? Do you know anyone willing to recode
>  it? Do you even know what algorithms it has?

No.  No. No. No.

We would ask all those questions if somebody proposed adding
Magnus to Sage.  All those no answers would likely cause
people to vote against it and it wouldn't get included.

>  I would hope to convince the Sage team that THE most important
>  contribution they can make is to provide a firm base for future
>  computational mathematics. Think of the science and the long
>  term. Insist that people document their code in a literate form
>  so that others can maintain and extend the code.

We insist that people document their code and that it passes
peer review.

> Your REAL issue is not the "4Ms".

Yes it is.  It's *my* personal real issue at least.

> They are going to die because all
>  companies die and they are going to disappear because dying
>  companies take their code with them (witness Symbolics and
>  Macsyma).

All that matters to me regarding the above comments are
the *next* 30 years, since after that I'll likely be "done".
And it's possible that none of Maple/Mathematica/Matlab
will die in the next 30 years.

> The REAL issue is the science of computational
>  mathematics.

Not for me.  I just want to "finish" Sage as soon as possible,
so I can do research and teaching using it.   From this point
of view, Sage is surprisingly close to where I want.
It's I think at most 1 or 2 years away.  One important thing that we aren't
yet close on is very good native Microsoft Windows support;
and I don't mean crippled Cygwin support or virtual machines.

>  Open source suffers from "project rot". Lead developers and
>  maintainers move on to other things and the projects die.
>  (Witness "Pinger", which was my open source implementation of
>  a closed source network management tool for Worldcom, another
>  company that "couldn't disappear" but did.)

Some open source projects don't die.  Witness Linux, which is
an operating system that "could easily disappear" but didn't.

>  > because Maxima (via pexpect) is too slow and,
>  > much more importantly, it is too hard for developers to improve
>  > and change.  This difficulty for developers has stopped dead
>  > promising Sage development projects related to symbolic
>  > calculus computation.   This symbolic manipulation rewrite
>  > is actually well on its way; Gary Furnish has been working on
>  > it day and night for a few months now, and has been funded
>  > by the NSF and Google (thanks!) to work on it full time at UW
>  > all summer.
>
>  Gee, wouldn't it be great if Gary could just read the literate
>  documentation of a system like Maxima and know the details of
>  how to implement the algorithm?
> This IS the late 90s and we can
^^^^^^^^^^^^^^^^^^^^

Last I checked it is not the late 90s.  ???

>  construct real documentation of real computational mathematics
>  if we want so that the science as a whole benefits. I hope that
>  Gary generates literate documents so I can re-implement his
>  algorithms in Axiom.

I'm sure he's not generating literate documents.  He's probably also
mostly not coming up with any new algorithms easier.   He's just
doing what he is doing because he is a very talented programming
and he needs the results to support his research interests.

 -- William



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From: "Ted Kosan" <ted.kosan@gmail.com>
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Subject: Re: [Axiom-developer] Re: Project
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Alfredo Portes wrote:

>  It seems that Sage is going to connect with OLPC.  If all those kids do their
>  math using Sage, I think there is no way around Sage anymore.  Sage can already
>  do many many things better than Axiom, I suppose, so we need really good
>  reasons to continue with Axiom, I think.  Maybe I should just redo the guessing
>  package in Python and be done with it?  Some time ago I said that I'll quit
>  Axiom if there are less than twenty contributors by the end of 2008.  However,
>  it seems to me that the number of algebra contributors actually went down!
>
>  I'd really like to hear some comments on the general plan.  Do you think it's
>  feasible to
>
>  a) attract other people, not working on Sage
>  b) merge our community into the Sage community

I recently spent 11 months with the Sage project working on marketing
ideas in general for Sage and specifically working on ways to make
Sage suitable for CAS beginners (like high school students and
university freshman and sophomores).  I identified many hurdles which
were blocking these goals and I also developed solutions for some of
them.  When the Sage project decided to focus its efforts on research
instead of eduction a couple of months ago, I stopped working on Sage
specifically but I continued to work on developing these solutions.
Sage and Axiom are similar enough that they have common hurdles so the
solutions I developed for Sage should also work for Axiom.

I very much like the Axiom project's strategic 30 year planning
horizon and I personally think that a large and active user base is an
important part of this strategy.  If the Axiom project desires to
significantly increase its user base, I think I know ways to do this.



Tim Daly wrote:

> >  A good unifying graphical interface is extremely important to creating
> >  something that is a viable alternative to
> >  Maple/Mathematica/Magma/Matlab.  In some sense it is perhaps it
> >  is *the* most important thing.
>
>I fully agree that a unifying graphical interface is extremely
>important. But I find that Sage is again not thinking "long term".
>...
>What causes me pause about the Sage notebook is that it is not
>very innovative.

One of my solutions for making Sage easier to use for CAS beginners
was the development of a "notebook" which was based on a different
approach than the Sage notebook uses.  Instead of calling it a
"notebook", however, I call this system a Mathematics Computing
Environment and its name is MathRider.

MathRider currently uses Yacas as its core computer algebra system but
I do not think it would take too much effort to also allow MathRider
to support Axiom.



>Axiom is working on a user interface based around a simple idea
called "the crystal".

MathRider is based on powerful enough technology to support almost any
vision you have for "the crystal".


Anyway, if anyone is interested in looking at some screen shots and a
flash demo of MathRider to see if it might be suitable for use with
Axiom, here is a link to its project website:

https://mathrider.dev.java.net/

Respectfully,

Ted Kosan



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Ted, 

That's a very pretty piece of work and it seems really well integrated
with yacas. I'm surprised that Sage wouldn't use it for education.
The dynamic graphing is perfect for the education market.

Tim



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William Stein wrote:
> I'm unconvinced that literate programming is a silver bullet that
> solves the problem of making code easier to understand later.   I do
> strongly
> advocate documenting and writing excellent test suites for code.
> All code that goes into Sage has every function tested, documented,
> and it is refereed by a different person (who may as well be somebody
> reading the code 15 years later...).  I think peer review is a valuable
> step in the right direction toward solving the problem you are addressing.
> That's what's done in mathematics to increase the chances that
> somebody can understand a math paper 15 years after it is written.

Well, literate programming may not be a silver bullet, but its "dual", 
reproducible research, is a concept I as a practitioner find *very* 
attractive. The base entity in reproducible research, as espoused by a 
number of people in the R community, is something called a "compendium". 
A compendium is a software package that contains all the code and data 
necessary to reproduce the research. No more generating pictures with R, 
exporting them to PDFs or Postscript, pasting them into a LaTeX 
document, only to discover that you have a bug, and having to go through 
the whole edit-test-cut-paste cycle all over again.

A lot of this magic right now is really only easy with R and the LaTeX 
editor LyX. But I can sit at my workstation and edit a paper in LyX, put 
the code in it to generate figures, put more code in it that's visible 
if I want to document an algorithm. At any time, I can push a button and 
get a PDF of the document, at the same time executing any other code 
that doesn't appear in the document. And with "RUnit", I can easily add 
unit tests.

Essentially all you need to do this (on Linux -- it doesn't work on 
Windows yet and I'm not sure about Macs or Solaris) is to install R and 
LyX and their dependencies. There's a contributed package that adds a 
bit of "glue logic" to the LyX configuration, but once you do that, the 
workflow is quite author-friendly.

> I guess that's true.  At some point in the future nobody in particular
> will be available.

Except Woody Allen ... as you probably know, he said, "I don't plan to 
achieve immortality through my works. I plan to achieve immortality by 
not dying." :)

>>  Lisp has already solved a lot of the problems Python has yet to
>>  face. But since that discussion is a prelude to a language war
>>  I'll end it here.
> 
> That's where you're a *lot* more fun to discuss mathematical
> software with that Richard Fateman!  Thanks for taking the
> time to write.

Well, there really are only two "perfect" languages, Lisp/Scheme and 
Forth. ;)

>> They are going to die because all
>>  companies die and they are going to disappear because dying
>>  companies take their code with them (witness Symbolics and
>>  Macsyma).

Well, Maxima isn't all that far removed from Macsyma and Vaxima.

> All that matters to me regarding the above comments are
> the *next* 30 years, since after that I'll likely be "done".
> And it's possible that none of Maple/Mathematica/Matlab
> will die in the next 30 years.

I'd be willing to bet Mathematica survives. I won't comment on the other 
two. Lisp will survive too, no matter how hard Paul Graham tries to 
"improve" it. :)

> Not for me.  I just want to "finish" Sage as soon as possible,
> so I can do research and teaching using it.   From this point
> of view, Sage is surprisingly close to where I want.
> It's I think at most 1 or 2 years away.  One important thing that we aren't
> yet close on is very good native Microsoft Windows support;
> and I don't mean crippled Cygwin support or virtual machines.

You aren't the only open source project that has poor Windows support. 
But there are some happy exceptions. I personally prefer the Windows UI 
for R to the "native" Linux one.





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>>  It seems that Sage is going to connect with OLPC.  If all those kids do their
>>  math using Sage, I think there is no way around Sage anymore.  Sage can already
>>  do many many things better than Axiom, I suppose, so we need really good
>>  reasons to continue with Axiom, I think.  Maybe I should just redo the guessing
>>  package in Python and be done with it?  Some time ago I said that I'll quit
>>  Axiom if there are less than twenty contributors by the end of 2008.  However,
>>  it seems to me that the number of algebra contributors actually went down!

Well, before you get your hopes up on the OLPC XO, let someone who owns 
two of them (me) inject a bit of realism into the discussion. The XO in 
its current platform has a 433 MHz AMD Geode processor -- essentially a 
low-power Athlon, 256 MB of RAM and a 1 GB flash disk, about 35 percent 
of which is full when you load the base software. I do have both R and 
wxMaxima running on them very well, but I don't think Sage would run 
without a *lot* of shoe-horning. And if you run out of RAM, there is 
*no* swapper and Linux just kills your process. :)

Is it a good platform for learning high-school math? I don't think so. 
You need something with more horsepower.



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Subject: [Axiom-developer] 20080420.01.tpd.patch (CATS Schaums-Axiom
	equivalence testing (13))
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Clearly I've exceeded my ability to simplify these expressions, or
Axiom gets the wrong answers, or Schaums has the wrong answers. 
Personally, I'm betting on the first case.

schaum13.input.pamphlet
  14:280 Axiom cannot simplify these expressions
  14:281 Axiom cannot simplify these expressions
  14:282 Axiom cannot simplify these expressions
  14:283 Axiom cannot simplify these expressions
  14:284 Axiom cannot simplify these expressions
  14:285 Axiom cannot simplify these expressions
  14:286 Axiom cannot simplify these expressions
  14:287 Axiom cannot simplify these expressions
  14:288 Axiom cannot simplify these expressions
  14:289 Axiom cannot simplify these expressions
  14:290 Axiom cannot simplify these expressions
  14:291 Axiom cannot simplify these expressions
  14:292 Axiom cannot simplify these expressions
  14:293 Axiom cannot simplify these expressions
  14:284 Axiom cannot simplify these expressions
  14:295 Axiom cannot compute this integral
  14:296 Axiom cannot compute this integral
  14:297 Axiom cannot compute this integral
  14:298 Axiom cannot compute this integral

========================================================================
diff --git a/changelog b/changelog
index d61af40..29750e1 100644
--- a/changelog
+++ b/changelog
@@ -1,3 +1,4 @@
+20080420 tpd src/input/schaum13.input show Schaums-Axiom equivalence
 20080419 tpd src/input/schaum12.input show Schaums-Axiom equivalence
 20080418 tpd src/input/schaum11.input show Schaums-Axiom equivalence
 20080418 tpd src/input/schaum10.input fix Schaums-Axiom equivalence
diff --git a/src/input/schaum13.input.pamphlet b/src/input/schaum13.input.pamphlet
index eb1a6eb..c4a0351 100644
--- a/src/input/schaum13.input.pamphlet
+++ b/src/input/schaum13.input.pamphlet
@@ -29,7 +29,7 @@ $$
 )set message auto off
 )clear all
 
---S 1 of 19
+--S 1
 aa:=integrate(1/sqrt(a*x^2+b*x+c),x)
 --R 
 --R
@@ -60,6 +60,183 @@ aa:=integrate(1/sqrt(a*x^2+b*x+c),x)
 --R                       \|- a
 --R                                     Type: Union(List Expression Integer,...)
 --E 
+
+--S 2
+bb1:=1/sqrt(a)*log(2*sqrt(a)*sqrt(a*x^2+b*x+c)*2*a*x+b)
+--R
+--R                     +--------------+
+--R                 +-+ |   2
+--R        log(4a x\|a \|a x  + b x + c  + b)
+--R   (2)  ----------------------------------
+--R                        +-+
+--R                       \|a
+--R                                                     Type: Expression Integer
+--E
+
+--S 3
+bb2:=-1/sqrt(-a)*asin((2*a*x+b)/sqrt(b^2-4*a*c))
+--R
+--R                  2a x + b
+--R          asin(--------------)
+--R                +-----------+
+--R                |          2
+--R               \|- 4a c + b
+--R   (3)  - --------------------
+--R                  +---+
+--R                 \|- a
+--R                                                     Type: Expression Integer
+--E
+
+--S 4
+bb3:=1/sqrt(a)*asinh((2*a*x+b)/sqrt(4*a*c-b^2))
+--R
+--R                2a x + b
+--R        asinh(------------)
+--R               +---------+
+--R               |        2
+--R              \|4a c - b
+--R   (4)  -------------------
+--R                 +-+
+--R                \|a
+--R                                                     Type: Expression Integer
+--E
+
+--S 5
+cc1:=bb1-aa.1
+--R
+--R   (5)
+--R                    +--------------+
+--R                +-+ |   2
+--R       log(4a x\|a \|a x  + b x + c  + b)
+--R     + 
+--R       -
+--R          log
+--R                                    +--------------+
+--R                    +-+ +-+         |   2                   +-+
+--R                 (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
+--R               + 
+--R                        2             +-+
+--R                 (- 2a x  - b x - 2c)\|a
+--R            /
+--R                     +--------------+
+--R                 +-+ |   2
+--R               2\|c \|a x  + b x + c  - b x - 2c
+--R  /
+--R      +-+
+--R     \|a
+--R                                                     Type: Expression Integer
+--E
+
+--S 6
+cc2:=bb1-aa.2
+--R
+--R   (6)
+--R                          +--------------+
+--R        +---+         +-+ |   2
+--R       \|- a log(4a x\|a \|a x  + b x + c  + b)
+--R     + 
+--R                          +--------------+
+--R                    +---+ |   2               +---+ +-+
+--R           +-+     \|- a \|a x  + b x + c  - \|- a \|c
+--R       - 2\|a atan(------------------------------------)
+--R                                    a x
+--R  /
+--R      +---+ +-+
+--R     \|- a \|a
+--R                                                     Type: Expression Integer
+--E
+
+--S 7
+cc3:=bb2-aa.1
+--R
+--R   (7)
+--R       -
+--R             +---+
+--R            \|- a
+--R         *
+--R            log
+--R                                      +--------------+
+--R                      +-+ +-+         |   2                   +-+
+--R                   (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
+--R                 + 
+--R                          2             +-+
+--R                   (- 2a x  - b x - 2c)\|a
+--R              /
+--R                       +--------------+
+--R                   +-+ |   2
+--R                 2\|c \|a x  + b x + c  - b x - 2c
+--R     + 
+--R          +-+        2a x + b
+--R       - \|a asin(--------------)
+--R                   +-----------+
+--R                   |          2
+--R                  \|- 4a c + b
+--R  /
+--R      +---+ +-+
+--R     \|- a \|a
+--R                                                     Type: Expression Integer
+--E
+
+--S 8
+cc4:=bb2-aa.2
+--R
+--R                       +--------------+
+--R                 +---+ |   2               +---+ +-+
+--R                \|- a \|a x  + b x + c  - \|- a \|c             2a x + b
+--R        - 2atan(------------------------------------) - asin(--------------)
+--R                                 a x                          +-----------+
+--R                                                              |          2
+--R                                                             \|- 4a c + b
+--R   (8)  --------------------------------------------------------------------
+--R                                        +---+
+--R                                       \|- a
+--R                                                     Type: Expression Integer
+--E
+
+--S 9
+cc5:=bb3-aa.1
+--R
+--R   (9)
+--R       -
+--R          log
+--R                                    +--------------+
+--R                    +-+ +-+         |   2                   +-+
+--R                 (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
+--R               + 
+--R                        2             +-+
+--R                 (- 2a x  - b x - 2c)\|a
+--R            /
+--R                     +--------------+
+--R                 +-+ |   2
+--R               2\|c \|a x  + b x + c  - b x - 2c
+--R     + 
+--R               2a x + b
+--R       asinh(------------)
+--R              +---------+
+--R              |        2
+--R             \|4a c - b
+--R  /
+--R      +-+
+--R     \|a
+--R                                                     Type: Expression Integer
+--E
+
+--S 10     14:280 Axiom cannot simplify these expressions
+cc6:=bb3-aa.2
+--R
+--R   (10)
+--R                      +--------------+
+--R                +---+ |   2               +---+ +-+
+--R       +-+     \|- a \|a x  + b x + c  - \|- a \|c      +---+        2a x + b
+--R   - 2\|a atan(------------------------------------) + \|- a asinh(------------)
+--R                                a x                                 +---------+
+--R                                                                    |        2
+--R                                                                   \|4a c - b
+--R   -----------------------------------------------------------------------------
+--R                                      +---+ +-+
+--R                                     \|- a \|a
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.281~~~~~$\displaystyle
@@ -70,7 +247,7 @@ $$
 <<*>>=
 )clear all
 
---S 2 of 19
+--S 11
 aa:=integrate(x/sqrt(a*x^2+b*x+c),x)
 --R 
 --R
@@ -121,6 +298,220 @@ aa:=integrate(x/sqrt(a*x^2+b*x+c),x)
 --R     ]
 --R                                     Type: Union(List Expression Integer,...)
 --E 
+
+--S 12
+t1:=integrate(1/sqrt(a*x^2+b*x+c),x)
+--R
+--R   (2)
+--R   [
+--R       log
+--R                                 +--------------+
+--R                 +-+ +-+         |   2                   +-+
+--R              (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
+--R            + 
+--R                     2             +-+
+--R              (- 2a x  - b x - 2c)\|a
+--R         /
+--R                  +--------------+
+--R              +-+ |   2
+--R            2\|c \|a x  + b x + c  - b x - 2c
+--R    /
+--R        +-+
+--R       \|a
+--R     ,
+--R                 +--------------+
+--R           +---+ |   2               +---+ +-+
+--R          \|- a \|a x  + b x + c  - \|- a \|c
+--R    2atan(------------------------------------)
+--R                           a x
+--R    -------------------------------------------]
+--R                        +---+
+--R                       \|- a
+--R                                     Type: Union(List Expression Integer,...)
+--E
+
+--S 13
+bb1:=sqrt(a*x^2+b*x+c)/a-b/(2*a)*t1.1
+--R
+--R   (3)
+--R       -
+--R            b
+--R         *
+--R            log
+--R                                      +--------------+
+--R                      +-+ +-+         |   2                   +-+
+--R                   (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
+--R                 + 
+--R                          2             +-+
+--R                   (- 2a x  - b x - 2c)\|a
+--R              /
+--R                       +--------------+
+--R                   +-+ |   2
+--R                 2\|c \|a x  + b x + c  - b x - 2c
+--R     + 
+--R             +--------------+
+--R         +-+ |   2
+--R       2\|a \|a x  + b x + c
+--R  /
+--R        +-+
+--R     2a\|a
+--R                                                     Type: Expression Integer
+--E
+
+--S 14
+bb2:=sqrt(a*x^2+b*x+c)/a-b/(2*a)*t1.2
+--R
+--R   (4)
+--R                   +--------------+
+--R             +---+ |   2               +---+ +-+           +--------------+
+--R            \|- a \|a x  + b x + c  - \|- a \|c      +---+ |   2
+--R   - b atan(------------------------------------) + \|- a \|a x  + b x + c
+--R                             a x
+--R   ------------------------------------------------------------------------
+--R                                      +---+
+--R                                    a\|- a
+--R                                                     Type: Expression Integer
+--E
+
+--S 15
+cc1:=bb1-aa.1
+--R
+--R   (5)
+--R                   +--------------+
+--R               +-+ |   2               2
+--R         (- 2b\|c \|a x  + b x + c  + b x + 2b c)
+--R      *
+--R         log
+--R                                   +--------------+
+--R                   +-+ +-+         |   2                   +-+
+--R                (2\|a \|c  + 2a x)\|a x  + b x + c  - 2a x\|c
+--R              + 
+--R                       2             +-+
+--R                (- 2a x  - b x - 2c)\|a
+--R           /
+--R                    +--------------+
+--R                +-+ |   2
+--R              2\|c \|a x  + b x + c  - b x - 2c
+--R     + 
+--R                   +--------------+
+--R               +-+ |   2               2
+--R         (- 2b\|c \|a x  + b x + c  + b x + 2b c)
+--R      *
+--R         log
+--R                                   +--------------+
+--R                   +-+ +-+         |   2                   +-+
+--R                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
+--R              + 
+--R                       2             +-+
+--R                (- 2a x  - b x - 2c)\|a
+--R           /
+--R                    +--------------+
+--R                +-+ |   2
+--R              2\|c \|a x  + b x + c  - b x - 2c
+--R     + 
+--R                +--------------+
+--R            +-+ |   2                          +-+ +-+
+--R       - 4c\|a \|a x  + b x + c  + (2b x + 4c)\|a \|c
+--R  /
+--R                +--------------+
+--R        +-+ +-+ |   2                                +-+
+--R     4a\|a \|c \|a x  + b x + c  + (- 2a b x - 4a c)\|a
+--R                                                     Type: Expression Integer
+--E
+
+--S 16
+cc2:=bb1-aa.2
+--R
+--R   (6)
+--R                         +--------------+
+--R               +---+ +-+ |   2                2          +---+
+--R         (- 2b\|- a \|c \|a x  + b x + c  + (b x + 2b c)\|- a )
+--R      *
+--R         log
+--R                                   +--------------+
+--R                   +-+ +-+         |   2                   +-+
+--R                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
+--R              + 
+--R                       2             +-+
+--R                (- 2a x  - b x - 2c)\|a
+--R           /
+--R                    +--------------+
+--R                +-+ |   2
+--R              2\|c \|a x  + b x + c  - b x - 2c
+--R     + 
+--R                     +--------------+
+--R             +-+ +-+ |   2                   2          +-+
+--R         (4b\|a \|c \|a x  + b x + c  + (- 2b x - 4b c)\|a )
+--R      *
+--R                     +--------------+
+--R               +---+ |   2               +---+ +-+
+--R              \|- a \|a x  + b x + c  - \|- a \|c
+--R         atan(------------------------------------)
+--R                               a x
+--R     + 
+--R                      +--------------+
+--R            +---+ +-+ |   2                          +---+ +-+ +-+
+--R       - 4c\|- a \|a \|a x  + b x + c  + (2b x + 4c)\|- a \|a \|c
+--R  /
+--R                      +--------------+
+--R        +---+ +-+ +-+ |   2                                +---+ +-+
+--R     4a\|- a \|a \|c \|a x  + b x + c  + (- 2a b x - 4a c)\|- a \|a
+--R                                                     Type: Expression Integer
+--E
+
+--S 17
+cc3:=bb2-aa.1
+--R
+--R   (7)
+--R                         +--------------+
+--R               +---+ +-+ |   2                2          +---+
+--R         (- 2b\|- a \|c \|a x  + b x + c  + (b x + 2b c)\|- a )
+--R      *
+--R         log
+--R                                   +--------------+
+--R                   +-+ +-+         |   2                   +-+
+--R                (2\|a \|c  + 2a x)\|a x  + b x + c  - 2a x\|c
+--R              + 
+--R                       2             +-+
+--R                (- 2a x  - b x - 2c)\|a
+--R           /
+--R                    +--------------+
+--R                +-+ |   2
+--R              2\|c \|a x  + b x + c  - b x - 2c
+--R     + 
+--R                       +--------------+
+--R               +-+ +-+ |   2                 2          +-+
+--R         (- 4b\|a \|c \|a x  + b x + c  + (2b x + 4b c)\|a )
+--R      *
+--R                     +--------------+
+--R               +---+ |   2               +---+ +-+
+--R              \|- a \|a x  + b x + c  - \|- a \|c
+--R         atan(------------------------------------)
+--R                               a x
+--R     + 
+--R                      +--------------+
+--R            +---+ +-+ |   2                          +---+ +-+ +-+
+--R       - 4c\|- a \|a \|a x  + b x + c  + (2b x + 4c)\|- a \|a \|c
+--R  /
+--R                      +--------------+
+--R        +---+ +-+ +-+ |   2                                +---+ +-+
+--R     4a\|- a \|a \|c \|a x  + b x + c  + (- 2a b x - 4a c)\|- a \|a
+--R                                                     Type: Expression Integer
+--E
+
+--S 18     14:281 Axiom cannot simplify these expressions
+cc4:=bb2-aa.2
+--R
+--R             +--------------+
+--R             |   2                         +-+
+--R        - 2c\|a x  + b x + c  + (b x + 2c)\|c
+--R   (8)  --------------------------------------
+--R               +--------------+
+--R           +-+ |   2
+--R        2a\|c \|a x  + b x + c  - a b x - 2a c
+--R                                                     Type: Expression Integer
+--E
+
 @
 
 \section{\cite{1}:14.282~~~~~$\displaystyle
@@ -132,7 +523,7 @@ $$
 <<*>>=
 )clear all
 
---S 3 of 19
+--S 19
 aa:=integrate(x^2/(a*x^2+b*x+c),x)
 --R 
 --R
@@ -177,7 +568,247 @@ aa:=integrate(x^2/(a*x^2+b*x+c),x)
 --R       2a \|4a c - b
 --R     ]
 --R                                     Type: Union(List Expression Integer,...)
---E 
+--E
+
+--S 20
+t1:=integrate(1/sqrt(a*x^2+b*x+c),x)
+--R
+--R   (2)
+--R   [
+--R       log
+--R                                 +--------------+
+--R                 +-+ +-+         |   2                   +-+
+--R              (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
+--R            + 
+--R                     2             +-+
+--R              (- 2a x  - b x - 2c)\|a
+--R         /
+--R                  +--------------+
+--R              +-+ |   2
+--R            2\|c \|a x  + b x + c  - b x - 2c
+--R    /
+--R        +-+
+--R       \|a
+--R     ,
+--R                 +--------------+
+--R           +---+ |   2               +---+ +-+
+--R          \|- a \|a x  + b x + c  - \|- a \|c
+--R    2atan(------------------------------------)
+--R                           a x
+--R    -------------------------------------------]
+--R                        +---+
+--R                       \|- a
+--R                                     Type: Union(List Expression Integer,...)
+--E
+
+--S 21
+bb1:=(2*a*x-3*b)/(4*a^2)*sqrt(a*x^2+b*x+c)+(3*b^2-4*a*c)/(8*a^2)*t1.1
+--R
+--R   (3)
+--R                     2
+--R         (- 4a c + 3b )
+--R      *
+--R         log
+--R                                   +--------------+
+--R                   +-+ +-+         |   2                   +-+
+--R                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
+--R              + 
+--R                       2             +-+
+--R                (- 2a x  - b x - 2c)\|a
+--R           /
+--R                    +--------------+
+--R                +-+ |   2
+--R              2\|c \|a x  + b x + c  - b x - 2c
+--R     + 
+--R                       +--------------+
+--R                   +-+ |   2
+--R       (4a x - 6b)\|a \|a x  + b x + c
+--R  /
+--R       2 +-+
+--R     8a \|a
+--R                                                     Type: Expression Integer
+--E
+
+--S 22
+bb2:=(2*a*x-3*b)/(4*a^2)*sqrt(a*x^2+b*x+c)+(3*b^2-4*a*c)/(8*a^2)*t1.2
+--R
+--R   (4)
+--R                                 +--------------+
+--R                           +---+ |   2               +---+ +-+
+--R                   2      \|- a \|a x  + b x + c  - \|- a \|c
+--R       (- 4a c + 3b )atan(------------------------------------)
+--R                                           a x
+--R     + 
+--R                         +--------------+
+--R                   +---+ |   2
+--R       (2a x - 3b)\|- a \|a x  + b x + c
+--R  /
+--R       2 +---+
+--R     4a \|- a
+--R                                                     Type: Expression Integer
+--E
+
+--S 23
+cc1:=aa.1-bb1
+--R
+--R   (5)
+--R                      +-----------+
+--R                   2  |          2
+--R         (4a c - 3b )\|- 4a c + b
+--R      *
+--R         log
+--R                                   +--------------+
+--R                   +-+ +-+         |   2                   +-+
+--R                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
+--R              + 
+--R                       2             +-+
+--R                (- 2a x  - b x - 2c)\|a
+--R           /
+--R                    +--------------+
+--R                +-+ |   2
+--R              2\|c \|a x  + b x + c  - b x - 2c
+--R     + 
+--R                   2  +-+
+--R         (8a c - 4b )\|a
+--R      *
+--R         log
+--R                                             +-----------+
+--R                   2 2                    2  |          2         2        2
+--R                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
+--R              + 
+--R                            3
+--R                - 4a b c + b
+--R           /
+--R                 2
+--R              a x  + b x + c
+--R     + 
+--R                     +-----------+     +--------------+
+--R                     |          2  +-+ |   2
+--R       (- 4a x + 6b)\|- 4a c + b  \|a \|a x  + b x + c
+--R     + 
+--R                                         +-----------+
+--R                    2                    |          2  +-+
+--R       (- 4b log(a x  + b x + c) + 8a x)\|- 4a c + b  \|a
+--R  /
+--R         +-----------+
+--R       2 |          2  +-+
+--R     8a \|- 4a c + b  \|a
+--R                                                     Type: Expression Integer
+--E
+
+--S 24
+cc2:=aa.2-bb1
+--R
+--R   (6)
+--R                      +---------+
+--R                   2  |        2
+--R         (4a c - 3b )\|4a c - b
+--R      *
+--R         log
+--R                                   +--------------+
+--R                   +-+ +-+         |   2                   +-+
+--R                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
+--R              + 
+--R                       2             +-+
+--R                (- 2a x  - b x - 2c)\|a
+--R           /
+--R                    +--------------+
+--R                +-+ |   2
+--R              2\|c \|a x  + b x + c  - b x - 2c
+--R     + 
+--R                                          +---------+
+--R                                          |        2
+--R                    2  +-+     (2a x + b)\|4a c - b
+--R       (- 16a c + 8b )\|a atan(----------------------)
+--R                                              2
+--R                                      4a c - b
+--R     + 
+--R                         +---------+ +--------------+
+--R                     +-+ |        2  |   2
+--R       (- 4a x + 6b)\|a \|4a c - b  \|a x  + b x + c
+--R     + 
+--R                                             +---------+
+--R                    2                    +-+ |        2
+--R       (- 4b log(a x  + b x + c) + 8a x)\|a \|4a c - b
+--R  /
+--R             +---------+
+--R       2 +-+ |        2
+--R     8a \|a \|4a c - b
+--R                                                     Type: Expression Integer
+--E
+
+--S 25
+cc3:=aa.2-bb1
+--R
+--R   (7)
+--R                      +---------+
+--R                   2  |        2
+--R         (4a c - 3b )\|4a c - b
+--R      *
+--R         log
+--R                                   +--------------+
+--R                   +-+ +-+         |   2                   +-+
+--R                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
+--R              + 
+--R                       2             +-+
+--R                (- 2a x  - b x - 2c)\|a
+--R           /
+--R                    +--------------+
+--R                +-+ |   2
+--R              2\|c \|a x  + b x + c  - b x - 2c
+--R     + 
+--R                                          +---------+
+--R                                          |        2
+--R                    2  +-+     (2a x + b)\|4a c - b
+--R       (- 16a c + 8b )\|a atan(----------------------)
+--R                                              2
+--R                                      4a c - b
+--R     + 
+--R                         +---------+ +--------------+
+--R                     +-+ |        2  |   2
+--R       (- 4a x + 6b)\|a \|4a c - b  \|a x  + b x + c
+--R     + 
+--R                                             +---------+
+--R                    2                    +-+ |        2
+--R       (- 4b log(a x  + b x + c) + 8a x)\|a \|4a c - b
+--R  /
+--R             +---------+
+--R       2 +-+ |        2
+--R     8a \|a \|4a c - b
+--R                                                     Type: Expression Integer
+--E
+
+--S 26     14:282 Axiom cannot simplify these expressions
+cc4:=aa.2-bb2
+--R
+--R   (8)
+--R                                           +--------------+
+--R                    +---------+      +---+ |   2               +---+ +-+
+--R                 2  |        2      \|- a \|a x  + b x + c  - \|- a \|c
+--R       (4a c - 3b )\|4a c - b  atan(------------------------------------)
+--R                                                     a x
+--R     + 
+--R                                           +---------+
+--R                                           |        2
+--R                   2  +---+     (2a x + b)\|4a c - b
+--R       (- 8a c + 4b )\|- a atan(----------------------)
+--R                                               2
+--R                                       4a c - b
+--R     + 
+--R                           +---------+ +--------------+
+--R                     +---+ |        2  |   2
+--R       (- 2a x + 3b)\|- a \|4a c - b  \|a x  + b x + c
+--R     + 
+--R                                               +---------+
+--R                    2                    +---+ |        2
+--R       (- 2b log(a x  + b x + c) + 4a x)\|- a \|4a c - b
+--R  /
+--R               +---------+
+--R       2 +---+ |        2
+--R     4a \|- a \|4a c - b
+--R                                                     Type: Expression Integer
+--E
+
 @
 
 \section{\cite{1}:14.283~~~~~$\displaystyle
@@ -200,7 +831,7 @@ $$
 <<*>>=
 )clear all
 
---S 4 of 19
+--S 27
 aa:=integrate(1/x*(a*x^2+b*x+c),x)
 --R 
 --R
@@ -210,6 +841,91 @@ aa:=integrate(1/x*(a*x^2+b*x+c),x)
 --R                   2
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 28
+bb1:=-1/sqrt(c)*log((2*sqrt(c)*sqrt(a*x^2+b*x+c)+b*x+2*c)/x)
+--R
+--R                    +--------------+
+--R                +-+ |   2
+--R              2\|c \|a x  + b x + c  + b x + 2c
+--R          log(---------------------------------)
+--R                              x
+--R   (2)  - --------------------------------------
+--R                            +-+
+--R                           \|c
+--R                                                     Type: Expression Integer
+--E
+
+--S 29
+bb2:=1/sqrt(-c)*asin((b*x+2*c)/(x*sqrt(b^2-4*a*c)))
+--R
+--R                 b x + 2c
+--R        asin(---------------)
+--R               +-----------+
+--R               |          2
+--R             x\|- 4a c + b
+--R   (3)  ---------------------
+--R                 +---+
+--R                \|- c
+--R                                                     Type: Expression Integer
+--E
+
+--S 30
+bb3:=-1/sqrt(c)*asinh((b*x+2*c)/(x*sqrt(b^2-4*a*c)))
+--R
+--R                    b x + 2c
+--R          asinh(---------------)
+--R                  +-----------+
+--R                  |          2
+--R                x\|- 4a c + b
+--R   (4)  - ----------------------
+--R                    +-+
+--R                   \|c
+--R                                                     Type: Expression Integer
+--E
+
+--S 31
+cc1:=aa-bb1
+--R
+--R   (5)
+--R              +--------------+
+--R          +-+ |   2
+--R        2\|c \|a x  + b x + c  + b x + 2c                    2         +-+
+--R   2log(---------------------------------) + (2c log(x) + a x  + 2b x)\|c
+--R                        x
+--R   -----------------------------------------------------------------------
+--R                                      +-+
+--R                                    2\|c
+--R                                                     Type: Expression Integer
+--E
+
+--S 32
+cc2:=aa-bb2
+--R
+--R                    b x + 2c                       2         +---+
+--R        - 2asin(---------------) + (2c log(x) + a x  + 2b x)\|- c
+--R                  +-----------+
+--R                  |          2
+--R                x\|- 4a c + b
+--R   (6)  ----------------------------------------------------------
+--R                                    +---+
+--R                                  2\|- c
+--R                                                     Type: Expression Integer
+--E
+
+--S 33     14:283 Axiom cannot simplify these expressions
+cc3:=aa-bb3
+--R
+--R                   b x + 2c                       2         +-+
+--R        2asinh(---------------) + (2c log(x) + a x  + 2b x)\|c
+--R                 +-----------+
+--R                 |          2
+--R               x\|- 4a c + b
+--R   (7)  -------------------------------------------------------
+--R                                   +-+
+--R                                 2\|c
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.284~~~~~$\displaystyle
@@ -220,7 +936,7 @@ $$
 <<*>>=
 )clear all
 
---S 5 of 19
+--S 34
 aa:=integrate(1/(x^2*(a*x^2+b*x+c)),x)
 --R 
 --R
@@ -266,6 +982,93 @@ aa:=integrate(1/(x^2*(a*x^2+b*x+c)),x)
 --R     ]
 --R                                     Type: Union(List Expression Integer,...)
 --E 
+
+--S 35
+t1:=integrate(1/(x*sqrt(a*x^2+b*x+c)),x)
+--R
+--R                  +--------------+
+--R              +-+ |   2
+--R            2\|c \|a x  + b x + c  - b x - 2c
+--R        log(---------------------------------)
+--R                            x
+--R   (2)  --------------------------------------
+--R                          +-+
+--R                         \|c
+--R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 36
+bb:=-sqrt(a*x^2+b*x+c)/(c*x)-b/(2*x)*t1
+--R
+--R                        +--------------+
+--R                    +-+ |   2                                +--------------+
+--R                  2\|c \|a x  + b x + c  - b x - 2c      +-+ |   2
+--R        - b c log(---------------------------------) - 2\|c \|a x  + b x + c
+--R                                  x
+--R   (3)  ---------------------------------------------------------------------
+--R                                            +-+
+--R                                       2c x\|c
+--R                                                     Type: Expression Integer
+--E
+
+--S 37
+cc1:=aa.1-bb1
+--R
+--R   (4)
+--R                  2
+--R         (2a c - b )x
+--R      *
+--R         log
+--R                                             +-----------+
+--R                   2 2                    2  |          2         2        2
+--R                (2a x  + 2a b x - 2a c + b )\|- 4a c + b   + (- 8a c + 2a b )x
+--R              + 
+--R                            3
+--R                - 4a b c + b
+--R           /
+--R                 2
+--R              a x  + b x + c
+--R     + 
+--R                                                               +-----------+
+--R                   2                                  2        |          2
+--R       (b x log(a x  + b x + c) - 2b x log(x) - 2bb1 c x - 2c)\|- 4a c + b
+--R  /
+--R          +-----------+
+--R       2  |          2
+--R     2c x\|- 4a c + b
+--R                                                     Type: Expression Integer
+--E
+
+--S 38     14:284 Axiom cannot simplify these expressions
+cc2:=aa.2-bb
+--R
+--R   (5)
+--R                                 +--------------+
+--R            +---------+      +-+ |   2
+--R          2 |        2     2\|c \|a x  + b x + c  - b x - 2c
+--R       b c \|4a c - b  log(---------------------------------)
+--R                                           x
+--R     + 
+--R                                          +---------+
+--R                                          |        2
+--R                   2   +-+     (2a x + b)\|4a c - b
+--R       (- 4a c + 2b )x\|c atan(----------------------)
+--R                                              2
+--R                                      4a c - b
+--R     + 
+--R              +---------+ +--------------+
+--R          +-+ |        2  |   2
+--R       2c\|c \|4a c - b  \|a x  + b x + c
+--R     + 
+--R                                                        +---------+
+--R                   2                                +-+ |        2
+--R       (b x log(a x  + b x + c) - 2b x log(x) - 2c)\|c \|4a c - b
+--R  /
+--R              +---------+
+--R       2  +-+ |        2
+--R     2c x\|c \|4a c - b
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.285~~~~~$\displaystyle
@@ -277,7 +1080,7 @@ $$
 <<*>>=
 )clear all
 
---S 6 of 19
+--S 39
 aa:=integrate(sqrt(a*x^2+b*x+c),x)
 --R 
 --R
@@ -361,6 +1164,228 @@ aa:=integrate(sqrt(a*x^2+b*x+c),x)
 --R     ]
 --R                                     Type: Union(List Expression Integer,...)
 --E 
+
+--S 40
+t1:=integrate(1/sqrt(a*x^2+b*x+c),x)
+--R
+--R   (2)
+--R   [
+--R       log
+--R                                 +--------------+
+--R                 +-+ +-+         |   2                   +-+
+--R              (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
+--R            + 
+--R                     2             +-+
+--R              (- 2a x  - b x - 2c)\|a
+--R         /
+--R                  +--------------+
+--R              +-+ |   2
+--R            2\|c \|a x  + b x + c  - b x - 2c
+--R    /
+--R        +-+
+--R       \|a
+--R     ,
+--R                 +--------------+
+--R           +---+ |   2               +---+ +-+
+--R          \|- a \|a x  + b x + c  - \|- a \|c
+--R    2atan(------------------------------------)
+--R                           a x
+--R    -------------------------------------------]
+--R                        +---+
+--R                       \|- a
+--R                                     Type: Union(List Expression Integer,...)
+--E
+
+--S 41
+bb1:=((2*a*x+b)*sqrt(a*x^2+b*x+c))/(4*a)+(4*a*c-b^2)/(8*a)*t1.1
+--R
+--R   (3)
+--R                  2
+--R         (4a c - b )
+--R      *
+--R         log
+--R                                   +--------------+
+--R                   +-+ +-+         |   2                   +-+
+--R                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
+--R              + 
+--R                       2             +-+
+--R                (- 2a x  - b x - 2c)\|a
+--R           /
+--R                    +--------------+
+--R                +-+ |   2
+--R              2\|c \|a x  + b x + c  - b x - 2c
+--R     + 
+--R                       +--------------+
+--R                   +-+ |   2
+--R       (4a x + 2b)\|a \|a x  + b x + c
+--R  /
+--R        +-+
+--R     8a\|a
+--R                                                     Type: Expression Integer
+--E
+
+--S 42
+bb2:=((2*a*x+b)*sqrt(a*x^2+b*x+c))/(4*a)+(4*a*c-b^2)/(8*a)*t1.2
+--R
+--R   (4)
+--R                              +--------------+
+--R                        +---+ |   2               +---+ +-+
+--R                2      \|- a \|a x  + b x + c  - \|- a \|c
+--R       (4a c - b )atan(------------------------------------)
+--R                                        a x
+--R     + 
+--R                        +--------------+
+--R                  +---+ |   2
+--R       (2a x + b)\|- a \|a x  + b x + c
+--R  /
+--R        +---+
+--R     4a\|- a
+--R                                                     Type: Expression Integer
+--E
+
+--S 43
+cc1:=aa.1-bb1
+--R
+--R   (5)
+--R                        +--------------+
+--R          2          2  |   2
+--R       (4b c x + 8b c )\|a x  + b x + c
+--R     + 
+--R                     3  2     2          2  +-+
+--R       ((- 4a b c - b )x  - 8b c x - 8b c )\|c
+--R  /
+--R                             +--------------+
+--R                         +-+ |   2                    2        2  2
+--R       (16a b x + 32a c)\|c \|a x  + b x + c  + (- 16a c - 4a b )x  - 32a b c x
+--R     + 
+--R              2
+--R       - 32a c
+--R                                                     Type: Expression Integer
+--E
+
+--S 44
+cc2:=aa.2-bb1
+--R
+--R   (6)
+--R                                                          +--------------+
+--R                           3          2     2   +---+ +-+ |   2
+--R           ((- 16a b c + 4b )x - 32a c  + 8b c)\|- a \|c \|a x  + b x + c
+--R         + 
+--R                2 2    4  2           2     3           3     2 2  +---+
+--R           ((16a c  - b )x  + (32a b c  - 8b c)x + 32a c  - 8b c )\|- a
+--R      *
+--R         log
+--R                                   +--------------+
+--R                   +-+ +-+         |   2                   +-+
+--R                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
+--R              + 
+--R                       2             +-+
+--R                (- 2a x  - b x - 2c)\|a
+--R           /
+--R                    +--------------+
+--R                +-+ |   2
+--R              2\|c \|a x  + b x + c  - b x - 2c
+--R     + 
+--R                                                       +--------------+
+--R                         3          2      2   +-+ +-+ |   2
+--R           ((32a b c - 8b )x + 64a c  - 16b c)\|a \|c \|a x  + b x + c
+--R         + 
+--R                  2 2     4  2             2      3           3      2 2  +-+
+--R           ((- 32a c  + 2b )x  + (- 64a b c  + 16b c)x - 64a c  + 16b c )\|a
+--R      *
+--R                     +--------------+
+--R               +---+ |   2               +---+ +-+
+--R              \|- a \|a x  + b x + c  - \|- a \|c
+--R         atan(------------------------------------)
+--R                               a x
+--R     + 
+--R                                   +--------------+
+--R          2           2  +---+ +-+ |   2
+--R       (8b c x + 16b c )\|- a \|a \|a x  + b x + c
+--R     + 
+--R                      3  2      2           2  +---+ +-+ +-+
+--R       ((- 8a b c - 2b )x  - 16b c x - 16b c )\|- a \|a \|c
+--R  /
+--R                                       +--------------+
+--R                         +---+ +-+ +-+ |   2
+--R       (32a b x + 64a c)\|- a \|a \|c \|a x  + b x + c
+--R     + 
+--R              2        2  2                    2  +---+ +-+
+--R       ((- 32a c - 8a b )x  - 64a b c x - 64a c )\|- a \|a
+--R                                                     Type: Expression Integer
+--E
+
+--S 45
+cc3:=aa.1-bb2
+--R
+--R   (7)
+--R                                                        +--------------+
+--R                         3          2     2   +---+ +-+ |   2
+--R           ((16a b c - 4b )x + 32a c  - 8b c)\|- a \|c \|a x  + b x + c
+--R         + 
+--R                  2 2    4  2             2     3           3     2 2  +---+
+--R           ((- 16a c  + b )x  + (- 32a b c  + 8b c)x - 32a c  + 8b c )\|- a
+--R      *
+--R         log
+--R                                   +--------------+
+--R                   +-+ +-+         |   2                   +-+
+--R                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
+--R              + 
+--R                       2             +-+
+--R                (- 2a x  - b x - 2c)\|a
+--R           /
+--R                    +--------------+
+--R                +-+ |   2
+--R              2\|c \|a x  + b x + c  - b x - 2c
+--R     + 
+--R                                                         +--------------+
+--R                           3          2      2   +-+ +-+ |   2
+--R           ((- 32a b c + 8b )x - 64a c  + 16b c)\|a \|c \|a x  + b x + c
+--R         + 
+--R                2 2     4  2           2      3           3      2 2  +-+
+--R           ((32a c  - 2b )x  + (64a b c  - 16b c)x + 64a c  - 16b c )\|a
+--R      *
+--R                     +--------------+
+--R               +---+ |   2               +---+ +-+
+--R              \|- a \|a x  + b x + c  - \|- a \|c
+--R         atan(------------------------------------)
+--R                               a x
+--R     + 
+--R                                   +--------------+
+--R          2           2  +---+ +-+ |   2
+--R       (8b c x + 16b c )\|- a \|a \|a x  + b x + c
+--R     + 
+--R                      3  2      2           2  +---+ +-+ +-+
+--R       ((- 8a b c - 2b )x  - 16b c x - 16b c )\|- a \|a \|c
+--R  /
+--R                                       +--------------+
+--R                         +---+ +-+ +-+ |   2
+--R       (32a b x + 64a c)\|- a \|a \|c \|a x  + b x + c
+--R     + 
+--R              2        2  2                    2  +---+ +-+
+--R       ((- 32a c - 8a b )x  - 64a b c x - 64a c )\|- a \|a
+--R                                                     Type: Expression Integer
+--E
+
+--S 46     14:285 Axiom cannot simplify these expressions
+cc4:=aa.2-bb2
+--R
+--R   (8)
+--R                        +--------------+
+--R          2          2  |   2
+--R       (4b c x + 8b c )\|a x  + b x + c
+--R     + 
+--R                     3  2     2          2  +-+
+--R       ((- 4a b c - b )x  - 8b c x - 8b c )\|c
+--R  /
+--R                             +--------------+
+--R                         +-+ |   2                    2        2  2
+--R       (16a b x + 32a c)\|c \|a x  + b x + c  + (- 16a c - 4a b )x  - 32a b c x
+--R     + 
+--R              2
+--R       - 32a c
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.286~~~~~$\displaystyle
@@ -378,7 +1403,7 @@ $$
 <<*>>=
 )clear all
 
---S 7 of 19
+--S 47
 aa:=integrate(x*sqrt(a*x^2+b*x+c),x)
 --R 
 --R
@@ -522,6 +1547,416 @@ aa:=integrate(x*sqrt(a*x^2+b*x+c),x)
 --R     ]
 --R                                     Type: Union(List Expression Integer,...)
 --E 
+
+--S 48
+t1:=integrate(1/sqrt(a*x^2+b*x+c),x)
+--R
+--R   (2)
+--R   [
+--R       log
+--R                                 +--------------+
+--R                 +-+ +-+         |   2                   +-+
+--R              (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
+--R            + 
+--R                     2             +-+
+--R              (- 2a x  - b x - 2c)\|a
+--R         /
+--R                  +--------------+
+--R              +-+ |   2
+--R            2\|c \|a x  + b x + c  - b x - 2c
+--R    /
+--R        +-+
+--R       \|a
+--R     ,
+--R                 +--------------+
+--R           +---+ |   2               +---+ +-+
+--R          \|- a \|a x  + b x + c  - \|- a \|c
+--R    2atan(------------------------------------)
+--R                           a x
+--R    -------------------------------------------]
+--R                        +---+
+--R                       \|- a
+--R                                     Type: Union(List Expression Integer,...)
+--E
+
+--S 49
+bb1:=(a*x^2+b*x+c)^(3/2)/(3*a)-(b*(2*a*x+b))/(8*a^2)*sqrt(a*x^2+b*x+c)-(b*(4*a*c-b^2))/(16*a^2)*t1.1
+--R
+--R   (3)
+--R                        3
+--R         (- 12a b c + 3b )
+--R      *
+--R         log
+--R                                   +--------------+
+--R                   +-+ +-+         |   2                   +-+
+--R                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
+--R              + 
+--R                       2             +-+
+--R                (- 2a x  - b x - 2c)\|a
+--R           /
+--R                    +--------------+
+--R                +-+ |   2
+--R              2\|c \|a x  + b x + c  - b x - 2c
+--R     + 
+--R                                           +--------------+
+--R           2 2                      2  +-+ |   2
+--R       (16a x  + 4a b x + 16a c - 6b )\|a \|a x  + b x + c
+--R  /
+--R        2 +-+
+--R     48a \|a
+--R                                                     Type: Expression Integer
+--E
+
+--S 50
+bb2:=(a*x^2+b*x+c)^(3/2)/(3*a)-(b*(2*a*x+b))/(8*a^2)*sqrt(a*x^2+b*x+c)-(b*(4*a*c-b^2))/(16*a^2)*t1.2
+--R
+--R   (4)
+--R                                    +--------------+
+--R                              +---+ |   2               +---+ +-+
+--R                      3      \|- a \|a x  + b x + c  - \|- a \|c
+--R       (- 12a b c + 3b )atan(------------------------------------)
+--R                                              a x
+--R     + 
+--R                                           +--------------+
+--R          2 2                     2  +---+ |   2
+--R       (8a x  + 2a b x + 8a c - 3b )\|- a \|a x  + b x + c
+--R  /
+--R        2 +---+
+--R     24a \|- a
+--R                                                     Type: Expression Integer
+--E
+
+--S 51
+cc1:=aa.1-bb1
+--R
+--R   (5)
+--R                   2   2        3       5  2          2 2      4              3
+--R               (96a b c  + 48a b c - 18b )x  + (384a b c  - 96b c)x + 384a b c
+--R             + 
+--R                    3 2
+--R               - 96b c
+--R          *
+--R                  +--------------+
+--R              +-+ |   2
+--R             \|c \|a x  + b x + c
+--R         + 
+--R                  2 2 2        4      6  3          2   3         3 2      5   2
+--R           (- 144a b c  + 24a b c + 3b )x  + (- 288a b c  - 144a b c  + 54b c)x
+--R         + 
+--R                    2 3       4 2             4      3 3
+--R           (- 576a b c  + 144b c )x - 384a b c  + 96b c
+--R      *
+--R         log
+--R                                   +--------------+
+--R                   +-+ +-+         |   2                   +-+
+--R                (2\|a \|c  + 2a x)\|a x  + b x + c  - 2a x\|c
+--R              + 
+--R                       2             +-+
+--R                (- 2a x  - b x - 2c)\|a
+--R           /
+--R                    +--------------+
+--R                +-+ |   2
+--R              2\|c \|a x  + b x + c  - b x - 2c
+--R     + 
+--R                   2   2        3       5  2          2 2      4              3
+--R               (96a b c  + 48a b c - 18b )x  + (384a b c  - 96b c)x + 384a b c
+--R             + 
+--R                    3 2
+--R               - 96b c
+--R          *
+--R                  +--------------+
+--R              +-+ |   2
+--R             \|c \|a x  + b x + c
+--R         + 
+--R                  2 2 2        4      6  3          2   3         3 2      5   2
+--R           (- 144a b c  + 24a b c + 3b )x  + (- 288a b c  - 144a b c  + 54b c)x
+--R         + 
+--R                    2 3       4 2             4      3 3
+--R           (- 576a b c  + 144b c )x - 384a b c  + 96b c
+--R      *
+--R         log
+--R                                   +--------------+
+--R                   +-+ +-+         |   2                   +-+
+--R                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
+--R              + 
+--R                       2             +-+
+--R                (- 2a x  - b x - 2c)\|a
+--R           /
+--R                    +--------------+
+--R                +-+ |   2
+--R              2\|c \|a x  + b x + c  - b x - 2c
+--R     + 
+--R                2 3        2 2      4   2            3       3 2           4
+--R           (128a c  + 48a b c  - 36b c)x  + (512a b c  - 192b c )x + 512a c
+--R         + 
+--R                 2 3
+--R           - 192b c
+--R      *
+--R              +--------------+
+--R          +-+ |   2
+--R         \|a \|a x  + b x + c
+--R     + 
+--R                  2   2        3      5  3          2 3         2 2       4   2
+--R           (- 192a b c  + 56a b c + 6b )x  + (- 384a c  - 144a b c  + 108b c)x
+--R         + 
+--R                      3       3 2           4       2 3
+--R           (- 768a b c  + 288b c )x - 512a c  + 192b c
+--R      *
+--R          +-+ +-+
+--R         \|a \|c
+--R  /
+--R                                                               +--------------+
+--R             3        2 2  2        2             2 2  +-+ +-+ |   2
+--R       ((384a c + 288a b )x  + 1536a b c x + 1536a c )\|a \|c \|a x  + b x + c
+--R     + 
+--R                  3         2 3  3           3 2       2 2   2        2   2
+--R           (- 576a b c - 48a b )x  + (- 1152a c  - 864a b c)x  - 2304a b c x
+--R         + 
+--R                  2 3
+--R           - 1536a c
+--R      *
+--R          +-+
+--R         \|a
+--R                                                     Type: Expression Integer
+--E
+
+--S 52
+cc2:=aa.2-bb1
+--R
+--R   (6)
+--R                   2   2        3       5  2          2 2      4              3
+--R               (96a b c  + 48a b c - 18b )x  + (384a b c  - 96b c)x + 384a b c
+--R             + 
+--R                    3 2
+--R               - 96b c
+--R          *
+--R                        +--------------+
+--R              +---+ +-+ |   2
+--R             \|- a \|c \|a x  + b x + c
+--R         + 
+--R                      2 2 2        4      6  3
+--R               (- 144a b c  + 24a b c + 3b )x
+--R             + 
+--R                      2   3         3 2      5   2            2 3       4 2
+--R               (- 288a b c  - 144a b c  + 54b c)x  + (- 576a b c  + 144b c )x
+--R             + 
+--R                         4      3 3
+--R               - 384a b c  + 96b c
+--R          *
+--R              +---+
+--R             \|- a
+--R      *
+--R         log
+--R                                   +--------------+
+--R                   +-+ +-+         |   2                   +-+
+--R                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
+--R              + 
+--R                       2             +-+
+--R                (- 2a x  - b x - 2c)\|a
+--R           /
+--R                    +--------------+
+--R                +-+ |   2
+--R              2\|c \|a x  + b x + c  - b x - 2c
+--R     + 
+--R                      2   2        3       5  2            2 2       4
+--R               (- 192a b c  - 96a b c + 36b )x  + (- 768a b c  + 192b c)x
+--R             + 
+--R                         3       3 2
+--R               - 768a b c  + 192b c
+--R          *
+--R                      +--------------+
+--R              +-+ +-+ |   2
+--R             \|a \|c \|a x  + b x + c
+--R         + 
+--R                    2 2 2        4      6  3
+--R               (288a b c  - 48a b c - 6b )x
+--R             + 
+--R                    2   3         3 2       5   2           2 3       4 2
+--R               (576a b c  + 288a b c  - 108b c)x  + (1152a b c  - 288b c )x
+--R             + 
+--R                       4       3 3
+--R               768a b c  - 192b c
+--R          *
+--R              +-+
+--R             \|a
+--R      *
+--R                     +--------------+
+--R               +---+ |   2               +---+ +-+
+--R              \|- a \|a x  + b x + c  - \|- a \|c
+--R         atan(------------------------------------)
+--R                               a x
+--R     + 
+--R                2 3        2 2      4   2            3       3 2           4
+--R           (128a c  + 48a b c  - 36b c)x  + (512a b c  - 192b c )x + 512a c
+--R         + 
+--R                 2 3
+--R           - 192b c
+--R      *
+--R                    +--------------+
+--R          +---+ +-+ |   2
+--R         \|- a \|a \|a x  + b x + c
+--R     + 
+--R                  2   2        3      5  3          2 3         2 2       4   2
+--R           (- 192a b c  + 56a b c + 6b )x  + (- 384a c  - 144a b c  + 108b c)x
+--R         + 
+--R                      3       3 2           4       2 3
+--R           (- 768a b c  + 288b c )x - 512a c  + 192b c
+--R      *
+--R          +---+ +-+ +-+
+--R         \|- a \|a \|c
+--R  /
+--R               3        2 2  2        2             2 2  +---+ +-+ +-+
+--R         ((384a c + 288a b )x  + 1536a b c x + 1536a c )\|- a \|a \|c
+--R      *
+--R          +--------------+
+--R          |   2
+--R         \|a x  + b x + c
+--R     + 
+--R                  3         2 3  3           3 2       2 2   2        2   2
+--R           (- 576a b c - 48a b )x  + (- 1152a c  - 864a b c)x  - 2304a b c x
+--R         + 
+--R                  2 3
+--R           - 1536a c
+--R      *
+--R          +---+ +-+
+--R         \|- a \|a
+--R                                                     Type: Expression Integer
+--E
+
+--S 53
+cc3:=aa.1-bb2
+--R
+--R   (7)
+--R                   2   2        3       5  2          2 2      4              3
+--R               (96a b c  + 48a b c - 18b )x  + (384a b c  - 96b c)x + 384a b c
+--R             + 
+--R                    3 2
+--R               - 96b c
+--R          *
+--R                        +--------------+
+--R              +---+ +-+ |   2
+--R             \|- a \|c \|a x  + b x + c
+--R         + 
+--R                      2 2 2        4      6  3
+--R               (- 144a b c  + 24a b c + 3b )x
+--R             + 
+--R                      2   3         3 2      5   2            2 3       4 2
+--R               (- 288a b c  - 144a b c  + 54b c)x  + (- 576a b c  + 144b c )x
+--R             + 
+--R                         4      3 3
+--R               - 384a b c  + 96b c
+--R          *
+--R              +---+
+--R             \|- a
+--R      *
+--R         log
+--R                                   +--------------+
+--R                   +-+ +-+         |   2                   +-+
+--R                (2\|a \|c  + 2a x)\|a x  + b x + c  - 2a x\|c
+--R              + 
+--R                       2             +-+
+--R                (- 2a x  - b x - 2c)\|a
+--R           /
+--R                    +--------------+
+--R                +-+ |   2
+--R              2\|c \|a x  + b x + c  - b x - 2c
+--R     + 
+--R                    2   2        3       5  2          2 2       4
+--R               (192a b c  + 96a b c - 36b )x  + (768a b c  - 192b c)x
+--R             + 
+--R                       3       3 2
+--R               768a b c  - 192b c
+--R          *
+--R                      +--------------+
+--R              +-+ +-+ |   2
+--R             \|a \|c \|a x  + b x + c
+--R         + 
+--R                      2 2 2        4      6  3
+--R               (- 288a b c  + 48a b c + 6b )x
+--R             + 
+--R                      2   3         3 2       5   2             2 3       4 2
+--R               (- 576a b c  - 288a b c  + 108b c)x  + (- 1152a b c  + 288b c )x
+--R             + 
+--R                         4       3 3
+--R               - 768a b c  + 192b c
+--R          *
+--R              +-+
+--R             \|a
+--R      *
+--R                     +--------------+
+--R               +---+ |   2               +---+ +-+
+--R              \|- a \|a x  + b x + c  - \|- a \|c
+--R         atan(------------------------------------)
+--R                               a x
+--R     + 
+--R                2 3        2 2      4   2            3       3 2           4
+--R           (128a c  + 48a b c  - 36b c)x  + (512a b c  - 192b c )x + 512a c
+--R         + 
+--R                 2 3
+--R           - 192b c
+--R      *
+--R                    +--------------+
+--R          +---+ +-+ |   2
+--R         \|- a \|a \|a x  + b x + c
+--R     + 
+--R                  2   2        3      5  3          2 3         2 2       4   2
+--R           (- 192a b c  + 56a b c + 6b )x  + (- 384a c  - 144a b c  + 108b c)x
+--R         + 
+--R                      3       3 2           4       2 3
+--R           (- 768a b c  + 288b c )x - 512a c  + 192b c
+--R      *
+--R          +---+ +-+ +-+
+--R         \|- a \|a \|c
+--R  /
+--R               3        2 2  2        2             2 2  +---+ +-+ +-+
+--R         ((384a c + 288a b )x  + 1536a b c x + 1536a c )\|- a \|a \|c
+--R      *
+--R          +--------------+
+--R          |   2
+--R         \|a x  + b x + c
+--R     + 
+--R                  3         2 3  3           3 2       2 2   2        2   2
+--R           (- 576a b c - 48a b )x  + (- 1152a c  - 864a b c)x  - 2304a b c x
+--R         + 
+--R                  2 3
+--R           - 1536a c
+--R      *
+--R          +---+ +-+
+--R         \|- a \|a
+--R                                                     Type: Expression Integer
+--E
+
+--S 54     14:286 Axiom cannot simplify these expressions
+cc4:=aa.2-bb2
+--R
+--R   (8)
+--R               2 3        2 2      4   2            3      3 2           4
+--R           (64a c  + 24a b c  - 18b c)x  + (256a b c  - 96b c )x + 256a c
+--R         + 
+--R                2 3
+--R           - 96b c
+--R      *
+--R          +--------------+
+--R          |   2
+--R         \|a x  + b x + c
+--R     + 
+--R                 2   2        3      5  3          2 3        2 2      4   2
+--R           (- 96a b c  + 28a b c + 3b )x  + (- 192a c  - 72a b c  + 54b c)x
+--R         + 
+--R                      3       3 2           4      2 3
+--R           (- 384a b c  + 144b c )x - 256a c  + 96b c
+--R      *
+--R          +-+
+--R         \|c
+--R  /
+--R                                                         +--------------+
+--R             3        2 2  2       2            2 2  +-+ |   2
+--R       ((192a c + 144a b )x  + 768a b c x + 768a c )\|c \|a x  + b x + c
+--R     + 
+--R            3         2 3  3          3 2       2 2   2        2   2        2 3
+--R     (- 288a b c - 24a b )x  + (- 576a c  - 432a b c)x  - 1152a b c x - 768a c
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.287~~~~~$\displaystyle
@@ -533,7 +1968,7 @@ $$
 <<*>>=
 )clear all
 
---S 8 of 19
+--S 55
 aa:=integrate(x^2*sqrt(a*x^2+b*x+c),x)
 --R 
 --R
@@ -763,7 +2198,891 @@ aa:=integrate(x^2*sqrt(a*x^2+b*x+c),x)
 --R           \|- a
 --R     ]
 --R                                     Type: Union(List Expression Integer,...)
---E 
+--E
+
+--S 56
+t1:=integrate(sqrt(a*x^2+b*x+c),x)
+--R
+--R   (2)
+--R   [
+--R                                                    +--------------+
+--R                           3          2     2   +-+ |   2
+--R             ((16a b c - 4b )x + 32a c  - 8b c)\|c \|a x  + b x + c
+--R           + 
+--R                   2 2    4  2             2     3           3     2 2
+--R             (- 16a c  + b )x  + (- 32a b c  + 8b c)x - 32a c  + 8b c
+--R        *
+--R           log
+--R                                     +--------------+
+--R                     +-+ +-+         |   2                   +-+
+--R                  (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
+--R                + 
+--R                         2             +-+
+--R                  (- 2a x  - b x - 2c)\|a
+--R             /
+--R                      +--------------+
+--R                  +-+ |   2
+--R                2\|c \|a x  + b x + c  - b x - 2c
+--R       + 
+--R                  2        2  3                  3  2           2     2     +-+
+--R           ((- 16a c - 4a b )x  + (- 40a b c - 2b )x  + (- 32a c  - 8b c)x)\|a
+--R        *
+--R            +--------------+
+--R            |   2
+--R           \|a x  + b x + c
+--R       + 
+--R                  2   4       2         2  3                3  2
+--R               16a b x  + (32a c + 24a b )x  + (56a b c + 6b )x
+--R             + 
+--R                     2     2
+--R               (32a c  + 8b c)x
+--R        *
+--R            +-+ +-+
+--R           \|a \|c
+--R    /
+--R                                   +--------------+
+--R                           +-+ +-+ |   2
+--R         (32a b x + 64a c)\|a \|c \|a x  + b x + c
+--R       + 
+--R                2        2  2                    2  +-+
+--R         ((- 32a c - 8a b )x  - 64a b c x - 64a c )\|a
+--R     ,
+--R
+--R                                                    +--------------+
+--R                           3          2     2   +-+ |   2
+--R             ((16a b c - 4b )x + 32a c  - 8b c)\|c \|a x  + b x + c
+--R           + 
+--R                   2 2    4  2             2     3           3     2 2
+--R             (- 16a c  + b )x  + (- 32a b c  + 8b c)x - 32a c  + 8b c
+--R        *
+--R                       +--------------+
+--R                 +---+ |   2               +---+ +-+
+--R                \|- a \|a x  + b x + c  - \|- a \|c
+--R           atan(------------------------------------)
+--R                                 a x
+--R       + 
+--R                 2        2  3                 3  2           2     2     +---+
+--R           ((- 8a c - 2a b )x  + (- 20a b c - b )x  + (- 16a c  - 4b c)x)\|- a
+--R        *
+--R            +--------------+
+--R            |   2
+--R           \|a x  + b x + c
+--R       + 
+--R              2   4       2         2  3                3  2         2     2
+--R           (8a b x  + (16a c + 12a b )x  + (28a b c + 3b )x  + (16a c  + 4b c)x)
+--R        *
+--R            +---+ +-+
+--R           \|- a \|c
+--R    /
+--R                                     +--------------+
+--R                           +---+ +-+ |   2
+--R         (16a b x + 32a c)\|- a \|c \|a x  + b x + c
+--R       + 
+--R                2        2  2                    2  +---+
+--R         ((- 16a c - 4a b )x  - 32a b c x - 32a c )\|- a
+--R     ]
+--R                                     Type: Union(List Expression Integer,...)
+--E
+
+--S 57
+bb1:=(6*a*x-5*b)/(24*a^2)*(a*x^2+b*x+c)^(3/2)+(5*b^2-4*a*c)/(16*a^2)*t1.1
+--R
+--R   (3)
+--R                     2   2         3       5         2 3         2 2       4
+--R             ((- 192a b c  + 288a b c - 60b )x - 384a c  + 576a b c  - 120b c)
+--R          *
+--R                  +--------------+
+--R              +-+ |   2
+--R             \|c \|a x  + b x + c
+--R         + 
+--R                3 3       2 2 2        4       6  2
+--R           (192a c  - 240a b c  - 12a b c + 15b )x
+--R         + 
+--R                2   3         3 2       5          2 4         2 3       4 2
+--R           (384a b c  - 576a b c  + 120b c)x + 384a c  - 576a b c  + 120b c
+--R      *
+--R         log
+--R                                   +--------------+
+--R                   +-+ +-+         |   2                   +-+
+--R                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
+--R              + 
+--R                       2             +-+
+--R                (- 2a x  - b x - 2c)\|a
+--R           /
+--R                    +--------------+
+--R                +-+ |   2
+--R              2\|c \|a x  + b x + c  - b x - 2c
+--R     + 
+--R                  4       3 2  5          3         2 3  4
+--R           (- 384a c - 96a b )x  + (- 832a b c - 16a b )x
+--R         + 
+--R                  3 2      2 2         4  3         2   2         3       5  2
+--R           (- 960a c  - 96a b c + 20a b )x  + (- 96a b c  + 144a b c - 30b )x
+--R         + 
+--R                  2 3         2 2       4              3
+--R           (- 384a c  + 896a b c  - 120b c)x + 640a b c
+--R      *
+--R              +--------------+
+--R          +-+ |   2
+--R         \|a \|a x  + b x + c
+--R     + 
+--R               4   6        4        3 2  5         3         2 3  4
+--R           384a b x  + (768a c + 448a b )x  + (1472a b c - 16a b )x
+--R         + 
+--R                 3 2       2 2         4  3         2   2         3       5  2
+--R           (1152a c  - 192a b c + 40a b )x  + (- 32a b c  - 512a b c + 90b )x
+--R         + 
+--R                2 3          2 2       4              3
+--R           (384a c  - 1216a b c  + 120b c)x - 640a b c
+--R      *
+--R          +-+ +-+
+--R         \|a \|c
+--R  /
+--R                                     +--------------+
+--R             3           3   +-+ +-+ |   2
+--R       (1536a b x + 3072a c)\|a \|c \|a x  + b x + c
+--R     + 
+--R                4        3 2  2        3             3 2  +-+
+--R       ((- 1536a c - 384a b )x  - 3072a b c x - 3072a c )\|a
+--R                                                     Type: Expression Integer
+--E
+
+--S 58
+bb2:=(6*a*x-5*b)/(24*a^2)*(a*x^2+b*x+c)^(3/2)+(5*b^2-4*a*c)/(16*a^2)*t1.2
+--R
+--R   (4)
+--R                     2   2         3       5         2 3         2 2       4
+--R             ((- 192a b c  + 288a b c - 60b )x - 384a c  + 576a b c  - 120b c)
+--R          *
+--R                  +--------------+
+--R              +-+ |   2
+--R             \|c \|a x  + b x + c
+--R         + 
+--R                3 3       2 2 2        4       6  2
+--R           (192a c  - 240a b c  - 12a b c + 15b )x
+--R         + 
+--R                2   3         3 2       5          2 4         2 3       4 2
+--R           (384a b c  - 576a b c  + 120b c)x + 384a c  - 576a b c  + 120b c
+--R      *
+--R                     +--------------+
+--R               +---+ |   2               +---+ +-+
+--R              \|- a \|a x  + b x + c  - \|- a \|c
+--R         atan(------------------------------------)
+--R                               a x
+--R     + 
+--R                  4       3 2  5          3        2 3  4
+--R           (- 192a c - 48a b )x  + (- 416a b c - 8a b )x
+--R         + 
+--R                  3 2      2 2         4  3         2   2        3       5  2
+--R           (- 480a c  - 48a b c + 10a b )x  + (- 48a b c  + 72a b c - 15b )x
+--R         + 
+--R                  2 3         2 2      4              3
+--R           (- 192a c  + 448a b c  - 60b c)x + 320a b c
+--R      *
+--R                +--------------+
+--R          +---+ |   2
+--R         \|- a \|a x  + b x + c
+--R     + 
+--R               4   6        4        3 2  5        3        2 3  4
+--R           192a b x  + (384a c + 224a b )x  + (736a b c - 8a b )x
+--R         + 
+--R                3 2      2 2         4  3         2   2         3       5  2
+--R           (576a c  - 96a b c + 20a b )x  + (- 16a b c  - 256a b c + 45b )x
+--R         + 
+--R                2 3         2 2      4              3
+--R           (192a c  - 608a b c  + 60b c)x - 320a b c
+--R      *
+--R          +---+ +-+
+--R         \|- a \|c
+--R  /
+--R                                      +--------------+
+--R            3           3   +---+ +-+ |   2
+--R       (768a b x + 1536a c)\|- a \|c \|a x  + b x + c
+--R     + 
+--R               4        3 2  2        3             3 2  +---+
+--R       ((- 768a c - 192a b )x  - 1536a b c x - 1536a c )\|- a
+--R                                                     Type: Expression Integer
+--E
+
+--S 59
+cc1:=aa.1-bb1
+--R
+--R   (5)
+--R                     4   4        3 3 3        2 5 2          7        9  5
+--R               (9216a b c  - 6144a b c  - 8064a b c  + 1536a b c + 180b )x
+--R             + 
+--R                      4 5         3 2 4         2 4 3        8   4
+--R               (18432a c  + 36864a b c  - 77568a b c  + 4200b c)x
+--R             + 
+--R                       3   5          2 3 4           5 3         7 2  3
+--R               (147456a b c  - 135168a b c  - 82944a b c  + 26880b c )x
+--R             + 
+--R                      3 6         2 2 5            4 4         6 3  2
+--R               (98304a c  + 73728a b c  - 301056a b c  + 69120b c )x
+--R             + 
+--R                       2   6            3 5         5 4           2 7
+--R               (245760a b c  - 368640a b c  + 76800b c )x + 98304a c
+--R             + 
+--R                          2 6         4 5
+--R               - 147456a b c  + 30720b c
+--R          *
+--R                  +--------------+
+--R              +-+ |   2
+--R             \|c \|a x  + b x + c
+--R         + 
+--R                      5 5        4 2 4         3 4 3       2 6 2         8
+--R               - 3072a c  - 6912a b c  + 13440a b c  + 672a b c  - 828a b c
+--R             + 
+--R                    10
+--R               - 15b
+--R          *
+--R              6
+--R             x
+--R         + 
+--R                    4   5         3 3 4         2 5 3          7 2        9   5
+--R           (- 55296a b c  + 36864a b c  + 48384a b c  - 9216a b c  - 1080b c)x
+--R         + 
+--R                    4 6          3 2 5          2 4 4         8 2  4
+--R           (- 55296a c  - 110592a b c  + 232704a b c  - 12600b c )x
+--R         + 
+--R                     3   6          2 3 5            5 4         7 3  3
+--R           (- 294912a b c  + 270336a b c  + 165888a b c  - 53760b c )x
+--R         + 
+--R                     3 7          2 2 6            4 5          6 4  2
+--R           (- 147456a c  - 110592a b c  + 451584a b c  - 103680b c )x
+--R         + 
+--R                     2   7            3 6         5 5           2 8
+--R           (- 294912a b c  + 442368a b c  - 92160b c )x - 98304a c
+--R         + 
+--R                    2 7         4 6
+--R           147456a b c  - 30720b c
+--R      *
+--R         log
+--R                                   +--------------+
+--R                   +-+ +-+         |   2                   +-+
+--R                (2\|a \|c  + 2a x)\|a x  + b x + c  - 2a x\|c
+--R              + 
+--R                       2             +-+
+--R                (- 2a x  - b x - 2c)\|a
+--R           /
+--R                    +--------------+
+--R                +-+ |   2
+--R              2\|c \|a x  + b x + c  - b x - 2c
+--R     + 
+--R                     4   4        3 3 3        2 5 2          7        9  5
+--R               (9216a b c  - 6144a b c  - 8064a b c  + 1536a b c + 180b )x
+--R             + 
+--R                      4 5         3 2 4         2 4 3        8   4
+--R               (18432a c  + 36864a b c  - 77568a b c  + 4200b c)x
+--R             + 
+--R                       3   5          2 3 4           5 3         7 2  3
+--R               (147456a b c  - 135168a b c  - 82944a b c  + 26880b c )x
+--R             + 
+--R                      3 6         2 2 5            4 4         6 3  2
+--R               (98304a c  + 73728a b c  - 301056a b c  + 69120b c )x
+--R             + 
+--R                       2   6            3 5         5 4           2 7
+--R               (245760a b c  - 368640a b c  + 76800b c )x + 98304a c
+--R             + 
+--R                          2 6         4 5
+--R               - 147456a b c  + 30720b c
+--R          *
+--R                  +--------------+
+--R              +-+ |   2
+--R             \|c \|a x  + b x + c
+--R         + 
+--R                      5 5        4 2 4         3 4 3       2 6 2         8
+--R               - 3072a c  - 6912a b c  + 13440a b c  + 672a b c  - 828a b c
+--R             + 
+--R                    10
+--R               - 15b
+--R          *
+--R              6
+--R             x
+--R         + 
+--R                    4   5         3 3 4         2 5 3          7 2        9   5
+--R           (- 55296a b c  + 36864a b c  + 48384a b c  - 9216a b c  - 1080b c)x
+--R         + 
+--R                    4 6          3 2 5          2 4 4         8 2  4
+--R           (- 55296a c  - 110592a b c  + 232704a b c  - 12600b c )x
+--R         + 
+--R                     3   6          2 3 5            5 4         7 3  3
+--R           (- 294912a b c  + 270336a b c  + 165888a b c  - 53760b c )x
+--R         + 
+--R                     3 7          2 2 6            4 5          6 4  2
+--R           (- 147456a c  - 110592a b c  + 451584a b c  - 103680b c )x
+--R         + 
+--R                     2   7            3 6         5 5           2 8
+--R           (- 294912a b c  + 442368a b c  - 92160b c )x - 98304a c
+--R         + 
+--R                    2 7         4 6
+--R           147456a b c  - 30720b c
+--R      *
+--R         log
+--R                                   +--------------+
+--R                   +-+ +-+         |   2                   +-+
+--R                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
+--R              + 
+--R                       2             +-+
+--R                (- 2a x  - b x - 2c)\|a
+--R           /
+--R                    +--------------+
+--R                +-+ |   2
+--R              2\|c \|a x  + b x + c  - b x - 2c
+--R     + 
+--R                    3 2 4         2 4 3         6 2  5
+--R           (- 15360a b c  - 12800a b c  - 960a b c )x
+--R         + 
+--R                    3   5          2 3 4           5 3  4
+--R           (- 30720a b c  - 107520a b c  - 22400a b c )x
+--R         + 
+--R                     2 2 5            4 4  3             2   6            3 5  2
+--R           (- 245760a b c  - 143360a b c )x  + (- 163840a b c  - 368640a b c )x
+--R         + 
+--R                      2 6               7
+--R           - 409600a b c x - 163840a b c
+--R      *
+--R              +--------------+
+--R          +-+ |   2
+--R         \|a \|a x  + b x + c
+--R     + 
+--R                 4   4         3 3 3        2 5 2        7   6
+--R           (5120a b c  + 19200a b c  + 4800a b c  + 80a b c)x
+--R         + 
+--R                  3 2 4         2 4 3          6 2  5
+--R           (92160a b c  + 76800a b c  + 5760a b c )x
+--R         + 
+--R                  3   5          2 3 4           5 3  4
+--R           (92160a b c  + 322560a b c  + 67200a b c )x
+--R         + 
+--R                   2 2 5            4 4  3           2   6            3 5  2
+--R           (491520a b c  + 286720a b c )x  + (245760a b c  + 552960a b c )x
+--R         + 
+--R                    2 6               7
+--R           491520a b c x + 163840a b c
+--R      *
+--R          +-+ +-+
+--R         \|a \|c
+--R  /
+--R                  5   2         4 3         3 5  5
+--R           (73728a b c  + 61440a b c + 4608a b )x
+--R         + 
+--R                   5 3          4 2 2          3 4   4
+--R           (147456a c  + 516096a b c  + 107520a b c)x
+--R         + 
+--R                    4   3          3 3 2  3           4 4           3 2 3  2
+--R           (1179648a b c  + 688128a b c )x  + (786432a c  + 1769472a b c )x
+--R         + 
+--R                   3   4           3 5
+--R           1966080a b c x + 786432a c
+--R      *
+--R                  +--------------+
+--R          +-+ +-+ |   2
+--R         \|a \|c \|a x  + b x + c
+--R     + 
+--R                    6 3         5 2 2         4 4        3 6  6
+--R           (- 24576a c  - 92160a b c  - 23040a b c - 384a b )x
+--R         + 
+--R                     5   3          4 3 2         3 5   5
+--R           (- 442368a b c  - 368640a b c  - 27648a b c)x
+--R         + 
+--R                     5 4           4 2 3          3 4 2  4
+--R           (- 442368a c  - 1548288a b c  - 322560a b c )x
+--R         + 
+--R                      4   4           3 3 3  3
+--R           (- 2359296a b c  - 1376256a b c )x
+--R         + 
+--R                      4 5           3 2 4  2           3   5           3 6
+--R           (- 1179648a c  - 2654208a b c )x  - 2359296a b c x - 786432a c
+--R      *
+--R          +-+
+--R         \|a
+--R                                                     Type: Expression Integer
+--E
+
+--S 60
+cc2:=aa.2-bb1
+--R
+--R   (6)
+--R                     4   4        3 3 3        2 5 2          7        9  5
+--R               (9216a b c  - 6144a b c  - 8064a b c  + 1536a b c + 180b )x
+--R             + 
+--R                      4 5         3 2 4         2 4 3        8   4
+--R               (18432a c  + 36864a b c  - 77568a b c  + 4200b c)x
+--R             + 
+--R                       3   5          2 3 4           5 3         7 2  3
+--R               (147456a b c  - 135168a b c  - 82944a b c  + 26880b c )x
+--R             + 
+--R                      3 6         2 2 5            4 4         6 3  2
+--R               (98304a c  + 73728a b c  - 301056a b c  + 69120b c )x
+--R             + 
+--R                       2   6            3 5         5 4           2 7
+--R               (245760a b c  - 368640a b c  + 76800b c )x + 98304a c
+--R             + 
+--R                          2 6         4 5
+--R               - 147456a b c  + 30720b c
+--R          *
+--R                        +--------------+
+--R              +---+ +-+ |   2
+--R             \|- a \|c \|a x  + b x + c
+--R         + 
+--R                          5 5        4 2 4         3 4 3       2 6 2         8
+--R                   - 3072a c  - 6912a b c  + 13440a b c  + 672a b c  - 828a b c
+--R                 + 
+--R                        10
+--R                   - 15b
+--R              *
+--R                  6
+--R                 x
+--R             + 
+--R                           4   5         3 3 4         2 5 3          7 2
+--R                   - 55296a b c  + 36864a b c  + 48384a b c  - 9216a b c
+--R                 + 
+--R                          9
+--R                   - 1080b c
+--R              *
+--R                  5
+--R                 x
+--R             + 
+--R                        4 6          3 2 5          2 4 4         8 2  4
+--R               (- 55296a c  - 110592a b c  + 232704a b c  - 12600b c )x
+--R             + 
+--R                         3   6          2 3 5            5 4         7 3  3
+--R               (- 294912a b c  + 270336a b c  + 165888a b c  - 53760b c )x
+--R             + 
+--R                         3 7          2 2 6            4 5          6 4  2
+--R               (- 147456a c  - 110592a b c  + 451584a b c  - 103680b c )x
+--R             + 
+--R                         2   7            3 6         5 5           2 8
+--R               (- 294912a b c  + 442368a b c  - 92160b c )x - 98304a c
+--R             + 
+--R                        2 7         4 6
+--R               147456a b c  - 30720b c
+--R          *
+--R              +---+
+--R             \|- a
+--R      *
+--R         log
+--R                                   +--------------+
+--R                   +-+ +-+         |   2                   +-+
+--R                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
+--R              + 
+--R                       2             +-+
+--R                (- 2a x  - b x - 2c)\|a
+--R           /
+--R                    +--------------+
+--R                +-+ |   2
+--R              2\|c \|a x  + b x + c  - b x - 2c
+--R     + 
+--R                        4   4         3 3 3         2 5 2          7        9  5
+--R               (- 18432a b c  + 12288a b c  + 16128a b c  - 3072a b c - 360b )x
+--R             + 
+--R                        4 5         3 2 4          2 4 3        8   4
+--R               (- 36864a c  - 73728a b c  + 155136a b c  - 8400b c)x
+--R             + 
+--R                         3   5          2 3 4            5 3         7 2  3
+--R               (- 294912a b c  + 270336a b c  + 165888a b c  - 53760b c )x
+--R             + 
+--R                         3 6          2 2 5            4 4          6 3  2
+--R               (- 196608a c  - 147456a b c  + 602112a b c  - 138240b c )x
+--R             + 
+--R                         2   6            3 5          5 4            2 7
+--R               (- 491520a b c  + 737280a b c  - 153600b c )x - 196608a c
+--R             + 
+--R                        2 6         4 5
+--R               294912a b c  - 61440b c
+--R          *
+--R                      +--------------+
+--R              +-+ +-+ |   2
+--R             \|a \|c \|a x  + b x + c
+--R         + 
+--R                        5 5         4 2 4         3 4 3        2 6 2          8
+--R                   6144a c  + 13824a b c  - 26880a b c  - 1344a b c  + 1656a b c
+--R                 + 
+--R                      10
+--R                   30b
+--R              *
+--R                  6
+--R                 x
+--R             + 
+--R                          4   5         3 3 4         2 5 3           7 2
+--R                   110592a b c  - 73728a b c  - 96768a b c  + 18432a b c
+--R                 + 
+--R                        9
+--R                   2160b c
+--R              *
+--R                  5
+--R                 x
+--R             + 
+--R                       4 6          3 2 5          2 4 4         8 2  4
+--R               (110592a c  + 221184a b c  - 465408a b c  + 25200b c )x
+--R             + 
+--R                       3   6          2 3 5            5 4          7 3  3
+--R               (589824a b c  - 540672a b c  - 331776a b c  + 107520b c )x
+--R             + 
+--R                       3 7          2 2 6            4 5          6 4  2
+--R               (294912a c  + 221184a b c  - 903168a b c  + 207360b c )x
+--R             + 
+--R                       2   7            3 6          5 5            2 8
+--R               (589824a b c  - 884736a b c  + 184320b c )x + 196608a c
+--R             + 
+--R                          2 7         4 6
+--R               - 294912a b c  + 61440b c
+--R          *
+--R              +-+
+--R             \|a
+--R      *
+--R                     +--------------+
+--R               +---+ |   2               +---+ +-+
+--R              \|- a \|a x  + b x + c  - \|- a \|c
+--R         atan(------------------------------------)
+--R                               a x
+--R     + 
+--R                    3 2 4         2 4 3         6 2  5
+--R           (- 15360a b c  - 12800a b c  - 960a b c )x
+--R         + 
+--R                    3   5          2 3 4           5 3  4
+--R           (- 30720a b c  - 107520a b c  - 22400a b c )x
+--R         + 
+--R                     2 2 5            4 4  3             2   6            3 5  2
+--R           (- 245760a b c  - 143360a b c )x  + (- 163840a b c  - 368640a b c )x
+--R         + 
+--R                      2 6               7
+--R           - 409600a b c x - 163840a b c
+--R      *
+--R                    +--------------+
+--R          +---+ +-+ |   2
+--R         \|- a \|a \|a x  + b x + c
+--R     + 
+--R                 4   4         3 3 3        2 5 2        7   6
+--R           (5120a b c  + 19200a b c  + 4800a b c  + 80a b c)x
+--R         + 
+--R                  3 2 4         2 4 3          6 2  5
+--R           (92160a b c  + 76800a b c  + 5760a b c )x
+--R         + 
+--R                  3   5          2 3 4           5 3  4
+--R           (92160a b c  + 322560a b c  + 67200a b c )x
+--R         + 
+--R                   2 2 5            4 4  3           2   6            3 5  2
+--R           (491520a b c  + 286720a b c )x  + (245760a b c  + 552960a b c )x
+--R         + 
+--R                    2 6               7
+--R           491520a b c x + 163840a b c
+--R      *
+--R          +---+ +-+ +-+
+--R         \|- a \|a \|c
+--R  /
+--R                  5   2         4 3         3 5  5
+--R           (73728a b c  + 61440a b c + 4608a b )x
+--R         + 
+--R                   5 3          4 2 2          3 4   4
+--R           (147456a c  + 516096a b c  + 107520a b c)x
+--R         + 
+--R                    4   3          3 3 2  3           4 4           3 2 3  2
+--R           (1179648a b c  + 688128a b c )x  + (786432a c  + 1769472a b c )x
+--R         + 
+--R                   3   4           3 5
+--R           1966080a b c x + 786432a c
+--R      *
+--R                        +--------------+
+--R          +---+ +-+ +-+ |   2
+--R         \|- a \|a \|c \|a x  + b x + c
+--R     + 
+--R                    6 3         5 2 2         4 4        3 6  6
+--R           (- 24576a c  - 92160a b c  - 23040a b c - 384a b )x
+--R         + 
+--R                     5   3          4 3 2         3 5   5
+--R           (- 442368a b c  - 368640a b c  - 27648a b c)x
+--R         + 
+--R                     5 4           4 2 3          3 4 2  4
+--R           (- 442368a c  - 1548288a b c  - 322560a b c )x
+--R         + 
+--R                      4   4           3 3 3  3
+--R           (- 2359296a b c  - 1376256a b c )x
+--R         + 
+--R                      4 5           3 2 4  2           3   5           3 6
+--R           (- 1179648a c  - 2654208a b c )x  - 2359296a b c x - 786432a c
+--R      *
+--R          +---+ +-+
+--R         \|- a \|a
+--R                                                     Type: Expression Integer
+--E
+
+--S 61
+cc3:=aa.1-bb2
+--R
+--R   (7)
+--R                     4   4        3 3 3        2 5 2          7        9  5
+--R               (9216a b c  - 6144a b c  - 8064a b c  + 1536a b c + 180b )x
+--R             + 
+--R                      4 5         3 2 4         2 4 3        8   4
+--R               (18432a c  + 36864a b c  - 77568a b c  + 4200b c)x
+--R             + 
+--R                       3   5          2 3 4           5 3         7 2  3
+--R               (147456a b c  - 135168a b c  - 82944a b c  + 26880b c )x
+--R             + 
+--R                      3 6         2 2 5            4 4         6 3  2
+--R               (98304a c  + 73728a b c  - 301056a b c  + 69120b c )x
+--R             + 
+--R                       2   6            3 5         5 4           2 7
+--R               (245760a b c  - 368640a b c  + 76800b c )x + 98304a c
+--R             + 
+--R                          2 6         4 5
+--R               - 147456a b c  + 30720b c
+--R          *
+--R                        +--------------+
+--R              +---+ +-+ |   2
+--R             \|- a \|c \|a x  + b x + c
+--R         + 
+--R                          5 5        4 2 4         3 4 3       2 6 2         8
+--R                   - 3072a c  - 6912a b c  + 13440a b c  + 672a b c  - 828a b c
+--R                 + 
+--R                        10
+--R                   - 15b
+--R              *
+--R                  6
+--R                 x
+--R             + 
+--R                           4   5         3 3 4         2 5 3          7 2
+--R                   - 55296a b c  + 36864a b c  + 48384a b c  - 9216a b c
+--R                 + 
+--R                          9
+--R                   - 1080b c
+--R              *
+--R                  5
+--R                 x
+--R             + 
+--R                        4 6          3 2 5          2 4 4         8 2  4
+--R               (- 55296a c  - 110592a b c  + 232704a b c  - 12600b c )x
+--R             + 
+--R                         3   6          2 3 5            5 4         7 3  3
+--R               (- 294912a b c  + 270336a b c  + 165888a b c  - 53760b c )x
+--R             + 
+--R                         3 7          2 2 6            4 5          6 4  2
+--R               (- 147456a c  - 110592a b c  + 451584a b c  - 103680b c )x
+--R             + 
+--R                         2   7            3 6         5 5           2 8
+--R               (- 294912a b c  + 442368a b c  - 92160b c )x - 98304a c
+--R             + 
+--R                        2 7         4 6
+--R               147456a b c  - 30720b c
+--R          *
+--R              +---+
+--R             \|- a
+--R      *
+--R         log
+--R                                   +--------------+
+--R                   +-+ +-+         |   2                   +-+
+--R                (2\|a \|c  + 2a x)\|a x  + b x + c  - 2a x\|c
+--R              + 
+--R                       2             +-+
+--R                (- 2a x  - b x - 2c)\|a
+--R           /
+--R                    +--------------+
+--R                +-+ |   2
+--R              2\|c \|a x  + b x + c  - b x - 2c
+--R     + 
+--R                      4   4         3 3 3         2 5 2          7        9  5
+--R               (18432a b c  - 12288a b c  - 16128a b c  + 3072a b c + 360b )x
+--R             + 
+--R                      4 5         3 2 4          2 4 3        8   4
+--R               (36864a c  + 73728a b c  - 155136a b c  + 8400b c)x
+--R             + 
+--R                       3   5          2 3 4            5 3         7 2  3
+--R               (294912a b c  - 270336a b c  - 165888a b c  + 53760b c )x
+--R             + 
+--R                       3 6          2 2 5            4 4          6 3  2
+--R               (196608a c  + 147456a b c  - 602112a b c  + 138240b c )x
+--R             + 
+--R                       2   6            3 5          5 4            2 7
+--R               (491520a b c  - 737280a b c  + 153600b c )x + 196608a c
+--R             + 
+--R                          2 6         4 5
+--R               - 294912a b c  + 61440b c
+--R          *
+--R                      +--------------+
+--R              +-+ +-+ |   2
+--R             \|a \|c \|a x  + b x + c
+--R         + 
+--R                          5 5         4 2 4         3 4 3        2 6 2
+--R                   - 6144a c  - 13824a b c  + 26880a b c  + 1344a b c
+--R                 + 
+--R                            8       10
+--R                   - 1656a b c - 30b
+--R              *
+--R                  6
+--R                 x
+--R             + 
+--R                            4   5         3 3 4         2 5 3           7 2
+--R                   - 110592a b c  + 73728a b c  + 96768a b c  - 18432a b c
+--R                 + 
+--R                          9
+--R                   - 2160b c
+--R              *
+--R                  5
+--R                 x
+--R             + 
+--R                         4 6          3 2 5          2 4 4         8 2  4
+--R               (- 110592a c  - 221184a b c  + 465408a b c  - 25200b c )x
+--R             + 
+--R                         3   6          2 3 5            5 4          7 3  3
+--R               (- 589824a b c  + 540672a b c  + 331776a b c  - 107520b c )x
+--R             + 
+--R                         3 7          2 2 6            4 5          6 4  2
+--R               (- 294912a c  - 221184a b c  + 903168a b c  - 207360b c )x
+--R             + 
+--R                         2   7            3 6          5 5            2 8
+--R               (- 589824a b c  + 884736a b c  - 184320b c )x - 196608a c
+--R             + 
+--R                        2 7         4 6
+--R               294912a b c  - 61440b c
+--R          *
+--R              +-+
+--R             \|a
+--R      *
+--R                     +--------------+
+--R               +---+ |   2               +---+ +-+
+--R              \|- a \|a x  + b x + c  - \|- a \|c
+--R         atan(------------------------------------)
+--R                               a x
+--R     + 
+--R                    3 2 4         2 4 3         6 2  5
+--R           (- 15360a b c  - 12800a b c  - 960a b c )x
+--R         + 
+--R                    3   5          2 3 4           5 3  4
+--R           (- 30720a b c  - 107520a b c  - 22400a b c )x
+--R         + 
+--R                     2 2 5            4 4  3             2   6            3 5  2
+--R           (- 245760a b c  - 143360a b c )x  + (- 163840a b c  - 368640a b c )x
+--R         + 
+--R                      2 6               7
+--R           - 409600a b c x - 163840a b c
+--R      *
+--R                    +--------------+
+--R          +---+ +-+ |   2
+--R         \|- a \|a \|a x  + b x + c
+--R     + 
+--R                 4   4         3 3 3        2 5 2        7   6
+--R           (5120a b c  + 19200a b c  + 4800a b c  + 80a b c)x
+--R         + 
+--R                  3 2 4         2 4 3          6 2  5
+--R           (92160a b c  + 76800a b c  + 5760a b c )x
+--R         + 
+--R                  3   5          2 3 4           5 3  4
+--R           (92160a b c  + 322560a b c  + 67200a b c )x
+--R         + 
+--R                   2 2 5            4 4  3           2   6            3 5  2
+--R           (491520a b c  + 286720a b c )x  + (245760a b c  + 552960a b c )x
+--R         + 
+--R                    2 6               7
+--R           491520a b c x + 163840a b c
+--R      *
+--R          +---+ +-+ +-+
+--R         \|- a \|a \|c
+--R  /
+--R                  5   2         4 3         3 5  5
+--R           (73728a b c  + 61440a b c + 4608a b )x
+--R         + 
+--R                   5 3          4 2 2          3 4   4
+--R           (147456a c  + 516096a b c  + 107520a b c)x
+--R         + 
+--R                    4   3          3 3 2  3           4 4           3 2 3  2
+--R           (1179648a b c  + 688128a b c )x  + (786432a c  + 1769472a b c )x
+--R         + 
+--R                   3   4           3 5
+--R           1966080a b c x + 786432a c
+--R      *
+--R                        +--------------+
+--R          +---+ +-+ +-+ |   2
+--R         \|- a \|a \|c \|a x  + b x + c
+--R     + 
+--R                    6 3         5 2 2         4 4        3 6  6
+--R           (- 24576a c  - 92160a b c  - 23040a b c - 384a b )x
+--R         + 
+--R                     5   3          4 3 2         3 5   5
+--R           (- 442368a b c  - 368640a b c  - 27648a b c)x
+--R         + 
+--R                     5 4           4 2 3          3 4 2  4
+--R           (- 442368a c  - 1548288a b c  - 322560a b c )x
+--R         + 
+--R                      4   4           3 3 3  3
+--R           (- 2359296a b c  - 1376256a b c )x
+--R         + 
+--R                      4 5           3 2 4  2           3   5           3 6
+--R           (- 1179648a c  - 2654208a b c )x  - 2359296a b c x - 786432a c
+--R      *
+--R          +---+ +-+
+--R         \|- a \|a
+--R                                                     Type: Expression Integer
+--E
+
+--S 62     14:287 Axiom cannot simplify these expressions
+cc4:=aa.2-bb2
+--R
+--R   (8)
+--R                  2 2 4         4 3      6 2  5
+--R           (- 960a b c  - 800a b c  - 60b c )x
+--R         + 
+--R                   2   5          3 4        5 3  4
+--R           (- 1920a b c  - 6720a b c  - 1400b c )x
+--R         + 
+--R                      2 5        4 4  3                6         3 5  2
+--R           (- 15360a b c  - 8960b c )x  + (- 10240a b c  - 23040b c )x
+--R         + 
+--R                   2 6            7
+--R           - 25600b c x - 10240b c
+--R      *
+--R          +--------------+
+--R          |   2
+--R         \|a x  + b x + c
+--R     + 
+--R                3   4        2 3 3         5 2     7   6
+--R           (320a b c  + 1200a b c  + 300a b c  + 5b c)x
+--R         + 
+--R                 2 2 4          4 3       6 2  5
+--R           (5760a b c  + 4800a b c  + 360b c )x
+--R         + 
+--R                 2   5           3 4        5 3  4            2 5         4 4  3
+--R           (5760a b c  + 20160a b c  + 4200b c )x  + (30720a b c  + 17920b c )x
+--R         + 
+--R                      6         3 5  2         2 6            7
+--R           (15360a b c  + 34560b c )x  + 30720b c x + 10240b c
+--R      *
+--R          +-+
+--R         \|c
+--R  /
+--R                 4   2        3 3        2 5  5
+--R           (4608a b c  + 3840a b c + 288a b )x
+--R         + 
+--R                 4 3         3 2 2        2 4   4
+--R           (9216a c  + 32256a b c  + 6720a b c)x
+--R         + 
+--R                  3   3         2 3 2  3          3 4          2 2 3  2
+--R           (73728a b c  + 43008a b c )x  + (49152a c  + 110592a b c )x
+--R         + 
+--R                  2   4          2 5
+--R           122880a b c x + 49152a c
+--R      *
+--R              +--------------+
+--R          +-+ |   2
+--R         \|c \|a x  + b x + c
+--R     + 
+--R               5 3        4 2 2        3 4       2 6  6
+--R       (- 1536a c  - 5760a b c  - 1440a b c - 24a b )x
+--R     + 
+--R                4   3         3 3 2        2 5   5
+--R       (- 27648a b c  - 23040a b c  - 1728a b c)x
+--R     + 
+--R                4 4         3 2 3         2 4 2  4
+--R       (- 27648a c  - 96768a b c  - 20160a b c )x
+--R     + 
+--R                 3   4         2 3 3  3            3 5          2 2 4  2
+--R       (- 147456a b c  - 86016a b c )x  + (- 73728a c  - 165888a b c )x
+--R     + 
+--R                2   5          2 6
+--R       - 147456a b c x - 49152a c
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.288~~~~~$\displaystyle
@@ -775,7 +3094,7 @@ $$
 <<*>>=
 )clear all
 
---S 9 of 19
+--S 63
 aa:=integrate(sqrt(a*x^2+b*x+c)/x,x)
 --R 
 --R
@@ -858,6 +3177,307 @@ aa:=integrate(sqrt(a*x^2+b*x+c)/x,x)
 --R     ]
 --R                                     Type: Union(List Expression Integer,...)
 --E
+
+--S 64
+t1:=integrate(1/sqrt(a*x^2+b*x+c),x)
+--R
+--R   (2)
+--R   [
+--R       log
+--R                                 +--------------+
+--R                 +-+ +-+         |   2                   +-+
+--R              (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
+--R            + 
+--R                     2             +-+
+--R              (- 2a x  - b x - 2c)\|a
+--R         /
+--R                  +--------------+
+--R              +-+ |   2
+--R            2\|c \|a x  + b x + c  - b x - 2c
+--R    /
+--R        +-+
+--R       \|a
+--R     ,
+--R                 +--------------+
+--R           +---+ |   2               +---+ +-+
+--R          \|- a \|a x  + b x + c  - \|- a \|c
+--R    2atan(------------------------------------)
+--R                           a x
+--R    -------------------------------------------]
+--R                        +---+
+--R                       \|- a
+--R                                     Type: Union(List Expression Integer,...)
+--E
+
+--S 65
+t2:=integrate(1/(x*sqrt(a*x^2+b*x+c)),x)
+--R
+--R                  +--------------+
+--R              +-+ |   2
+--R            2\|c \|a x  + b x + c  - b x - 2c
+--R        log(---------------------------------)
+--R                            x
+--R   (3)  --------------------------------------
+--R                          +-+
+--R                         \|c
+--R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 66
+bb1:=sqrt(a*x^2+b*x+c)+b/2*t1.1+c*t2
+--R
+--R   (4)
+--R                       +--------------+
+--R                   +-+ |   2
+--R          +-+    2\|c \|a x  + b x + c  - b x - 2c
+--R       2c\|a log(---------------------------------)
+--R                                 x
+--R     + 
+--R           +-+
+--R         b\|c
+--R      *
+--R         log
+--R                                   +--------------+
+--R                   +-+ +-+         |   2                   +-+
+--R                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
+--R              + 
+--R                       2             +-+
+--R                (- 2a x  - b x - 2c)\|a
+--R           /
+--R                    +--------------+
+--R                +-+ |   2
+--R              2\|c \|a x  + b x + c  - b x - 2c
+--R     + 
+--R                 +--------------+
+--R         +-+ +-+ |   2
+--R       2\|a \|c \|a x  + b x + c
+--R  /
+--R       +-+ +-+
+--R     2\|a \|c
+--R                                                     Type: Expression Integer
+--E
+
+--S 67
+bb2:=sqrt(a*x^2+b*x+c)+b/2*t1.2+c*t2
+--R
+--R   (5)
+--R                        +--------------+
+--R                    +-+ |   2
+--R         +---+    2\|c \|a x  + b x + c  - b x - 2c
+--R       c\|- a log(---------------------------------)
+--R                                  x
+--R     + 
+--R                        +--------------+
+--R                  +---+ |   2               +---+ +-+
+--R         +-+     \|- a \|a x  + b x + c  - \|- a \|c
+--R       b\|c atan(------------------------------------)
+--R                                  a x
+--R     + 
+--R                  +--------------+
+--R        +---+ +-+ |   2
+--R       \|- a \|c \|a x  + b x + c
+--R  /
+--R      +---+ +-+
+--R     \|- a \|c
+--R                                                     Type: Expression Integer
+--E
+
+--S 68
+cc1:=aa.1-bb1
+--R
+--R   (6)
+--R                         +--------------+
+--R                     +-+ |   2
+--R            +-+    2\|c \|a x  + b x + c  - b x - 2c
+--R       - 2c\|a log(---------------------------------)
+--R                                   x
+--R     + 
+--R                       +--------------+
+--R                   +-+ |   2
+--R          +-+    2\|c \|a x  + b x + c  - b x - 2c
+--R       2c\|a log(---------------------------------)
+--R                                  +-+
+--R                               2x\|c
+--R     + 
+--R       -
+--R              +-+
+--R            b\|c
+--R         *
+--R            log
+--R                                      +--------------+
+--R                      +-+ +-+         |   2                   +-+
+--R                   (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
+--R                 + 
+--R                          2             +-+
+--R                   (- 2a x  - b x - 2c)\|a
+--R              /
+--R                       +--------------+
+--R                   +-+ |   2
+--R                 2\|c \|a x  + b x + c  - b x - 2c
+--R     + 
+--R           +-+
+--R         b\|c
+--R      *
+--R         log
+--R                            2           +-+          2              2  +-+
+--R                  ((- 2a b x  - 8a c x)\|c  + (4a c x  + 4b c x + 8c )\|a )
+--R               *
+--R                   +--------------+
+--R                   |   2
+--R                  \|a x  + b x + c
+--R              + 
+--R                         3              2  2              2  +-+ +-+     2   3
+--R                (- 2a b x  + (- 8a c - b )x  - 8b c x - 8c )\|a \|c  + 4a c x
+--R              + 
+--R                        2       2
+--R                6a b c x  + 8a c x
+--R           /
+--R                               +--------------+
+--R                            2  |   2
+--R                (4b c x + 8c )\|a x  + b x + c
+--R              + 
+--R                            2  2              2  +-+
+--R                ((- 4a c - b )x  - 8b c x - 8c )\|c
+--R     + 
+--R          +-+
+--R       2c\|a
+--R  /
+--R       +-+ +-+
+--R     2\|a \|c
+--R                                                     Type: Expression Integer
+--E
+
+--S 69
+cc2:=aa.2-bb1
+--R
+--R   (7)
+--R                               +--------------+
+--R                           +-+ |   2
+--R            +---+ +-+    2\|c \|a x  + b x + c  - b x - 2c
+--R       - 2c\|- a \|a log(---------------------------------)
+--R                                         x
+--R     + 
+--R                             +--------------+
+--R                         +-+ |   2
+--R          +---+ +-+    2\|c \|a x  + b x + c  - b x - 2c
+--R       2c\|- a \|a log(---------------------------------)
+--R                                        +-+
+--R                                     2x\|c
+--R     + 
+--R       -
+--R              +---+ +-+
+--R            b\|- a \|c
+--R         *
+--R            log
+--R                                      +--------------+
+--R                      +-+ +-+         |   2                   +-+
+--R                   (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
+--R                 + 
+--R                          2             +-+
+--R                   (- 2a x  - b x - 2c)\|a
+--R              /
+--R                       +--------------+
+--R                   +-+ |   2
+--R                 2\|c \|a x  + b x + c  - b x - 2c
+--R     + 
+--R                                 +--------------+
+--R                       +---+ +-+ |   2                +---+
+--R          +-+ +-+     \|- a \|c \|a x  + b x + c  - c\|- a        +---+ +-+
+--R       2b\|a \|c atan(-------------------------------------) + 2c\|- a \|a
+--R                                         +-+
+--R                                     a x\|c
+--R  /
+--R       +---+ +-+ +-+
+--R     2\|- a \|a \|c
+--R                                                     Type: Expression Integer
+--E
+
+--S 70
+cc3:=aa.1-bb2
+--R
+--R   (8)
+--R                               +--------------+
+--R                           +-+ |   2
+--R            +---+ +-+    2\|c \|a x  + b x + c  - b x - 2c
+--R       - 2c\|- a \|a log(---------------------------------)
+--R                                         x
+--R     + 
+--R                             +--------------+
+--R                         +-+ |   2
+--R          +---+ +-+    2\|c \|a x  + b x + c  - b x - 2c
+--R       2c\|- a \|a log(---------------------------------)
+--R                                        +-+
+--R                                     2x\|c
+--R     + 
+--R           +---+ +-+
+--R         b\|- a \|c
+--R      *
+--R         log
+--R                            2           +-+          2              2  +-+
+--R                  ((- 2a b x  - 8a c x)\|c  + (4a c x  + 4b c x + 8c )\|a )
+--R               *
+--R                   +--------------+
+--R                   |   2
+--R                  \|a x  + b x + c
+--R              + 
+--R                         3              2  2              2  +-+ +-+     2   3
+--R                (- 2a b x  + (- 8a c - b )x  - 8b c x - 8c )\|a \|c  + 4a c x
+--R              + 
+--R                        2       2
+--R                6a b c x  + 8a c x
+--R           /
+--R                               +--------------+
+--R                            2  |   2
+--R                (4b c x + 8c )\|a x  + b x + c
+--R              + 
+--R                            2  2              2  +-+
+--R                ((- 4a c - b )x  - 8b c x - 8c )\|c
+--R     + 
+--R                               +--------------+
+--R                         +---+ |   2               +---+ +-+
+--R            +-+ +-+     \|- a \|a x  + b x + c  - \|- a \|c        +---+ +-+
+--R       - 2b\|a \|c atan(------------------------------------) + 2c\|- a \|a
+--R                                         a x
+--R  /
+--R       +---+ +-+ +-+
+--R     2\|- a \|a \|c
+--R                                                     Type: Expression Integer
+--E
+
+--S 71     14:288 Axiom cannot simplify these expressions
+cc4:=aa.2-bb2
+--R
+--R   (9)
+--R                          +--------------+
+--R                      +-+ |   2
+--R           +---+    2\|c \|a x  + b x + c  - b x - 2c
+--R       - c\|- a log(---------------------------------)
+--R                                    x
+--R     + 
+--R                        +--------------+
+--R                    +-+ |   2
+--R         +---+    2\|c \|a x  + b x + c  - b x - 2c
+--R       c\|- a log(---------------------------------)
+--R                                   +-+
+--R                                2x\|c
+--R     + 
+--R                            +--------------+
+--R                  +---+ +-+ |   2                +---+
+--R         +-+     \|- a \|c \|a x  + b x + c  - c\|- a
+--R       b\|c atan(-------------------------------------)
+--R                                    +-+
+--R                                a x\|c
+--R     + 
+--R                          +--------------+
+--R                    +---+ |   2               +---+ +-+
+--R           +-+     \|- a \|a x  + b x + c  - \|- a \|c       +---+
+--R       - b\|c atan(------------------------------------) + c\|- a
+--R                                    a x
+--R  /
+--R      +---+ +-+
+--R     \|- a \|c
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.289~~~~~$\displaystyle
@@ -870,7 +3490,7 @@ $$
 <<*>>=
 )clear all
 
---S 10 of 19
+--S 72
 aa:=integrate(sqrt(a*x^2+b*x+c)/x^2,x)
 --R 
 --R
@@ -937,7 +3557,345 @@ aa:=integrate(sqrt(a*x^2+b*x+c)/x^2,x)
 --R       8c x\|a x  + b x + c  + (- 4b x  - 8c x)\|c
 --R     ]
 --R                                     Type: Union(List Expression Integer,...)
---E 
+--E
+
+--S 73
+t1:=integrate(1/sqrt(a*x^2+b*x+c),x)
+--R
+--R   (2)
+--R   [
+--R       log
+--R                                 +--------------+
+--R                 +-+ +-+         |   2                   +-+
+--R              (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
+--R            + 
+--R                     2             +-+
+--R              (- 2a x  - b x - 2c)\|a
+--R         /
+--R                  +--------------+
+--R              +-+ |   2
+--R            2\|c \|a x  + b x + c  - b x - 2c
+--R    /
+--R        +-+
+--R       \|a
+--R     ,
+--R                 +--------------+
+--R           +---+ |   2               +---+ +-+
+--R          \|- a \|a x  + b x + c  - \|- a \|c
+--R    2atan(------------------------------------)
+--R                           a x
+--R    -------------------------------------------]
+--R                        +---+
+--R                       \|- a
+--R                                     Type: Union(List Expression Integer,...)
+--E
+
+--S 74
+t2:=integrate(1/(x*sqrt(a*x^2+b*x+c)),x)
+--R
+--R                  +--------------+
+--R              +-+ |   2
+--R            2\|c \|a x  + b x + c  - b x - 2c
+--R        log(---------------------------------)
+--R                            x
+--R   (3)  --------------------------------------
+--R                          +-+
+--R                         \|c
+--R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 75
+bb1:=-sqrt(a*x^2+b*x+c)/x+a*t1.1+b/2*t2
+--R
+--R   (4)
+--R                        +--------------+
+--R                    +-+ |   2
+--R           +-+    2\|c \|a x  + b x + c  - b x - 2c
+--R       b x\|a log(---------------------------------)
+--R                                  x
+--R     + 
+--R              +-+
+--R         2a x\|c
+--R      *
+--R         log
+--R                                   +--------------+
+--R                   +-+ +-+         |   2                   +-+
+--R                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
+--R              + 
+--R                       2             +-+
+--R                (- 2a x  - b x - 2c)\|a
+--R           /
+--R                    +--------------+
+--R                +-+ |   2
+--R              2\|c \|a x  + b x + c  - b x - 2c
+--R     + 
+--R                   +--------------+
+--R           +-+ +-+ |   2
+--R       - 2\|a \|c \|a x  + b x + c
+--R  /
+--R        +-+ +-+
+--R     2x\|a \|c
+--R                                                     Type: Expression Integer
+--E
+
+--S 76
+bb2:=-sqrt(a*x^2+b*x+c)/x+a*t1.2+b/2*t2
+--R
+--R   (5)
+--R                          +--------------+
+--R                      +-+ |   2
+--R           +---+    2\|c \|a x  + b x + c  - b x - 2c
+--R       b x\|- a log(---------------------------------)
+--R                                    x
+--R     + 
+--R                           +--------------+
+--R                     +---+ |   2               +---+ +-+
+--R            +-+     \|- a \|a x  + b x + c  - \|- a \|c
+--R       4a x\|c atan(------------------------------------)
+--R                                     a x
+--R     + 
+--R                     +--------------+
+--R           +---+ +-+ |   2
+--R       - 2\|- a \|c \|a x  + b x + c
+--R  /
+--R        +---+ +-+
+--R     2x\|- a \|c
+--R                                                     Type: Expression Integer
+--E
+
+--S 77
+cc1:=aa.1-bb1
+--R
+--R   (6)
+--R                     +--------------+
+--R                 +-+ |   2                 2          +-+ +-+
+--R         (- 4b c\|a \|a x  + b x + c  + (2b x + 4b c)\|a \|c )
+--R      *
+--R                   +--------------+
+--R               +-+ |   2
+--R             2\|c \|a x  + b x + c  - b x - 2c
+--R         log(---------------------------------)
+--R                             x
+--R     + 
+--R                   +--------------+
+--R               +-+ |   2                   2          +-+ +-+
+--R         (4b c\|a \|a x  + b x + c  + (- 2b x - 4b c)\|a \|c )
+--R      *
+--R                +--------------+
+--R                |   2                           +-+
+--R             2c\|a x  + b x + c  + (- b x - 2c)\|c
+--R         log(--------------------------------------)
+--R                              2c x
+--R     + 
+--R                     +--------------+
+--R                 +-+ |   2                             2
+--R         (- 8a c\|c \|a x  + b x + c  + 4a b c x + 8a c )
+--R      *
+--R         log
+--R                                   +--------------+
+--R                   +-+ +-+         |   2                   +-+
+--R                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
+--R              + 
+--R                       2             +-+
+--R                (- 2a x  - b x - 2c)\|a
+--R           /
+--R                    +--------------+
+--R                +-+ |   2
+--R              2\|c \|a x  + b x + c  - b x - 2c
+--R     + 
+--R                   +--------------+
+--R               +-+ |   2                             2
+--R         (8a c\|c \|a x  + b x + c  - 4a b c x - 8a c )
+--R      *
+--R                              +--------------+
+--R                +-+      +-+  |   2                 +-+ +-+       2
+--R             (2\|c  - 2x\|a )\|a x  + b x + c  + 2x\|a \|c  - 2a x  - b x - 2c
+--R         log(-----------------------------------------------------------------)
+--R                                   +--------------+
+--R                               +-+ |   2
+--R                             2\|c \|a x  + b x + c  - b x - 2c
+--R     + 
+--R                  +--------------+
+--R              +-+ |   2                2          +-+ +-+
+--R       - 2b c\|a \|a x  + b x + c  + (b x + 2b c)\|a \|c
+--R  /
+--R                +--------------+
+--R        +-+ +-+ |   2                            2  +-+
+--R     8c\|a \|c \|a x  + b x + c  + (- 4b c x - 8c )\|a
+--R                                                     Type: Expression Integer
+--E
+
+--S 78
+cc2:=aa.2-bb1
+--R
+--R   (7)
+--R                     +--------------+
+--R                 +-+ |   2                 2          +-+ +-+
+--R         (- 4b c\|a \|a x  + b x + c  + (2b x + 4b c)\|a \|c )
+--R      *
+--R                   +--------------+
+--R               +-+ |   2
+--R             2\|c \|a x  + b x + c  - b x - 2c
+--R         log(---------------------------------)
+--R                             x
+--R     + 
+--R                   +--------------+
+--R               +-+ |   2                   2          +-+ +-+
+--R         (4b c\|a \|a x  + b x + c  + (- 2b x - 4b c)\|a \|c )
+--R      *
+--R                +--------------+
+--R                |   2                           +-+
+--R             2c\|a x  + b x + c  + (- b x - 2c)\|c
+--R         log(--------------------------------------)
+--R                              2c x
+--R     + 
+--R                     +--------------+
+--R                 +-+ |   2                             2
+--R         (- 8a c\|c \|a x  + b x + c  + 4a b c x + 8a c )
+--R      *
+--R         log
+--R                                   +--------------+
+--R                   +-+ +-+         |   2                   +-+
+--R                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
+--R              + 
+--R                       2             +-+
+--R                (- 2a x  - b x - 2c)\|a
+--R           /
+--R                    +--------------+
+--R                +-+ |   2
+--R              2\|c \|a x  + b x + c  - b x - 2c
+--R     + 
+--R                            +--------------+
+--R              +---+ +-+ +-+ |   2                             2  +---+ +-+
+--R         (16c\|- a \|a \|c \|a x  + b x + c  + (- 8b c x - 16c )\|- a \|a )
+--R      *
+--R               +--------------+
+--R               |   2               +-+
+--R              \|a x  + b x + c  - \|c
+--R         atan(------------------------)
+--R                         +---+
+--R                       x\|- a
+--R     + 
+--R                  +--------------+
+--R              +-+ |   2                2          +-+ +-+
+--R       - 2b c\|a \|a x  + b x + c  + (b x + 2b c)\|a \|c
+--R  /
+--R                +--------------+
+--R        +-+ +-+ |   2                            2  +-+
+--R     8c\|a \|c \|a x  + b x + c  + (- 4b c x - 8c )\|a
+--R                                                     Type: Expression Integer
+--E
+
+--S 79
+cc3:=aa.1-bb2
+--R
+--R   (8)
+--R                       +--------------+
+--R                 +---+ |   2                 2          +---+ +-+
+--R         (- 4b c\|- a \|a x  + b x + c  + (2b x + 4b c)\|- a \|c )
+--R      *
+--R                   +--------------+
+--R               +-+ |   2
+--R             2\|c \|a x  + b x + c  - b x - 2c
+--R         log(---------------------------------)
+--R                             x
+--R     + 
+--R                     +--------------+
+--R               +---+ |   2                   2          +---+ +-+
+--R         (4b c\|- a \|a x  + b x + c  + (- 2b x - 4b c)\|- a \|c )
+--R      *
+--R                +--------------+
+--R                |   2                           +-+
+--R             2c\|a x  + b x + c  + (- b x - 2c)\|c
+--R         log(--------------------------------------)
+--R                              2c x
+--R     + 
+--R                           +--------------+
+--R             +---+ +-+ +-+ |   2                            2  +---+ +-+
+--R         (8c\|- a \|a \|c \|a x  + b x + c  + (- 4b c x - 8c )\|- a \|a )
+--R      *
+--R                              +--------------+
+--R                +-+      +-+  |   2                 +-+ +-+       2
+--R             (2\|c  - 2x\|a )\|a x  + b x + c  + 2x\|a \|c  - 2a x  - b x - 2c
+--R         log(-----------------------------------------------------------------)
+--R                                   +--------------+
+--R                               +-+ |   2
+--R                             2\|c \|a x  + b x + c  - b x - 2c
+--R     + 
+--R                      +--------------+
+--R                  +-+ |   2                              2
+--R         (- 16a c\|c \|a x  + b x + c  + 8a b c x + 16a c )
+--R      *
+--R                     +--------------+
+--R               +---+ |   2               +---+ +-+
+--R              \|- a \|a x  + b x + c  - \|- a \|c
+--R         atan(------------------------------------)
+--R                               a x
+--R     + 
+--R                    +--------------+
+--R              +---+ |   2                2          +---+ +-+
+--R       - 2b c\|- a \|a x  + b x + c  + (b x + 2b c)\|- a \|c
+--R  /
+--R                  +--------------+
+--R        +---+ +-+ |   2                            2  +---+
+--R     8c\|- a \|c \|a x  + b x + c  + (- 4b c x - 8c )\|- a
+--R                                                     Type: Expression Integer
+--E
+
+--S 80     14:289 Axiom cannot simplify these expressions
+cc4:=aa.2-bb2
+--R
+--R   (9)
+--R                       +--------------+
+--R                 +---+ |   2                 2          +---+ +-+
+--R         (- 4b c\|- a \|a x  + b x + c  + (2b x + 4b c)\|- a \|c )
+--R      *
+--R                   +--------------+
+--R               +-+ |   2
+--R             2\|c \|a x  + b x + c  - b x - 2c
+--R         log(---------------------------------)
+--R                             x
+--R     + 
+--R                     +--------------+
+--R               +---+ |   2                   2          +---+ +-+
+--R         (4b c\|- a \|a x  + b x + c  + (- 2b x - 4b c)\|- a \|c )
+--R      *
+--R                +--------------+
+--R                |   2                           +-+
+--R             2c\|a x  + b x + c  + (- b x - 2c)\|c
+--R         log(--------------------------------------)
+--R                              2c x
+--R     + 
+--R                      +--------------+
+--R                  +-+ |   2                              2
+--R         (- 16a c\|c \|a x  + b x + c  + 8a b c x + 16a c )
+--R      *
+--R                     +--------------+
+--R               +---+ |   2               +---+ +-+
+--R              \|- a \|a x  + b x + c  - \|- a \|c
+--R         atan(------------------------------------)
+--R                               a x
+--R     + 
+--R                      +--------------+
+--R                  +-+ |   2                              2
+--R         (- 16a c\|c \|a x  + b x + c  + 8a b c x + 16a c )
+--R      *
+--R               +--------------+
+--R               |   2               +-+
+--R              \|a x  + b x + c  - \|c
+--R         atan(------------------------)
+--R                         +---+
+--R                       x\|- a
+--R     + 
+--R                    +--------------+
+--R              +---+ |   2                2          +---+ +-+
+--R       - 2b c\|- a \|a x  + b x + c  + (b x + 2b c)\|- a \|c
+--R  /
+--R                  +--------------+
+--R        +---+ +-+ |   2                            2  +---+
+--R     8c\|- a \|c \|a x  + b x + c  + (- 4b c x - 8c )\|- a
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.290~~~~~$\displaystyle
@@ -949,7 +3907,7 @@ $$
 <<*>>=
 )clear all
 
---S 11 of 19
+--S 81
 aa:=integrate(1/(a*x^2+b*x+c)^(3/2),x)
 --R 
 --R
@@ -962,6 +3920,31 @@ aa:=integrate(1/(a*x^2+b*x+c)^(3/2),x)
 --R        (b x + 2c)\|c \|a x  + b x + c  - 2a c x  - 2b c x - 2c
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 82
+bb:=(2*(2*a*x+b))/((4*a*c-b^2)*sqrt(a*x^2+b*x+c))
+--R
+--R                  4a x + 2b
+--R   (2)  ----------------------------
+--R                    +--------------+
+--R                 2  |   2
+--R        (4a c - b )\|a x  + b x + c
+--R                                                     Type: Expression Integer
+--E
+
+--S 83     14:290 Axiom cannot simplify these expressions
+cc:=aa-bb
+--R
+--R   (3)
+--R                           +--------------+
+--R                       +-+ |   2                2
+--R                    4b\|c \|a x  + b x + c  - 2b x - 4b c
+--R   -----------------------------------------------------------------------
+--R                  +--------------+
+--R        2     2   |   2                            3         2     2   +-+
+--R   (8a c  - 2b c)\|a x  + b x + c  + ((- 4a b c + b )x - 8a c  + 2b c)\|c
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.291~~~~~$\displaystyle
@@ -972,7 +3955,7 @@ $$
 <<*>>=
 )clear all
 
---S 12 of 19
+--S 84
 aa:=integrate(x/(a*x^2+b*x+c)^(3/2),x)
 --R 
 --R
@@ -984,6 +3967,31 @@ aa:=integrate(x/(a*x^2+b*x+c)^(3/2),x)
 --R        (b x + 2c)\|c \|a x  + b x + c  - 2a c x  - 2b c x - 2c
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 85
+bb:=(2*(b*x+2*c))/((b^2-4*a*c)*sqrt(a*x^2+b*x+c))
+--R
+--R                 - 2b x - 4c
+--R   (2)  ----------------------------
+--R                    +--------------+
+--R                 2  |   2
+--R        (4a c - b )\|a x  + b x + c
+--R                                                     Type: Expression Integer
+--E
+
+--S 86     14:291 Axiom cannot simplify these expressions
+cc:=aa-bb
+--R
+--R   (3)
+--R                            +--------------+
+--R                        +-+ |   2                         2
+--R                   - 8c\|c \|a x  + b x + c  + 4b c x + 8c
+--R   -----------------------------------------------------------------------
+--R                  +--------------+
+--R        2     2   |   2                            3         2     2   +-+
+--R   (8a c  - 2b c)\|a x  + b x + c  + ((- 4a b c + b )x - 8a c  + 2b c)\|c
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.292~~~~~$\displaystyle
@@ -995,7 +4003,7 @@ $$
 <<*>>=
 )clear all
 
---S 13 of 19
+--S 87
 aa:=integrate(x^2/(a*x^2+b*x+c)^(3/2),x)
 --R 
 --R
@@ -1052,6 +4060,356 @@ aa:=integrate(x^2/(a*x^2+b*x+c)^(3/2),x)
 --R     ]
 --R                                     Type: Union(List Expression Integer,...)
 --E 
+
+--S 88
+t1:=integrate(1/sqrt(a*x^2+b*x+c),x)
+--R
+--R   (2)
+--R   [
+--R       log
+--R                                 +--------------+
+--R                 +-+ +-+         |   2                   +-+
+--R              (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
+--R            + 
+--R                     2             +-+
+--R              (- 2a x  - b x - 2c)\|a
+--R         /
+--R                  +--------------+
+--R              +-+ |   2
+--R            2\|c \|a x  + b x + c  - b x - 2c
+--R    /
+--R        +-+
+--R       \|a
+--R     ,
+--R                 +--------------+
+--R           +---+ |   2               +---+ +-+
+--R          \|- a \|a x  + b x + c  - \|- a \|c
+--R    2atan(------------------------------------)
+--R                           a x
+--R    -------------------------------------------]
+--R                        +---+
+--R                       \|- a
+--R                                     Type: Union(List Expression Integer,...)
+--E
+
+--S 89
+bb1:=((2*b^2-4*a*c)*x+2*b*c)/(4*(4*a*c-b^2)*sqrt(a*x^2+b*x+c))+1/a*t1.1
+--R
+--R   (3)
+--R                      +--------------+
+--R                   2  |   2
+--R         (8a c - 2b )\|a x  + b x + c
+--R      *
+--R         log
+--R                                   +--------------+
+--R                   +-+ +-+         |   2                   +-+
+--R                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
+--R              + 
+--R                       2             +-+
+--R                (- 2a x  - b x - 2c)\|a
+--R           /
+--R                    +--------------+
+--R                +-+ |   2
+--R              2\|c \|a x  + b x + c  - b x - 2c
+--R     + 
+--R             2       2            +-+
+--R       ((- 2a c + a b )x + a b c)\|a
+--R  /
+--R                        +--------------+
+--R        2        2  +-+ |   2
+--R     (8a c - 2a b )\|a \|a x  + b x + c
+--R                                                     Type: Expression Integer
+--E
+
+--S 90
+bb2:=((2*b^2-4*a*c)*x+2*b*c)/(4*(4*a*c-b^2)*sqrt(a*x^2+b*x+c))+1/a*t1.2
+--R
+--R   (4)
+--R                                                 +--------------+
+--R                     +--------------+      +---+ |   2               +---+ +-+
+--R                  2  |   2                \|- a \|a x  + b x + c  - \|- a \|c
+--R       (16a c - 4b )\|a x  + b x + c atan(------------------------------------)
+--R                                                           a x
+--R     + 
+--R             2       2            +---+
+--R       ((- 2a c + a b )x + a b c)\|- a
+--R  /
+--R                          +--------------+
+--R        2        2  +---+ |   2
+--R     (8a c - 2a b )\|- a \|a x  + b x + c
+--R                                                     Type: Expression Integer
+--E
+
+--S 91
+cc1:=aa.1-bb1
+--R
+--R   (5)
+--R                 2                     3  2         2        2            2
+--R           ((- 2a  + 16a)b c + (a - 4)b )x  + ((- 4a  + 16a)c  + (3a - 4)b c)x
+--R         + 
+--R                 2
+--R           2a b c
+--R      *
+--R              +--------------+
+--R          +-+ |   2
+--R         \|c \|a x  + b x + c
+--R     + 
+--R           3      2  2        2       2   3
+--R       ((4a  - 16a )c  + (- 2a  + 4a)b c)x
+--R     + 
+--R           2          2              3   2       2        3              2 2
+--R       ((2a  - 16a)b c  + (- 2a + 4)b c)x  + ((4a  - 16a)c  + (- 4a + 4)b c )x
+--R     + 
+--R               3
+--R       - 2a b c
+--R  /
+--R              3 2     2 2   2       2   2       3         2 3       2 2
+--R         ((16a c  - 4a b c)x  + (16a b c  - 4a b c)x + 16a c  - 4a b c )
+--R      *
+--R          +--------------+
+--R          |   2
+--R         \|a x  + b x + c
+--R     + 
+--R                3        2 3  3         3 2     2 2        4  2
+--R           (- 8a b c + 2a b )x  + (- 16a c  - 4a b c + 2a b )x
+--R         + 
+--R                 2   2       3         2 3       2 2
+--R           (- 24a b c  + 6a b c)x - 16a c  + 4a b c
+--R      *
+--R          +-+
+--R         \|c
+--R                                                     Type: Expression Integer
+--E
+
+--S 92
+cc2:=aa.2-bb1
+--R
+--R   (6)
+--R                    2 2       2   2             2     3           3     2 2
+--R             ((- 16a c  + 4a b c)x  + (- 16a b c  + 4b c)x - 16a c  + 4b c )
+--R          *
+--R                    +--------------+
+--R              +---+ |   2
+--R             \|- a \|a x  + b x + c
+--R         + 
+--R                  2          3  3       2 2       2      4  2
+--R               (8a b c - 2a b )x  + (16a c  + 4a b c - 2b )x
+--R             + 
+--R                       2     3           3     2 2
+--R               (24a b c  - 6b c)x + 16a c  - 4b c
+--R          *
+--R              +---+ +-+
+--R             \|- a \|c
+--R      *
+--R         log
+--R                                   +--------------+
+--R                   +-+ +-+         |   2                   +-+
+--R                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
+--R              + 
+--R                       2             +-+
+--R                (- 2a x  - b x - 2c)\|a
+--R           /
+--R                    +--------------+
+--R                +-+ |   2
+--R              2\|c \|a x  + b x + c  - b x - 2c
+--R     + 
+--R                  2 2       2   2           2     3           3     2 2  +-+
+--R             ((32a c  - 8a b c)x  + (32a b c  - 8b c)x + 32a c  - 8b c )\|a
+--R          *
+--R              +--------------+
+--R              |   2
+--R             \|a x  + b x + c
+--R         + 
+--R                     2          3  3         2 2       2      4  2
+--R               (- 16a b c + 4a b )x  + (- 32a c  - 8a b c + 4b )x
+--R             + 
+--R                         2      3           3     2 2
+--R               (- 48a b c  + 12b c)x - 32a c  + 8b c
+--R          *
+--R              +-+ +-+
+--R             \|a \|c
+--R      *
+--R                     +--------------+
+--R               +---+ |   2               +---+ +-+
+--R              \|- a \|a x  + b x + c  - \|- a \|c
+--R         atan(------------------------------------)
+--R                               a x
+--R     + 
+--R                 2                     3  2         2        2            2
+--R           ((- 2a  + 16a)b c + (a - 4)b )x  + ((- 4a  + 16a)c  + (3a - 4)b c)x
+--R         + 
+--R                 2
+--R           2a b c
+--R      *
+--R                        +--------------+
+--R          +---+ +-+ +-+ |   2
+--R         \|- a \|a \|c \|a x  + b x + c
+--R     + 
+--R               3      2  2        2       2   3
+--R           ((4a  - 16a )c  + (- 2a  + 4a)b c)x
+--R         + 
+--R               2          2              3   2
+--R           ((2a  - 16a)b c  + (- 2a + 4)b c)x
+--R         + 
+--R               2        3              2 2           3
+--R           ((4a  - 16a)c  + (- 4a + 4)b c )x - 2a b c
+--R      *
+--R          +---+ +-+
+--R         \|- a \|a
+--R  /
+--R              3 2     2 2   2       2   2       3         2 3       2 2  +---+
+--R         ((16a c  - 4a b c)x  + (16a b c  - 4a b c)x + 16a c  - 4a b c )\|- a
+--R      *
+--R              +--------------+
+--R          +-+ |   2
+--R         \|a \|a x  + b x + c
+--R     + 
+--R                3        2 3  3         3 2     2 2        4  2
+--R           (- 8a b c + 2a b )x  + (- 16a c  - 4a b c + 2a b )x
+--R         + 
+--R                 2   2       3         2 3       2 2
+--R           (- 24a b c  + 6a b c)x - 16a c  + 4a b c
+--R      *
+--R          +---+ +-+ +-+
+--R         \|- a \|a \|c
+--R                                                     Type: Expression Integer
+--E
+
+--S 93
+cc3:=aa.1-bb2
+--R
+--R   (7)
+--R                  2 2       2   2           2     3           3     2 2  +---+
+--R             ((16a c  - 4a b c)x  + (16a b c  - 4b c)x + 16a c  - 4b c )\|- a
+--R          *
+--R              +--------------+
+--R              |   2
+--R             \|a x  + b x + c
+--R         + 
+--R                    2          3  3         2 2       2      4  2
+--R               (- 8a b c + 2a b )x  + (- 16a c  - 4a b c + 2b )x
+--R             + 
+--R                         2     3           3     2 2
+--R               (- 24a b c  + 6b c)x - 16a c  + 4b c
+--R          *
+--R              +---+ +-+
+--R             \|- a \|c
+--R      *
+--R         log
+--R                                   +--------------+
+--R                   +-+ +-+         |   2                   +-+
+--R                (2\|a \|c  - 2a x)\|a x  + b x + c  + 2a x\|c
+--R              + 
+--R                       2             +-+
+--R                (- 2a x  - b x - 2c)\|a
+--R           /
+--R                    +--------------+
+--R                +-+ |   2
+--R              2\|c \|a x  + b x + c  - b x - 2c
+--R     + 
+--R                    2 2       2   2             2     3           3     2 2  +-+
+--R             ((- 32a c  + 8a b c)x  + (- 32a b c  + 8b c)x - 32a c  + 8b c )\|a
+--R          *
+--R              +--------------+
+--R              |   2
+--R             \|a x  + b x + c
+--R         + 
+--R                   2          3  3       2 2       2      4  2
+--R               (16a b c - 4a b )x  + (32a c  + 8a b c - 4b )x
+--R             + 
+--R                       2      3           3     2 2
+--R               (48a b c  - 12b c)x + 32a c  - 8b c
+--R          *
+--R              +-+ +-+
+--R             \|a \|c
+--R      *
+--R                     +--------------+
+--R               +---+ |   2               +---+ +-+
+--R              \|- a \|a x  + b x + c  - \|- a \|c
+--R         atan(------------------------------------)
+--R                               a x
+--R     + 
+--R                 2                     3  2         2        2            2
+--R           ((- 2a  + 16a)b c + (a - 4)b )x  + ((- 4a  + 16a)c  + (3a - 4)b c)x
+--R         + 
+--R                 2
+--R           2a b c
+--R      *
+--R                        +--------------+
+--R          +---+ +-+ +-+ |   2
+--R         \|- a \|a \|c \|a x  + b x + c
+--R     + 
+--R               3      2  2        2       2   3
+--R           ((4a  - 16a )c  + (- 2a  + 4a)b c)x
+--R         + 
+--R               2          2              3   2
+--R           ((2a  - 16a)b c  + (- 2a + 4)b c)x
+--R         + 
+--R               2        3              2 2           3
+--R           ((4a  - 16a)c  + (- 4a + 4)b c )x - 2a b c
+--R      *
+--R          +---+ +-+
+--R         \|- a \|a
+--R  /
+--R              3 2     2 2   2       2   2       3         2 3       2 2  +---+
+--R         ((16a c  - 4a b c)x  + (16a b c  - 4a b c)x + 16a c  - 4a b c )\|- a
+--R      *
+--R              +--------------+
+--R          +-+ |   2
+--R         \|a \|a x  + b x + c
+--R     + 
+--R                3        2 3  3         3 2     2 2        4  2
+--R           (- 8a b c + 2a b )x  + (- 16a c  - 4a b c + 2a b )x
+--R         + 
+--R                 2   2       3         2 3       2 2
+--R           (- 24a b c  + 6a b c)x - 16a c  + 4a b c
+--R      *
+--R          +---+ +-+ +-+
+--R         \|- a \|a \|c
+--R                                                     Type: Expression Integer
+--E
+
+--S 94     14:292 Axiom cannot simplify these expressions
+cc4:=aa.2-bb2
+--R
+--R   (8)
+--R                 2                     3  2         2        2            2
+--R           ((- 2a  + 16a)b c + (a - 4)b )x  + ((- 4a  + 16a)c  + (3a - 4)b c)x
+--R         + 
+--R                 2
+--R           2a b c
+--R      *
+--R              +--------------+
+--R          +-+ |   2
+--R         \|c \|a x  + b x + c
+--R     + 
+--R           3      2  2        2       2   3
+--R       ((4a  - 16a )c  + (- 2a  + 4a)b c)x
+--R     + 
+--R           2          2              3   2       2        3              2 2
+--R       ((2a  - 16a)b c  + (- 2a + 4)b c)x  + ((4a  - 16a)c  + (- 4a + 4)b c )x
+--R     + 
+--R               3
+--R       - 2a b c
+--R  /
+--R              3 2     2 2   2       2   2       3         2 3       2 2
+--R         ((16a c  - 4a b c)x  + (16a b c  - 4a b c)x + 16a c  - 4a b c )
+--R      *
+--R          +--------------+
+--R          |   2
+--R         \|a x  + b x + c
+--R     + 
+--R                3        2 3  3         3 2     2 2        4  2
+--R           (- 8a b c + 2a b )x  + (- 16a c  - 4a b c + 2a b )x
+--R         + 
+--R                 2   2       3         2 3       2 2
+--R           (- 24a b c  + 6a b c)x - 16a c  + 4a b c
+--R      *
+--R          +-+
+--R         \|c
+--R                                                     Type: Expression Integer
+--E
+
 @
 
 \section{\cite{1}:14.293~~~~~$\displaystyle
@@ -1064,7 +4422,7 @@ $$
 <<*>>=
 )clear all
 
---S 14 of 19
+--S 95
 aa:=integrate(1/(x*(a*x^2+b*x+c)^(3/2)),x)
 --R 
 --R
@@ -1089,6 +4447,110 @@ aa:=integrate(1/(x*(a*x^2+b*x+c)^(3/2)),x)
 --R     (b c x + 2c )\|c \|a x  + b x + c  - 2a c x  - 2b c x - 2c
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 96
+t1:=integrate(1/(x*sqrt(a*x^2+b*x+c)),x)
+--R
+--R                  +--------------+
+--R              +-+ |   2
+--R            2\|c \|a x  + b x + c  - b x - 2c
+--R        log(---------------------------------)
+--R                            x
+--R   (2)  --------------------------------------
+--R                          +-+
+--R                         \|c
+--R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 97
+t2:=integrate(1/(a*x^2+b*x+c)^(3/2),x)
+--R
+--R                          +--------------+
+--R                          |   2                 +-+
+--R                     - 2x\|a x  + b x + c  + 2x\|c
+--R   (3)  --------------------------------------------------------
+--R                       +--------------+
+--R                   +-+ |   2                    2              2
+--R        (b x + 2c)\|c \|a x  + b x + c  - 2a c x  - 2b c x - 2c
+--R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 98
+bb:=1/(c*sqrt(a*x^2+b*x+c))+1/c*t1-b/(2*c)*t2
+--R
+--R   (4)
+--R                                    +--------------+
+--R                  2              2  |   2
+--R           (2a c x  + 2b c x + 2c )\|a x  + b x + c
+--R         + 
+--R                   3              2  2              2  +-+
+--R           (- a b x  + (- 2a c - b )x  - 3b c x - 2c )\|c
+--R      *
+--R                   +--------------+
+--R               +-+ |   2
+--R             2\|c \|a x  + b x + c  - b x - 2c
+--R         log(---------------------------------)
+--R                             x
+--R     + 
+--R             +--------------+
+--R           2 |   2                      3            2  2             2  +-+
+--R       - 2c \|a x  + b x + c  + (- a b x  + (2a c - b )x  + b c x + 2c )\|c
+--R  /
+--R                                    +--------------+
+--R            2 2       2      3  +-+ |   2                   2 3
+--R       (2a c x  + 2b c x + 2c )\|c \|a x  + b x + c  - a b c x
+--R     + 
+--R              3    2 2  2       3      4
+--R       (- 2a c  - b c )x  - 3b c x - 2c
+--R                                                     Type: Expression Integer
+--E
+
+--S 99     14:293 Axiom cannot simplify these expressions
+cc:=aa-bb
+--R
+--R   (5)
+--R                                            +--------------+
+--R                       2  2              2  |   2
+--R           ((- 4a c - b )x  - 8b c x - 8c )\|a x  + b x + c
+--R         + 
+--R                  3             2  2               2  +-+
+--R           (4a b x  + (8a c + 4b )x  + 12b c x + 8c )\|c
+--R      *
+--R                   +--------------+
+--R               +-+ |   2
+--R             2\|c \|a x  + b x + c  - b x - 2c
+--R         log(---------------------------------)
+--R                             x
+--R     + 
+--R                                          +--------------+
+--R                     2  2              2  |   2
+--R           ((4a c + b )x  + 8b c x + 8c )\|a x  + b x + c
+--R         + 
+--R                    3               2  2               2  +-+
+--R           (- 4a b x  + (- 8a c - 4b )x  - 12b c x - 8c )\|c
+--R      *
+--R                   +--------------+
+--R               +-+ |   2
+--R             2\|c \|a x  + b x + c  - b x - 2c
+--R         log(---------------------------------)
+--R                              +-+
+--R                           2x\|c
+--R     + 
+--R                                      +--------------+
+--R                 2  2              2  |   2
+--R       ((4a c + b )x  + 8b c x + 8c )\|a x  + b x + c
+--R     + 
+--R                3               2  2               2  +-+
+--R       (- 4a b x  + (- 8a c - 4b )x  - 12b c x - 8c )\|c
+--R  /
+--R                                            +--------------+
+--R             2    2   2       2      3  +-+ |   2                    2 3
+--R       ((4a c  + b c)x  + 8b c x + 8c )\|c \|a x  + b x + c  - 4a b c x
+--R     + 
+--R              3     2 2  2        3      4
+--R       (- 8a c  - 4b c )x  - 12b c x - 8c
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.294~~~~~$\displaystyle
@@ -1105,7 +4567,7 @@ $$
 <<*>>=
 )clear all
 
---S 15 of 19
+--S 100
 aa:=integrate(1/(x^2*(a*x^2+b*x+c)^(3/2)),x)
 --R 
 --R
@@ -1145,6 +4607,149 @@ aa:=integrate(1/(x^2*(a*x^2+b*x+c)^(3/2)),x)
 --R       (- 16a b c x  + (- 32a c  - 16b c )x  - 48b c x  - 32c x)\|c
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 101
+t1:=integrate(1/(a*x^2+b*x+c)^(3/2),x)
+--R
+--R                          +--------------+
+--R                          |   2                 +-+
+--R                     - 2x\|a x  + b x + c  + 2x\|c
+--R   (2)  --------------------------------------------------------
+--R                       +--------------+
+--R                   +-+ |   2                    2              2
+--R        (b x + 2c)\|c \|a x  + b x + c  - 2a c x  - 2b c x - 2c
+--R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 102
+t2:=integrate(1/(x*sqrt(a*x^2+b*x+c)),x)
+--R
+--R                  +--------------+
+--R              +-+ |   2
+--R            2\|c \|a x  + b x + c  - b x - 2c
+--R        log(---------------------------------)
+--R                            x
+--R   (3)  --------------------------------------
+--R                          +-+
+--R                         \|c
+--R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 103
+bb:=-(a*x^2+b*x+c)/(c^2*x*sqrt(a*x^2+b*x+c))+(b^2-2*a*c)/(2*c^2)*t1-(3*b)/(2*c^2)*t2
+--R
+--R   (4)
+--R                                            +--------------+
+--R                      3     2   2       2   |   2
+--R           (- 6a b c x  - 6b c x  - 6b c x)\|a x  + b x + c
+--R         + 
+--R                2 4               3  3     2   2       2   +-+
+--R           (3a b x  + (6a b c + 3b )x  + 9b c x  + 6b c x)\|c
+--R      *
+--R                   +--------------+
+--R               +-+ |   2
+--R             2\|c \|a x  + b x + c  - b x - 2c
+--R         log(---------------------------------)
+--R                             x
+--R     + 
+--R                                            +--------------+
+--R                3       2 2       2      3  |   2
+--R       (2a b c x  + 8a c x  + 6b c x + 4c )\|a x  + b x + c
+--R     + 
+--R                2        2  4                  3  3           2     2   2
+--R           (- 8a c + 2a b )x  + (- 12a b c + 2b )x  + (- 12a c  - 2b c)x
+--R         + 
+--R                 2      3
+--R           - 8b c x - 4c
+--R      *
+--R          +-+
+--R         \|c
+--R  /
+--R                                      +--------------+
+--R            3 3       3 2     4   +-+ |   2                    3 4
+--R       (4a c x  + 4b c x  + 4c x)\|c \|a x  + b x + c  - 2a b c x
+--R     + 
+--R              4     2 3  3       4 2     5
+--R       (- 4a c  - 2b c )x  - 6b c x  - 4c x
+--R                                                     Type: Expression Integer
+--E
+
+--S 104    14:284 Axiom cannot simplify these expressions
+cc:=aa-bb
+--R
+--R   (5)
+--R                    2      4  3            2       3   2       2 2          3
+--R             ((72a b c + 6b )x  + (144a b c  + 108b c)x  + 288b c x + 192b c )
+--R          *
+--R                  +--------------+
+--R              +-+ |   2
+--R             \|c \|a x  + b x + c
+--R         + 
+--R                 2   2        3   4            2 2      4   3
+--R           (- 48a b c  - 36a b c)x  + (- 240a b c  - 36b c)x
+--R         + 
+--R                      3       3 2  2       2 3          4
+--R           (- 240a b c  - 228b c )x  - 384b c x - 192b c
+--R      *
+--R                   +--------------+
+--R               +-+ |   2
+--R             2\|c \|a x  + b x + c  - b x - 2c
+--R         log(---------------------------------)
+--R                             x
+--R     + 
+--R                         2      4  3              2       3   2       2 2
+--R                 (- 72a b c - 6b )x  + (- 144a b c  - 108b c)x  - 288b c x
+--R               + 
+--R                         3
+--R                 - 192b c
+--R          *
+--R                  +--------------+
+--R              +-+ |   2
+--R             \|c \|a x  + b x + c
+--R         + 
+--R               2   2        3   4          2 2      4   3
+--R           (48a b c  + 36a b c)x  + (240a b c  + 36b c)x
+--R         + 
+--R                    3       3 2  2       2 3          4
+--R           (240a b c  + 228b c )x  + 384b c x + 192b c
+--R      *
+--R                   +--------------+
+--R               +-+ |   2
+--R             2\|c \|a x  + b x + c  - b x - 2c
+--R         log(---------------------------------)
+--R                              +-+
+--R                           2x\|c
+--R     + 
+--R                  2      4  3             2      3   2       2 2         3  +-+
+--R         ((- 60a b c - 5b )x  + (- 88a b c  - 66b c)x  - 112b c x - 32b c )\|c
+--R      *
+--R          +--------------+
+--R          |   2
+--R         \|a x  + b x + c
+--R     + 
+--R           2   2        3   4          2 2      4   3            3       3 2  2
+--R       (40a b c  + 30a b c)x  + (152a b c  + 26b c)x  + (104a b c  + 118b c )x
+--R     + 
+--R           2 3         4
+--R       128b c x + 32b c
+--R  /
+--R                  4     3 3  3         5      2 4  2         5        6
+--R         ((48a b c  + 4b c )x  + (96a c  + 72b c )x  + 192b c x + 128c )
+--R      *
+--R          +--------------+
+--R          |   2
+--R         \|a x  + b x + c
+--R     + 
+--R                 2 4        2 3  4              4      3 3  3
+--R           (- 32a c  - 24a b c )x  + (- 160a b c  - 24b c )x
+--R         + 
+--R                    5       2 4  2         5        6
+--R           (- 160a c  - 152b c )x  - 256b c x - 128c
+--R      *
+--R          +-+
+--R         \|c
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.295~~~~~$\displaystyle
@@ -1160,7 +4765,7 @@ $$
 <<*>>=
 )clear all
 
---S 16 of 19
+--S 105    14:295 Axiom cannot compute this integral
 aa:=integrate((a*x^2+b*x+c)^(n+1/2),x)
 --R 
 --R
@@ -1182,7 +4787,7 @@ $$
 <<*>>=
 )clear all
 
---S 17 of 19
+--S 106    14:296 Axiom cannot compute this integral
 aa:=integrate(x*(a*x^2+b*x+c)^(n+1/2),x)
 --R 
 --R
@@ -1208,7 +4813,7 @@ $$
 <<*>>=
 )clear all
 
---S 18 of 19
+--S 107    14:297 Axiom cannot compute this integral
 aa:=integrate(1/(a*x^2+b*x+c)^(n+1/2),x)
 --R 
 --R
@@ -1239,7 +4844,7 @@ $$
 <<*>>=
 )clear all
 
---S 19 of 19
+--S 108    14:298 Axiom cannot compute this integral
 aa:=integrate(1/(x*(a*x^2+b*x+c)^(n+1/2)),x)
 --R 
 --R



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Subject: [Axiom-developer] East Coast Computer Algebra Day
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On Saturday, May 10, the next East Coast Computer Algebra Day is being
held.
The contributors to Sage might find it an interesting meeting.
<http://www.shepherd.edu/eccad2008/>

I know that Sage sent a student last year.

Tim



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Subject: [Axiom-developer] 20080421.01.tpd.patch (CATS Schaum2-Axiom
	equivalence testing (14-16))
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schaum14.input.pamphlet
  14:299 Schaums and Axiom agree
  14:300 Schaums and Axiom agree
  14:301 Schaums and Axiom agree
  14:302 Schaums and Axiom agree
  14:303 Schaums and Axiom agree
  14:304 Schaums and Axiom agree
  14:305 Schaums and Axiom agree
  14:306 Schaums and Axiom agree
  14:307 Schaums and Axiom agree
  14:308 Schaums and Axiom agree
  14:309 Axiom cannot compute this integral
  14:310 Axiom cannot compute this integral

schaum15.input.pamphlet
  14:311 Schaums and Axiom differ by a constant
  14:312 Schaums and Axiom agree
  14:313 Schaums and Axiom differ by a constant
  14:314 Schaums and Axiom agree
  14:315 Schaums and Axiom agree
  14:316 Schaums and Axiom differ by a constant
  14:317 Schaums and Axiom agree
  14:318 Schaums and Axiom agree
  14:319 Schaums and Axiom agree
  14:320 Schaums and Axiom agree
  14:321 Schaums and Axiom agree
  14:322 Schaums and Axiom agree
  14:323 Schaums and Axiom agree
  14:324 Schaums and Axiom agree

schaum16.input.pamphlet
  14:325 Axiom cannot simplify this expression
  14:326 Schaums and Axiom agree
  14:327 Axiom cannot compute this integral
  14:328 Axiom cannot compute this integral
  14:329 Schaums and Axiom differ by a constant
  14:330 Schaums and Axiom agree
  14:331 Schaums and Axiom agree
  14:332 Axiom cannot compute this integral
  14:333 Axiom cannot compute this integral
  14:334 Axiom cannot simplify this expression
  14:335 Axiom cannot compute this integral
  14:336 Axiom cannot compute this integral
  14:337 Axiom cannot compute this integral
  14:338 Axiom cannot compute this integral

======================================================================
diff --git a/changelog b/changelog
index 29750e1..4b454b8 100644
--- a/changelog
+++ b/changelog
@@ -1,3 +1,6 @@
+20080421 tpd src/input/schaum16.input show Schaums-Axiom equivalence
+20080421 tpd src/input/schaum15.input show Schaums-Axiom equivalence
+20080421 tpd src/input/schaum14.input show Schaums-Axiom equivalence
 20080420 tpd src/input/schaum13.input show Schaums-Axiom equivalence
 20080419 tpd src/input/schaum12.input show Schaums-Axiom equivalence
 20080418 tpd src/input/schaum11.input show Schaums-Axiom equivalence
diff --git a/src/input/schaum14.input.pamphlet b/src/input/schaum14.input.pamphlet
index 532a38a..3452b30 100644
--- a/src/input/schaum14.input.pamphlet
+++ b/src/input/schaum14.input.pamphlet
@@ -19,7 +19,7 @@ $$
 )set message auto off
 )clear all
 
---S 1 of 12
+--S 1
 aa:=integrate(1/(x^3+a^3),x)
 --R 
 --R
@@ -32,6 +32,41 @@ aa:=integrate(1/(x^3+a^3),x)
 --R                                     6a \|3
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 2
+bb:=1/(6*a^2)*log((x+a)^2/(x^2-a*x+a^2))+1/(a^2*sqrt(3))*atan((2*x-a)/(a*sqrt(3)))
+--R
+--R             2           2                       +-+
+--R            x  + 2a x + a       +-+     (2x - a)\|3
+--R        log(--------------) + 2\|3 atan(------------)
+--R              2          2                   3a
+--R             x  - a x + a
+--R   (2)  ---------------------------------------------
+--R                               2
+--R                             6a
+--R                                                     Type: Expression Integer
+--E
+
+--S 3
+cc:=aa-bb
+--R
+--R                                                  2           2
+--R               2          2                      x  + 2a x + a
+--R        - log(x  - a x + a ) + 2log(x + a) - log(--------------)
+--R                                                   2          2
+--R                                                  x  - a x + a
+--R   (3)  --------------------------------------------------------
+--R                                     2
+--R                                   6a
+--R                                                     Type: Expression Integer
+--E
+
+--S 4      14:299 Schaums and Axiom agree
+dd:=expandLog cc
+--R
+--R   (4)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.300~~~~~$\displaystyle
@@ -43,7 +78,7 @@ $$
 <<*>>=
 )clear all
 
---S 2 of 12
+--S 5
 aa:=integrate(x/(x^3+a^3),x)
 --R 
 --R
@@ -56,6 +91,39 @@ aa:=integrate(x/(x^3+a^3),x)
 --R                                    6a\|3
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 6
+bb:=1/(6*a)*log((x^2-a*x+a^2)/(x+a)^2)+1/(a*sqrt(3))*atan((2*x-a)/(a*sqrt(3)))
+--R
+--R              2          2                       +-+
+--R             x  - a x + a       +-+     (2x - a)\|3
+--R        log(--------------) + 2\|3 atan(------------)
+--R             2           2                   3a
+--R            x  + 2a x + a
+--R   (2)  ---------------------------------------------
+--R                              6a
+--R                                                     Type: Expression Integer
+--E
+
+--S 7
+cc:=aa-bb
+--R
+--R                                                 2          2
+--R             2          2                       x  - a x + a
+--R        log(x  - a x + a ) - 2log(x + a) - log(--------------)
+--R                                                2           2
+--R                                               x  + 2a x + a
+--R   (3)  ------------------------------------------------------
+--R                                  6a
+--R                                                     Type: Expression Integer
+--E
+
+--S 8      14:300 Schaums and Axiom agree
+dd:=expandLog cc
+--R
+--R   (4)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.301~~~~~$\displaystyle
@@ -66,7 +134,7 @@ $$
 <<*>>=
 )clear all
 
---S 3 of 12
+--S 9
 aa:=integrate(x^2/(x^3+a^3),x)
 --R 
 --R
@@ -76,6 +144,23 @@ aa:=integrate(x^2/(x^3+a^3),x)
 --R              3
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 10
+bb:=1/3*log(x^3+a^3)
+--R
+--R             3    3
+--R        log(x  + a )
+--R   (2)  ------------
+--R              3
+--R                                                     Type: Expression Integer
+--E
+
+--S 11     14:301 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.302~~~~~$\displaystyle
@@ -86,7 +171,7 @@ $$
 <<*>>=
 )clear all
 
---S 4 of 12
+--S 12
 aa:=integrate(1/(x*(x^3+a^3)),x)
 --R 
 --R
@@ -97,6 +182,41 @@ aa:=integrate(1/(x*(x^3+a^3)),x)
 --R                   3a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 13
+bb:=1/(3*a^3)*log(x^3/(x^3+a^3))
+--R
+--R                3
+--R               x
+--R        log(-------)
+--R             3    3
+--R            x  + a
+--R   (2)  ------------
+--R               3
+--R             3a
+--R                                                     Type: Expression Integer
+--E
+
+--S 14
+cc:=aa-bb
+--R
+--R                                           3
+--R               3    3                     x
+--R        - log(x  + a ) + 3log(x) - log(-------)
+--R                                        3    3
+--R                                       x  + a
+--R   (3)  ---------------------------------------
+--R                            3
+--R                          3a
+--R                                                     Type: Expression Integer
+--E
+
+--S 15     14:302 Schaums and Axiom agree
+dd:=expandLog cc
+--R
+--R   (4)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.303~~~~~$\displaystyle
@@ -108,7 +228,7 @@ $$
 <<*>>=
 )clear all
 
---S 5 of 12
+--S 15
 aa:=integrate(1/(x^2*(x^3+a^3)),x)
 --R 
 --R
@@ -121,7 +241,42 @@ aa:=integrate(1/(x^2*(x^3+a^3)),x)
 --R                                        4  +-+
 --R                                      6a x\|3
 --R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 16
+bb:=-1/(a^3*x)-1/(6*a^4)*log((x^2-a*x+a^2)/(x+a)^2)-1/(a^4*sqrt(3))*atan((2*x-a)/(a*sqrt(3)))
+--R
+--R                  2          2                        +-+
+--R                 x  - a x + a        +-+     (2x - a)\|3
+--R        - x log(--------------) - 2x\|3 atan(------------) - 6a
+--R                 2           2                    3a
+--R                x  + 2a x + a
+--R   (2)  -------------------------------------------------------
+--R                                    4
+--R                                  6a x
+--R                                                     Type: Expression Integer
 --E 
+
+--S 17
+cc:=aa-bb
+--R
+--R                                                   2          2
+--R               2          2                       x  - a x + a
+--R        - log(x  - a x + a ) + 2log(x + a) + log(--------------)
+--R                                                  2           2
+--R                                                 x  + 2a x + a
+--R   (3)  --------------------------------------------------------
+--R                                     4
+--R                                   6a
+--R                                                     Type: Expression Integer
+--E
+
+--S 18     14:303 Schaums and Axiom agree
+dd:=expandLog cc
+--R
+--R   (4)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.304~~~~~$\displaystyle
@@ -134,7 +289,7 @@ $$
 <<*>>=
 )clear all
 
---S 6 of 12
+--S 19
 aa:=integrate(1/(x^3+a^3)^2,x)
 --R 
 --R
@@ -151,6 +306,42 @@ aa:=integrate(1/(x^3+a^3)^2,x)
 --R     (9a x  + 9a )\|3
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 20
+bb:=x/(3*a^3*(x^3+a^3))+1/(9*a^5)*log((x+a)^2/(x^2-a*x+a^2))+2/(3*a^5*sqrt(3))*atan((2*x-a)/(a*sqrt(3)))
+--R
+--R   (2)
+--R                 2           2                                 +-+
+--R     3    3     x  + 2a x + a        3     3  +-+     (2x - a)\|3       2
+--R   (x  + a )log(--------------) + (2x  + 2a )\|3 atan(------------) + 3a x
+--R                  2          2                             3a
+--R                 x  - a x + a
+--R   -----------------------------------------------------------------------
+--R                                   5 3     8
+--R                                 9a x  + 9a
+--R                                                     Type: Expression Integer
+--E
+
+--S 21
+cc:=aa-bb
+--R
+--R                                                  2           2
+--R               2          2                      x  + 2a x + a
+--R        - log(x  - a x + a ) + 2log(x + a) - log(--------------)
+--R                                                   2          2
+--R                                                  x  - a x + a
+--R   (3)  --------------------------------------------------------
+--R                                     5
+--R                                   9a
+--R                                                     Type: Expression Integer
+--E
+
+--S 22     14:304 Schaums and Axiom agree
+dd:=expandLog cc
+--R
+--R   (4)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.305~~~~~$\displaystyle
@@ -163,7 +354,7 @@ $$
 <<*>>=
 )clear all
 
---S 7 of 12
+--S 23
 aa:=integrate(x/(x^3+a^3)^2,x)
 --R 
 --R
@@ -180,6 +371,42 @@ aa:=integrate(x/(x^3+a^3)^2,x)
 --R     (18a x  + 18a )\|3
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 24
+bb:=x^2/(3*a^3*(x^3+a^3))+1/(18*a^4)*log((x^2-a*x+a^2)/(x+a)^2)+1/(3*a^4*sqrt(3))*atan((2*x-a)/(a*sqrt(3)))
+--R
+--R   (2)
+--R                  2          2                                 +-+
+--R     3    3      x  - a x + a        3     3  +-+     (2x - a)\|3         2
+--R   (x  + a )log(--------------) + (2x  + 2a )\|3 atan(------------) + 6a x
+--R                 2           2                             3a
+--R                x  + 2a x + a
+--R   ------------------------------------------------------------------------
+--R                                    4 3      7
+--R                                 18a x  + 18a
+--R                                                     Type: Expression Integer
+--E
+
+--S 25
+cc:=aa-bb
+--R
+--R                                                 2          2
+--R             2          2                       x  - a x + a
+--R        log(x  - a x + a ) - 2log(x + a) - log(--------------)
+--R                                                2           2
+--R                                               x  + 2a x + a
+--R   (3)  ------------------------------------------------------
+--R                                    4
+--R                                 18a
+--R                                                     Type: Expression Integer
+--E
+
+--S 26     14:305 Schaums and Axiom agree
+dd:=expandLog cc
+--R
+--R   (4)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.306~~~~~$\displaystyle
@@ -190,7 +417,7 @@ $$
 <<*>>=
 )clear all
 
---S 8 of 12
+--S 27
 aa:=integrate(x^2/(x^3+a^3)^2,x)
 --R 
 --R
@@ -199,7 +426,24 @@ aa:=integrate(x^2/(x^3+a^3)^2,x)
 --R            3     3
 --R          3x  + 3a
 --R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 28
+bb:=-1/(3*(x^3+a^3))
+--R
+--R              1
+--R   (2)  - ---------
+--R            3     3
+--R          3x  + 3a
+--R                                            Type: Fraction Polynomial Integer
 --E 
+
+--S 29     14:306 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.307~~~~~$\displaystyle
@@ -210,7 +454,7 @@ $$
 <<*>>=
 )clear all
 
---S 9 of 12
+--S 30
 aa:=integrate(1/(x*(x^3+a^3)^2),x)
 --R 
 --R
@@ -221,6 +465,41 @@ aa:=integrate(1/(x*(x^3+a^3)^2),x)
 --R                           3a x  + 3a
 --R                                          Type: Union(Expression Integer,...)
 --E
+
+--S 31
+bb:=1/(3*a^3*(x^3+a^3))+1/(3*a^6)*log(x^3/(x^3+a^3))
+--R
+--R                         3
+--R          3    3        x        3
+--R        (x  + a )log(-------) + a
+--R                      3    3
+--R                     x  + a
+--R   (2)  --------------------------
+--R                  6 3     9
+--R                3a x  + 3a
+--R                                                     Type: Expression Integer
+--E
+
+--S 32
+cc:=aa-bb
+--R
+--R                                           3
+--R               3    3                     x
+--R        - log(x  + a ) + 3log(x) - log(-------)
+--R                                        3    3
+--R                                       x  + a
+--R   (3)  ---------------------------------------
+--R                            6
+--R                          3a
+--R                                                     Type: Expression Integer
+--E
+
+--S 33     14:307 Schaums and Axiom agree
+dd:=expandLog cc
+--R
+--R   (4)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.308~~~~~$\displaystyle
@@ -232,7 +511,7 @@ $$
 <<*>>=
 )clear all
 
---S 10 of 12
+--S 34
 aa:=integrate(1/(x^2*(x^3+a^3)^2),x)
 --R 
 --R
@@ -248,7 +527,44 @@ aa:=integrate(1/(x^2*(x^3+a^3)^2),x)
 --R        7 4     10   +-+
 --R     (9a x  + 9a  x)\|3
 --R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 35
+t1:=integrate(x/(x^3+a^3),x)
+--R
+--R                                                                  +-+
+--R         +-+     2          2      +-+                   (2x - a)\|3
+--R        \|3 log(x  - a x + a ) - 2\|3 log(x + a) + 6atan(------------)
+--R                                                              3a
+--R   (2)  --------------------------------------------------------------
+--R                                       +-+
+--R                                    6a\|3
+--R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 36
+bb:=-1/(a^6*x)-x^2/(3*a^6*(x^3+a^3))-4/(3*a^6)*t1
+--R
+--R   (3)
+--R            4     3   +-+     2          2       4     3   +-+
+--R       (- 2x  - 2a x)\|3 log(x  - a x + a ) + (4x  + 4a x)\|3 log(x + a)
+--R     + 
+--R                                     +-+
+--R             4      3       (2x - a)\|3             3     4  +-+
+--R       (- 12x  - 12a x)atan(------------) + (- 12a x  - 9a )\|3
+--R                                 3a
+--R  /
+--R        7 4     10   +-+
+--R     (9a x  + 9a  x)\|3
+--R                                                     Type: Expression Integer
 --E 
+
+--S 37     14:308 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (4)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.309~~~~~$\displaystyle
@@ -259,7 +575,7 @@ $$
 <<*>>=
 )clear all
 
---S 11 of 12
+--S 38     14:309 Axiom cannot compute this integral
 aa:=integrate(x^m/(x^3+a^3),x)
 --R 
 --R
@@ -269,7 +585,7 @@ aa:=integrate(x^m/(x^3+a^3),x)
 --R        ++    3     3
 --I             a  + %L
 --R                                          Type: Union(Expression Integer,...)
---E 
+--E
 @
 
 \section{\cite{1}:14.310~~~~~$\displaystyle
@@ -280,7 +596,7 @@ $$
 <<*>>=
 )clear all
 
---S 12 of 12
+--S 39     14:310 Axiom cannot compute this integral
 aa:=integrate(1/(x^n*(x^3+a^3)),x)
 --R 
 --R
diff --git a/src/input/schaum15.input.pamphlet b/src/input/schaum15.input.pamphlet
index 51a6094..0c01fbb 100644
--- a/src/input/schaum15.input.pamphlet
+++ b/src/input/schaum15.input.pamphlet
@@ -20,7 +20,7 @@ $$
 )set message auto off
 )clear all
 
---S 1 of 14
+--S 1
 aa:=integrate(1/(x^4+a^4),x)
 --R 
 --R
@@ -53,6 +53,202 @@ aa:=integrate(1/(x^4+a^4),x)
 --R     \|2
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 2
+bb:=1/(4*a^3*sqrt(2))*log((x^2+a*x*sqrt(2)+a^2)/(x^2-a*x*sqrt(2)+a^2))-1/(2*a^3*sqrt(2))*atan((a*x*sqrt(2))/(x^2-a^2))
+--R
+--R                      +-+    2    2                  +-+
+--R         +-+    - a x\|2  - x  - a       +-+     a x\|2
+--R        \|2 log(-------------------) - 2\|2 atan(-------)
+--R                     +-+    2    2                2    2
+--R                 a x\|2  - x  - a                x  - a
+--R   (2)  -------------------------------------------------
+--R                                 3
+--R                               8a
+--R                                                     Type: Expression Integer
+--E
+
+--S 3
+cc:=aa-bb
+--R
+--R   (3)
+--R            +------+          +------+2            +------+
+--R         3  |   1          8  |   1        4  +-+  |   1      2
+--R       4a   |------ log(16a   |------  + 4a x\|2   |------ + x )
+--R           4|    12          4|    12             4|    12
+--R           \|256a            \|256a               \|256a
+--R     + 
+--R              +------+          +------+2            +------+
+--R           3  |   1          8  |   1        4  +-+  |   1      2
+--R       - 4a   |------ log(16a   |------  - 4a x\|2   |------ + x )
+--R             4|    12          4|    12             4|    12
+--R             \|256a            \|256a               \|256a
+--R     + 
+--R                                  +------+
+--R                               4  |   1
+--R                             4a   |------
+--R            +------+             4|    12
+--R         3  |   1                \|256a
+--R       8a   |------ atan(--------------------)
+--R           4|    12           +------+
+--R           \|256a          4  |   1       +-+
+--R                         4a   |------ - x\|2
+--R                             4|    12
+--R                             \|256a
+--R     + 
+--R                                    +------+
+--R                                 4  |   1
+--R                               4a   |------
+--R              +------+             4|    12                 +-+    2    2
+--R           3  |   1                \|256a             - a x\|2  - x  - a
+--R       - 8a   |------ atan(-------------------- - log(-------------------)
+--R             4|    12           +------+                   +-+    2    2
+--R             \|256a          4  |   1       +-+        a x\|2  - x  - a
+--R                           4a   |------ + x\|2
+--R                               4|    12
+--R                               \|256a
+--R     + 
+--R                 +-+
+--R             a x\|2
+--R       2atan(-------)
+--R              2    2
+--R             x  - a
+--R  /
+--R       3 +-+
+--R     4a \|2
+--R                                                     Type: Expression Integer
+--E
+
+--S 4
+atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
+--R
+--R                            - x + %i
+--R                     %i log(--------)
+--R                             x + %i
+--R   (4)  atan(x) == - ----------------
+--R                             2
+--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
+--E
+
+--S 5
+dd:=atanrule cc
+--R
+--R   (5)
+--R            +------+          +------+2            +------+
+--R         3  |   1          8  |   1        4  +-+  |   1      2
+--R       4a   |------ log(16a   |------  + 4a x\|2   |------ + x )
+--R           4|    12          4|    12             4|    12
+--R           \|256a            \|256a               \|256a
+--R     + 
+--R              +------+          +------+2            +------+
+--R           3  |   1          8  |   1        4  +-+  |   1      2
+--R       - 4a   |------ log(16a   |------  - 4a x\|2   |------ + x )
+--R             4|    12          4|    12             4|    12
+--R             \|256a            \|256a               \|256a
+--R     + 
+--R                                          +------+
+--R                                       4  |   1          +-+
+--R                           (- 4 + 4%i)a   |------ + %i x\|2
+--R               +------+                  4|    12
+--R            3  |   1                     \|256a
+--R       4%i a   |------ log(---------------------------------)
+--R              4|    12                   +------+
+--R              \|256a                  4  |   1          +-+
+--R                            (4 + 4%i)a   |------ + %i x\|2
+--R                                        4|    12
+--R                                        \|256a
+--R     + 
+--R                                            +------+
+--R                                         4  |   1          +-+
+--R                             (- 4 + 4%i)a   |------ - %i x\|2
+--R                 +------+                  4|    12
+--R              3  |   1                     \|256a
+--R       - 4%i a   |------ log(---------------------------------)
+--R                4|    12                   +------+
+--R                \|256a                  4  |   1          +-+
+--R                              (4 + 4%i)a   |------ - %i x\|2
+--R                                          4|    12
+--R                                          \|256a
+--R     + 
+--R                      +-+       2       2              +-+    2    2
+--R                - a x\|2  + %i x  - %i a         - a x\|2  - x  - a
+--R       - %i log(-------------------------) - log(-------------------)
+--R                     +-+       2       2              +-+    2    2
+--R                 a x\|2  + %i x  - %i a           a x\|2  - x  - a
+--R  /
+--R       3 +-+
+--R     4a \|2
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 6
+ee:=rootSimp dd
+--R
+--R   (6)
+--R                                         +-+
+--R               +-+    2    2           x\|2  + (1 + %i)a
+--R       log(a x\|2  + x  + a ) + %i log(-----------------)
+--R                                         +-+
+--R                                       x\|2  + (1 - %i)a
+--R     + 
+--R                  +-+                               +-+       2       2
+--R                x\|2  + (- 1 - %i)a           - a x\|2  + %i x  - %i a
+--R       - %i log(-------------------) - %i log(-------------------------)
+--R                  +-+                              +-+       2       2
+--R                x\|2  + (- 1 + %i)a            a x\|2  + %i x  - %i a
+--R     + 
+--R                   +-+    2    2
+--R             - a x\|2  - x  - a               +-+    2    2
+--R       - log(-------------------) - log(- a x\|2  + x  + a )
+--R                  +-+    2    2
+--R              a x\|2  - x  - a
+--R  /
+--R       3 +-+
+--R     4a \|2
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 7
+ff:=expandLog ee
+--R
+--R   (7)
+--R                  +-+       2       2               +-+       2       2
+--R       %i log(a x\|2  + %i x  - %i a ) - %i log(a x\|2  - %i x  + %i a )
+--R     + 
+--R                +-+                         +-+
+--R       %i log(x\|2  + (1 + %i)a) - %i log(x\|2  + (1 - %i)a)
+--R     + 
+--R                +-+                           +-+
+--R       %i log(x\|2  + (- 1 + %i)a) - %i log(x\|2  + (- 1 - %i)a)
+--R     + 
+--R       (- 2 - %i)log(- 1)
+--R  /
+--R       3 +-+
+--R     4a \|2
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 8
+gg:=complexNormalize ff
+--R
+--R               %i             %i
+--R        %i log(--) - %i log(- --) + (- 2 - %i)log(- 1)
+--R                2              2
+--R   (8)  ----------------------------------------------
+--R                              3 +-+
+--R                            4a \|2
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 9      14:311 Schaums and Axiom differ by a constant
+hh:=expandLog gg
+--R
+--R        %i log(%i) - %i log(- %i) + (- 2 - %i)log(- 1)
+--R   (9)  ----------------------------------------------
+--R                              3 +-+
+--R                            4a \|2
+--R                                             Type: Expression Complex Integer
+--E
 @
 
 \section{\cite{1}:14.312~~~~~$\displaystyle
@@ -63,7 +259,7 @@ $$
 <<*>>=
 )clear all
 
---S 2 of 14
+--S 10
 aa:=integrate(x/(x^4+a^4),x)
 --R 
 --R
@@ -77,6 +273,27 @@ aa:=integrate(x/(x^4+a^4),x)
 --R           2a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 11
+bb:=1/(2*a^2)*atan(x^2/a^2)
+--R
+--R              2
+--R             x
+--R        atan(--)
+--R              2
+--R             a
+--R   (2)  --------
+--R             2
+--R           2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 12     14:312 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.313~~~~~$\displaystyle
@@ -89,7 +306,7 @@ $$
 <<*>>=
 )clear all
 
---S 3 of 14
+--S 13
 aa:=integrate(x^2/(x^4+a^4),x)
 --R 
 --R
@@ -122,6 +339,213 @@ aa:=integrate(x^2/(x^4+a^4),x)
 --R     \|2
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 14
+bb:=1/(4*a*sqrt(2))*log((x^2-a*x*sqrt(2)+a^2)/(x^2+a*x*sqrt(2)+a^2))-1/(2*a*sqrt(2))*atan((a*x*sqrt(2))/(x^2-a^2))
+--R
+--R                      +-+    2    2                  +-+
+--R         +-+    - a x\|2  + x  + a       +-+     a x\|2
+--R        \|2 log(-------------------) - 2\|2 atan(-------)
+--R                     +-+    2    2                2    2
+--R                 a x\|2  + x  + a                x  - a
+--R   (2)  -------------------------------------------------
+--R                                8a
+--R                                                     Type: Expression Integer
+--E
+
+--S 15
+cc:=aa-bb
+--R
+--R   (3)
+--R             +-----+               +-----+3        +-----+2
+--R             |  1          4  +-+  |  1         4  |  1       2
+--R       - 4a  |----- log(64a x\|2   |-----  + 16a   |-----  + x )
+--R            4|    4               4|    4         4|    4
+--R            \|256a                \|256a          \|256a
+--R     + 
+--R           +-----+                 +-----+3        +-----+2
+--R           |  1            4  +-+  |  1         4  |  1       2
+--R       4a  |----- log(- 64a x\|2   |-----  + 16a   |-----  + x )
+--R          4|    4                 4|    4         4|    4
+--R          \|256a                  \|256a          \|256a
+--R     + 
+--R                                 +-----+3
+--R                              4  |  1
+--R                           64a   |-----
+--R           +-----+              4|    4
+--R           |  1                 \|256a
+--R       8a  |----- atan(---------------------)
+--R          4|    4            +-----+3
+--R          \|256a          4  |  1        +-+
+--R                       64a   |-----  - x\|2
+--R                            4|    4
+--R                            \|256a
+--R     + 
+--R                                   +-----+3
+--R                                4  |  1
+--R                             64a   |-----
+--R             +-----+              4|    4                  +-+    2    2
+--R             |  1                 \|256a             - a x\|2  + x  + a
+--R       - 8a  |----- atan(--------------------- - log(-------------------)
+--R            4|    4            +-----+3                   +-+    2    2
+--R            \|256a          4  |  1        +-+        a x\|2  + x  + a
+--R                         64a   |-----  + x\|2
+--R                              4|    4
+--R                              \|256a
+--R     + 
+--R                 +-+
+--R             a x\|2
+--R       2atan(-------)
+--R              2    2
+--R             x  - a
+--R  /
+--R        +-+
+--R     4a\|2
+--R                                                     Type: Expression Integer
+--E
+
+--S 16
+atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
+--R
+--R                            - x + %i
+--R                     %i log(--------)
+--R                             x + %i
+--R   (4)  atan(x) == - ----------------
+--R                             2
+--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
+--E
+
+--S 17
+dd:=atanrule cc
+--R
+--R   (5)
+--R             +-----+               +-----+3        +-----+2
+--R             |  1          4  +-+  |  1         4  |  1       2
+--R       - 4a  |----- log(64a x\|2   |-----  + 16a   |-----  + x )
+--R            4|    4               4|    4         4|    4
+--R            \|256a                \|256a          \|256a
+--R     + 
+--R                                          +-----+3
+--R                                       4  |  1           +-+
+--R                         (- 64 + 64%i)a   |-----  + %i x\|2
+--R              +-----+                    4|    4
+--R              |  1                       \|256a
+--R       4%i a  |----- log(-----------------------------------)
+--R             4|    4                     +-----+3
+--R             \|256a                   4  |  1           +-+
+--R                          (64 + 64%i)a   |-----  + %i x\|2
+--R                                        4|    4
+--R                                        \|256a
+--R     + 
+--R                                            +-----+3
+--R                                         4  |  1           +-+
+--R                           (- 64 + 64%i)a   |-----  - %i x\|2
+--R                +-----+                    4|    4
+--R                |  1                       \|256a
+--R       - 4%i a  |----- log(-----------------------------------)
+--R               4|    4                     +-----+3
+--R               \|256a                   4  |  1           +-+
+--R                            (64 + 64%i)a   |-----  - %i x\|2
+--R                                          4|    4
+--R                                          \|256a
+--R     + 
+--R           +-----+                 +-----+3        +-----+2
+--R           |  1            4  +-+  |  1         4  |  1       2
+--R       4a  |----- log(- 64a x\|2   |-----  + 16a   |-----  + x )
+--R          4|    4                 4|    4         4|    4
+--R          \|256a                  \|256a          \|256a
+--R     + 
+--R                   +-+    2    2                 +-+       2       2
+--R             - a x\|2  + x  + a            - a x\|2  + %i x  - %i a
+--R       - log(-------------------) - %i log(-------------------------)
+--R                  +-+    2    2                 +-+       2       2
+--R              a x\|2  + x  + a              a x\|2  + %i x  - %i a
+--R  /
+--R        +-+
+--R     4a\|2
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 18
+ee:=expandLog dd
+--R
+--R   (6)
+--R             +-----+               +-----+3        +-----+2
+--R             |  1          4  +-+  |  1         4  |  1       2
+--R       - 4a  |----- log(64a x\|2   |-----  + 16a   |-----  + x )
+--R            4|    4               4|    4         4|    4
+--R            \|256a                \|256a          \|256a
+--R     + 
+--R           +-----+               +-----+3        +-----+2
+--R           |  1          4  +-+  |  1         4  |  1       2
+--R       4a  |----- log(64a x\|2   |-----  - 16a   |-----  - x )
+--R          4|    4               4|    4         4|    4
+--R          \|256a                \|256a          \|256a
+--R     + 
+--R              +-----+                   +-----+3
+--R              |  1                   4  |  1        +-+
+--R       4%i a  |----- log((64 + 64%i)a   |-----  + x\|2 )
+--R             4|    4                   4|    4
+--R             \|256a                    \|256a
+--R     + 
+--R                +-----+                   +-----+3
+--R                |  1                   4  |  1           +-+
+--R       - 4%i a  |----- log((64 + 64%i)a   |-----  + %i x\|2 )
+--R               4|    4                   4|    4
+--R               \|256a                    \|256a
+--R     + 
+--R              +-----+                   +-----+3
+--R              |  1                   4  |  1           +-+
+--R       4%i a  |----- log((64 + 64%i)a   |-----  - %i x\|2 )
+--R             4|    4                   4|    4
+--R             \|256a                    \|256a
+--R     + 
+--R                +-----+                   +-----+3                       +-----+
+--R                |  1                   4  |  1        +-+                |  1
+--R       - 4%i a  |----- log((64 + 64%i)a   |-----  - x\|2  + 4a log(- 1)  |-----
+--R               4|    4                   4|    4                        4|    4
+--R               \|256a                    \|256a                         \|256a
+--R     + 
+--R               +-+    2    2               +-+       2       2
+--R       log(a x\|2  + x  + a ) + %i log(a x\|2  + %i x  - %i a )
+--R     + 
+--R                    +-+       2       2            +-+    2    2
+--R       - %i log(a x\|2  - %i x  + %i a ) - log(a x\|2  - x  - a )
+--R     + 
+--R       (- 1 - %i)log(- 1)
+--R  /
+--R        +-+
+--R     4a\|2
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 19
+ff:=rootSimp ee
+--R
+--R   (7)
+--R                  +-+       2       2               +-+       2       2
+--R       %i log(a x\|2  + %i x  - %i a ) - %i log(a x\|2  - %i x  + %i a )
+--R     + 
+--R                +-+                            +-+
+--R       %i log(x\|2  + (1 + %i)a) - %i log(%i x\|2  + (1 + %i)a)
+--R     + 
+--R                   +-+                           +-+
+--R     %i log(- %i x\|2  + (1 + %i)a) - %i log(- x\|2  + (1 + %i)a) - %i log(- 1)
+--R  /
+--R        +-+
+--R     4a\|2
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 20     14:313 Schaums and Axiom differ by a constant
+gg:=complexNormalize ff
+--R
+--R        %i log(2) - %i log(- 1) - %i log(- 2)
+--R   (8)  -------------------------------------
+--R                           +-+
+--R                        4a\|2
+--R                                             Type: Expression Complex Integer
+--E
 @
 
 \section{\cite{1}:14.314~~~~~$\displaystyle
@@ -132,7 +556,7 @@ $$
 <<*>>=
 )clear all
 
---S 4 of 14
+--S 21
 aa:=integrate(x^3/(x^4+a^4),x)
 --R 
 --R
@@ -141,7 +565,24 @@ aa:=integrate(x^3/(x^4+a^4),x)
 --R   (1)  ------------
 --R              4
 --R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 22
+bb:=1/4*log(x^4+a^4)
+--R
+--R             4    4
+--R        log(x  + a )
+--R   (2)  ------------
+--R              4
+--R                                                     Type: Expression Integer
 --E 
+
+--S 23     14:314 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.315~~~~~$\displaystyle
@@ -152,7 +593,7 @@ $$
 <<*>>=
 )clear all
 
---S 5 of 14
+--S 24
 aa:=integrate(1/(x*(x^4+a^4)),x)
 --R 
 --R
@@ -163,6 +604,41 @@ aa:=integrate(1/(x*(x^4+a^4)),x)
 --R                   4a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 25
+bb:=1/(4*a^4)*log(x^4/(x^4+a^4))
+--R
+--R                4
+--R               x
+--R        log(-------)
+--R             4    4
+--R            x  + a
+--R   (2)  ------------
+--R               4
+--R             4a
+--R                                                     Type: Expression Integer
+--E
+
+--S 26
+cc:=aa-bb
+--R
+--R                                           4
+--R               4    4                     x
+--R        - log(x  + a ) + 4log(x) - log(-------)
+--R                                        4    4
+--R                                       x  + a
+--R   (3)  ---------------------------------------
+--R                            4
+--R                          4a
+--R                                                     Type: Expression Integer
+--E
+
+--S 27     14:315 Schaums and Axiom agree
+dd:=expandLog cc
+--R
+--R   (4)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.316~~~~~$\displaystyle
@@ -175,7 +651,7 @@ $$
 <<*>>=
 )clear all
 
---S 6 of 14
+--S 28
 aa:=integrate(1/(x^2*(x^4+a^4)),x)
 --R 
 --R
@@ -220,6 +696,220 @@ aa:=integrate(1/(x^2*(x^4+a^4)),x)
 --R     a x\|2
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 29
+bb:=-1/(a^4*x)-1/(4*a^5*sqrt(2))*log((x^2-a*x*sqrt(2)+a^2)/(x^2+a*x*sqrt(2)+a^2))+1/(2*a^5*sqrt(2))*atan((a*x*sqrt(2))/(x^2-a^2))
+--R
+--R                         +-+    2    2                   +-+
+--R            +-+    - a x\|2  + x  + a        +-+     a x\|2
+--R        - x\|2 log(-------------------) + 2x\|2 atan(-------) - 8a
+--R                        +-+    2    2                 2    2
+--R                    a x\|2  + x  + a                 x  - a
+--R   (2)  ----------------------------------------------------------
+--R                                     5
+--R                                   8a x
+--R                                                     Type: Expression Integer
+--E
+
+--S 30
+cc:=aa-bb
+--R
+--R   (3)
+--R            +------+                +------+3         +------+2
+--R         5  |   1          16  +-+  |   1         12  |   1       2
+--R       4a   |------ log(64a  x\|2   |------  + 16a    |------  + x )
+--R           4|    20                4|    20          4|    20
+--R           \|256a                  \|256a            \|256a
+--R     + 
+--R              +------+                  +------+3         +------+2
+--R           5  |   1            16  +-+  |   1         12  |   1       2
+--R       - 4a   |------ log(- 64a  x\|2   |------  + 16a    |------  + x )
+--R             4|    20                  4|    20          4|    20
+--R             \|256a                    \|256a            \|256a
+--R     + 
+--R                                      +------+3
+--R                                  16  |   1
+--R                               64a    |------
+--R              +------+               4|    20
+--R           5  |   1                  \|256a
+--R       - 8a   |------ atan(-----------------------)
+--R             4|    20             +------+3
+--R             \|256a           16  |   1        +-+
+--R                           64a    |------  - x\|2
+--R                                 4|    20
+--R                                 \|256a
+--R     + 
+--R                                    +------+3
+--R                                16  |   1
+--R                             64a    |------
+--R            +------+               4|    20                  +-+    2    2
+--R         5  |   1                  \|256a              - a x\|2  + x  + a
+--R       8a   |------ atan(----------------------- + log(-------------------)
+--R           4|    20             +------+3                   +-+    2    2
+--R           \|256a           16  |   1        +-+        a x\|2  + x  + a
+--R                         64a    |------  + x\|2
+--R                               4|    20
+--R                               \|256a
+--R     + 
+--R                   +-+
+--R               a x\|2
+--R       - 2atan(-------)
+--R                2    2
+--R               x  - a
+--R  /
+--R       5 +-+
+--R     4a \|2
+--R                                                     Type: Expression Integer
+--E
+
+--S 31
+atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
+--R
+--R                            - x + %i
+--R                     %i log(--------)
+--R                             x + %i
+--R   (4)  atan(x) == - ----------------
+--R                             2
+--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
+--E
+
+--S 32
+dd:=atanrule cc
+--R
+--R   (5)
+--R            +------+                +------+3         +------+2
+--R         5  |   1          16  +-+  |   1         12  |   1       2
+--R       4a   |------ log(64a  x\|2   |------  + 16a    |------  + x )
+--R           4|    20                4|    20          4|    20
+--R           \|256a                  \|256a            \|256a
+--R     + 
+--R                                               +------+3
+--R                                           16  |   1           +-+
+--R                             (- 64 + 64%i)a    |------  + %i x\|2
+--R                 +------+                     4|    20
+--R              5  |   1                        \|256a
+--R       - 4%i a   |------ log(-------------------------------------)
+--R                4|    20                      +------+3
+--R                \|256a                    16  |   1           +-+
+--R                              (64 + 64%i)a    |------  + %i x\|2
+--R                                             4|    20
+--R                                             \|256a
+--R     + 
+--R                                             +------+3
+--R                                         16  |   1           +-+
+--R                           (- 64 + 64%i)a    |------  - %i x\|2
+--R               +------+                     4|    20
+--R            5  |   1                        \|256a
+--R       4%i a   |------ log(-------------------------------------)
+--R              4|    20                      +------+3
+--R              \|256a                    16  |   1           +-+
+--R                            (64 + 64%i)a    |------  - %i x\|2
+--R                                           4|    20
+--R                                           \|256a
+--R     + 
+--R              +------+                  +------+3         +------+2
+--R           5  |   1            16  +-+  |   1         12  |   1       2
+--R       - 4a   |------ log(- 64a  x\|2   |------  + 16a    |------  + x )
+--R             4|    20                  4|    20          4|    20
+--R             \|256a                    \|256a            \|256a
+--R     + 
+--R                 +-+    2    2                 +-+       2       2
+--R           - a x\|2  + x  + a            - a x\|2  + %i x  - %i a
+--R       log(-------------------) + %i log(-------------------------)
+--R                +-+    2    2                 +-+       2       2
+--R            a x\|2  + x  + a              a x\|2  + %i x  - %i a
+--R  /
+--R       5 +-+
+--R     4a \|2
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 33
+ee:=expandLog dd
+--R
+--R   (6)
+--R            +------+                +------+3         +------+2
+--R         5  |   1          16  +-+  |   1         12  |   1       2
+--R       4a   |------ log(64a  x\|2   |------  + 16a    |------  + x )
+--R           4|    20                4|    20          4|    20
+--R           \|256a                  \|256a            \|256a
+--R     + 
+--R              +------+                +------+3         +------+2
+--R           5  |   1          16  +-+  |   1         12  |   1       2
+--R       - 4a   |------ log(64a  x\|2   |------  - 16a    |------  - x )
+--R             4|    20                4|    20          4|    20
+--R             \|256a                  \|256a            \|256a
+--R     + 
+--R                 +------+                    +------+3
+--R              5  |   1                   16  |   1        +-+
+--R       - 4%i a   |------ log((64 + 64%i)a    |------  + x\|2 )
+--R                4|    20                    4|    20
+--R                \|256a                      \|256a
+--R     + 
+--R               +------+                    +------+3
+--R            5  |   1                   16  |   1           +-+
+--R       4%i a   |------ log((64 + 64%i)a    |------  + %i x\|2 )
+--R              4|    20                    4|    20
+--R              \|256a                      \|256a
+--R     + 
+--R                 +------+                    +------+3
+--R              5  |   1                   16  |   1           +-+
+--R       - 4%i a   |------ log((64 + 64%i)a    |------  - %i x\|2 )
+--R                4|    20                    4|    20
+--R                \|256a                      \|256a
+--R     + 
+--R               +------+                    +------+3
+--R            5  |   1                   16  |   1        +-+
+--R       4%i a   |------ log((64 + 64%i)a    |------  - x\|2 )
+--R              4|    20                    4|    20
+--R              \|256a                      \|256a
+--R     + 
+--R                      +------+
+--R           5          |   1             +-+    2    2
+--R       - 4a log(- 1)  |------ - log(a x\|2  + x  + a )
+--R                     4|    20
+--R                     \|256a
+--R     + 
+--R                    +-+       2       2               +-+       2       2
+--R       - %i log(a x\|2  + %i x  - %i a ) + %i log(a x\|2  - %i x  + %i a )
+--R     + 
+--R               +-+    2    2
+--R       log(a x\|2  - x  - a ) + (1 + %i)log(- 1)
+--R  /
+--R       5 +-+
+--R     4a \|2
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 34
+ff:=rootSimp ee
+--R
+--R   (7)
+--R                    +-+       2       2               +-+       2       2
+--R       - %i log(a x\|2  + %i x  - %i a ) + %i log(a x\|2  - %i x  + %i a )
+--R     + 
+--R                  +-+                            +-+
+--R       - %i log(x\|2  + (1 + %i)a) + %i log(%i x\|2  + (1 + %i)a)
+--R     + 
+--R                       +-+                           +-+
+--R       - %i log(- %i x\|2  + (1 + %i)a) + %i log(- x\|2  + (1 + %i)a)
+--R     + 
+--R       %i log(- 1)
+--R  /
+--R       5 +-+
+--R     4a \|2
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 35     14:316 Schaums and Axiom differ by a constant
+gg:=complexNormalize ff
+--R
+--R        - %i log(2) + %i log(- 1) + %i log(- 2)
+--R   (8)  ---------------------------------------
+--R                          5 +-+
+--R                        4a \|2
+--R                                             Type: Expression Complex Integer
+--E
 @
 
 \section{\cite{1}:14.317~~~~~$\displaystyle
@@ -230,7 +920,7 @@ $$
 <<*>>=
 )clear all
 
---S 7 of 14
+--S 36
 aa:=integrate(1/(x^3*(x^4+a^4)),x)
 --R 
 --R
@@ -244,6 +934,27 @@ aa:=integrate(1/(x^3*(x^4+a^4)),x)
 --R              2a x
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 37
+bb:=-1/(2*a^4*x^2)-1/(2*a^6)*atan(x^2/a^2)
+--R
+--R                  2
+--R           2     x      2
+--R        - x atan(--) - a
+--R                  2
+--R                 a
+--R   (2)  -----------------
+--R                6 2
+--R              2a x
+--R                                                     Type: Expression Integer
+--E
+
+--S 38     14:317 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.318~~~~~$\displaystyle
@@ -255,7 +966,7 @@ $$
 <<*>>=
 )clear all
 
---S 8 of 14
+--S 39
 aa:=integrate(1/(x^4-a^4),x)
 --R 
 --R
@@ -267,6 +978,37 @@ aa:=integrate(1/(x^4-a^4),x)
 --R                         4a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 40
+bb:=1/(4*a^3)*log((x-a)/(x+a))-1/(2*a^3)*atan(x/a)
+--R
+--R            x - a          x
+--R        log(-----) - 2atan(-)
+--R            x + a          a
+--R   (2)  ---------------------
+--R                   3
+--R                 4a
+--R                                                     Type: Expression Integer
+--E
+
+--S 41
+cc:=aa-bb
+--R
+--R                                        x - a
+--R        - log(x + a) + log(x - a) - log(-----)
+--R                                        x + a
+--R   (3)  --------------------------------------
+--R                            3
+--R                          4a
+--R                                                     Type: Expression Integer
+--E
+
+--S 42     14:318 Schaums and Axiom agree
+dd:=expandLog cc
+--R
+--R   (4)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.319~~~~~$\displaystyle
@@ -277,7 +1019,7 @@ $$
 <<*>>=
 )clear all
 
---S 9 of 14
+--S 43
 aa:=integrate(x/(x^4-a^4),x)
 --R 
 --R
@@ -288,6 +1030,41 @@ aa:=integrate(x/(x^4-a^4),x)
 --R                     4a
 --R                                          Type: Union(Expression Integer,...)
 --E
+
+--S 44
+bb:=1/(4*a^2)*log((x^2-a^2)/(x^2+a^2))
+--R
+--R             2    2
+--R            x  - a
+--R        log(-------)
+--R             2    2
+--R            x  + a
+--R   (2)  ------------
+--R               2
+--R             4a
+--R                                                     Type: Expression Integer
+--E
+
+--S 45
+cc:=aa-bb
+--R
+--R                                             2    2
+--R               2    2         2    2        x  - a
+--R        - log(x  + a ) + log(x  - a ) - log(-------)
+--R                                             2    2
+--R                                            x  + a
+--R   (3)  --------------------------------------------
+--R                               2
+--R                             4a
+--R                                                     Type: Expression Integer
+--E
+
+--S 46     14:319 Schaums and Axiom agree
+dd:=expandLog cc
+--R
+--R   (4)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.320~~~~~$\displaystyle
@@ -299,7 +1076,7 @@ $$
 <<*>>=
 )clear all
 
---S 10 of 14
+--S 47
 aa:=integrate(x^2/(x^4-a^4),x)
 --R 
 --R
@@ -309,7 +1086,36 @@ aa:=integrate(x^2/(x^4-a^4),x)
 --R   (1)  ------------------------------------
 --R                         4a
 --R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 48
+bb:=1/(4*a)*log((x-a)/(x+a))+1/(2*a)*atan(x/a)
+--R
+--R            x - a          x
+--R        log(-----) + 2atan(-)
+--R            x + a          a
+--R   (2)  ---------------------
+--R                  4a
+--R                                                     Type: Expression Integer
 --E 
+
+--S 49
+cc:=aa-bb
+--R
+--R                                        x - a
+--R        - log(x + a) + log(x - a) - log(-----)
+--R                                        x + a
+--R   (3)  --------------------------------------
+--R                          4a
+--R                                                     Type: Expression Integer
+--E
+
+--S 50     14:320 Schaums and Axiom agree
+dd:=expandLog cc
+--R
+--R   (4)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.321~~~~~$\displaystyle
@@ -320,7 +1126,7 @@ $$
 <<*>>=
 )clear all
 
---S 11 of 14
+--S 51
 aa:=integrate(x^3/(x^4-a^4),x)
 --R 
 --R
@@ -330,6 +1136,23 @@ aa:=integrate(x^3/(x^4-a^4),x)
 --R              4
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 52
+bb:=1/4*log(x^4-a^4)
+--R
+--R             4    4
+--R        log(x  - a )
+--R   (2)  ------------
+--R              4
+--R                                                     Type: Expression Integer
+--E
+
+--S 53     14:321 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.322~~~~~$\displaystyle
@@ -340,7 +1163,7 @@ $$
 <<*>>=
 )clear all
 
---S 12 of 14
+--S 54
 aa:=integrate(1/(x*(x^4-a^4)),x)
 --R 
 --R
@@ -350,7 +1173,42 @@ aa:=integrate(1/(x*(x^4-a^4)),x)
 --R                    4
 --R                  4a
 --R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 55
+bb:=1/(4*a^4)*log((x^4-a^4)/x^4)
+--R
+--R             4    4
+--R            x  - a
+--R        log(-------)
+--R                4
+--R               x
+--R   (2)  ------------
+--R               4
+--R             4a
+--R                                                     Type: Expression Integer
 --E 
+
+--S 56
+cc:=aa-bb
+--R
+--R                                      4    4
+--R             4    4                  x  - a
+--R        log(x  - a ) - 4log(x) - log(-------)
+--R                                         4
+--R                                        x
+--R   (3)  -------------------------------------
+--R                           4
+--R                         4a
+--R                                                     Type: Expression Integer
+--E
+
+--S 57     14:322 Schaums and Axiom agree
+dd:=expandLog cc
+--R
+--R   (4)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.323~~~~~$\displaystyle
@@ -362,7 +1220,7 @@ $$
 <<*>>=
 )clear all
 
---S 13 of 14
+--S 58
 aa:=integrate(1/(x^2*(x^4-a^4)),x)
 --R 
 --R
@@ -374,6 +1232,37 @@ aa:=integrate(1/(x^2*(x^4-a^4)),x)
 --R                              4a x
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 59
+bb:=1/(a^4*x)+1/(4*a^5)*log((x-a)/(x+a))+1/(2*a^5)*atan(x/a)
+--R
+--R              x - a            x
+--R        x log(-----) + 2x atan(-) + 4a
+--R              x + a            a
+--R   (2)  ------------------------------
+--R                       5
+--R                     4a x
+--R                                                     Type: Expression Integer
+--E
+
+--S 60
+cc:=aa-bb
+--R
+--R                                        x - a
+--R        - log(x + a) + log(x - a) - log(-----)
+--R                                        x + a
+--R   (3)  --------------------------------------
+--R                            5
+--R                          4a
+--R                                                     Type: Expression Integer
+--E
+
+--S 61     14:323 Schaums and Axiom agree
+dd:=expandLog cc
+--R
+--R   (4)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.324~~~~~$\displaystyle
@@ -384,7 +1273,7 @@ $$
 <<*>>=
 )clear all
 
---S 14 of 14
+--S 62
 aa:=integrate(1/(x^3*(x^4-a^4)),x)
 --R 
 --R
@@ -396,6 +1285,40 @@ aa:=integrate(1/(x^3*(x^4-a^4)),x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
 
+--S 63
+bb:=1/(2*a^4*x^2)+1/(4*a^6)*log((x^2-a^2)/(x^2+a^2))
+--R
+--R               2    2
+--R         2    x  - a       2
+--R        x log(-------) + 2a
+--R               2    2
+--R              x  + a
+--R   (2)  --------------------
+--R                  6 2
+--R                4a x
+--R                                                     Type: Expression Integer
+--E
+
+--S 64
+cc:=aa-bb
+--R
+--R                                             2    2
+--R               2    2         2    2        x  - a
+--R        - log(x  + a ) + log(x  - a ) - log(-------)
+--R                                             2    2
+--R                                            x  + a
+--R   (3)  --------------------------------------------
+--R                               6
+--R                             4a
+--R                                                     Type: Expression Integer
+--E
+
+--S 65     14:324 Schaums and Axiom agree
+dd:=expandLog cc
+--R
+--R   (4)  0
+--R                                                     Type: Expression Integer
+--E
 )spool
 )lisp (bye)
 @
diff --git a/src/input/schaum16.input.pamphlet b/src/input/schaum16.input.pamphlet
index f6b849c..b058a54 100644
--- a/src/input/schaum16.input.pamphlet
+++ b/src/input/schaum16.input.pamphlet
@@ -18,7 +18,7 @@ $$
 )set message auto off
 )clear all
 
---S 1 of 14
+--S 1
 aa:=integrate(1/x*(x^n+a^n),x)
 --R 
 --R
@@ -28,6 +28,79 @@ aa:=integrate(1/x*(x^n+a^n),x)
 --R                   n
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 2
+bb:=1/(n*a^n)*log(x^n/(x^n+a^n))
+--R
+--R                n
+--R               x
+--R        log(-------)
+--R             n    n
+--R            x  + a
+--R   (2)  ------------
+--R               n
+--R            n a
+--R                                                     Type: Expression Integer
+--E
+
+--S 3
+cc:=aa-bb
+--R
+--R                  n
+--R                 x        n  n log(x)             n 2
+--R        - log(-------) + a %e         + n log(x)(a )
+--R               n    n
+--R              x  + a
+--R   (3)  ---------------------------------------------
+--R                                n
+--R                             n a
+--R                                                     Type: Expression Integer
+--E
+
+--S 4
+dd:=expandLog cc
+--R
+--R             n    n         n     n  n log(x)            2n
+--R        log(x  + a ) - log(x ) + a %e         + n log(x)a
+--R   (4)  ---------------------------------------------------
+--R                                   n
+--R                                n a
+--R                                                     Type: Expression Integer
+--E
+
+--S 5
+ee:=complexNormalize dd
+--R
+--R   (5)
+--R             n log(x)     n log(a)      n log(a)  n log(x)
+--R       log(%e         + %e        ) + %e        %e
+--R     + 
+--R                  n log(a) 2
+--R       n log(x)(%e        )  - n log(x)
+--R  /
+--R         n log(a)
+--R     n %e
+--R                                                     Type: Expression Integer
+--E
+
+--S 6
+explog:=rule(%e^(n*log(x)) == x^n)
+--R
+--R          n log(x)     n
+--R   (6)  %e         == x
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 7      14:325 Axiom cannot simplify this expression
+ff:=explog ee
+--R
+--R             n    n     n n            2n
+--R        log(x  + a ) + a x  + n log(x)a   - n log(x)
+--R   (7)  --------------------------------------------
+--R                               n
+--R                            n a
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.326~~~~~$\displaystyle
@@ -38,7 +111,7 @@ $$
 <<*>>=
 )clear all
 
---S 2 of 14
+--S 8
 aa:=integrate(x^(n-1)/(x^n+a^n),x)
 --R 
 --R
@@ -48,6 +121,41 @@ aa:=integrate(x^(n-1)/(x^n+a^n),x)
 --R                  n
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 9
+bb:=1/n*log(x^n+a^n)
+--R
+--R             n    n
+--R        log(x  + a )
+--R   (2)  ------------
+--R              n
+--R                                                     Type: Expression Integer
+--E
+
+--S 10
+cc:=aa-bb
+--R
+--R              n log(x)    n         n    n
+--R        log(%e         + a ) - log(x  + a )
+--R   (3)  -----------------------------------
+--R                         n
+--R                                                     Type: Expression Integer
+--E
+
+--S 11
+explog:=rule(%e^(n*log(x)) == x^n)
+--R
+--R          n log(x)     n
+--R   (4)  %e         == x
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 12     14:326 Schaums and Axiom agree
+dd:=explog cc
+--R
+--R   (5)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.327~~~~~$\displaystyle
@@ -59,7 +167,7 @@ $$
 <<*>>=
 )clear all
 
---S 3 of 14
+--S 13     14:327 Axiom cannot compute this integral
 aa:=integrate(x^m/(x^n+a^n)^r,x)
 --R 
 --R
@@ -81,7 +189,7 @@ $$
 <<*>>=
 )clear all
 
---S 4 of 14
+--S 14     14:328 Axiom cannot compute this integral
 aa:=integrate(1/(x^m*(x^n+a^n)^r),x)
 --R 
 --R
@@ -103,7 +211,7 @@ $$
 <<*>>=
 )clear all
 
---S 5 of 14
+--S 15
 aa:=integrate(1/(x*sqrt(x^n+a^n)),x)
 --R 
 --R
@@ -130,6 +238,114 @@ aa:=integrate(1/(x*sqrt(x^n+a^n)),x)
 --R                  n\|- a
 --R                                     Type: Union(List Expression Integer,...)
 --E 
+
+--S 16
+bb:=1/(n*sqrt(a^n))*log((sqrt(x^n+a^n)-sqrt(a^n))/(sqrt(x^n+a^n)+sqrt(a^n)))
+--R
+--R             +-------+    +--+
+--R             | n    n     | n
+--R            \|x  + a   - \|a
+--R        log(------------------)
+--R             +-------+    +--+
+--R             | n    n     | n
+--R            \|x  + a   + \|a
+--R   (2)  -----------------------
+--R                   +--+
+--R                   | n
+--R                 n\|a
+--R                                                     Type: Expression Integer
+--E
+
+--S 17
+cc1:=aa.1-bb
+--R
+--R   (3)
+--R                 +---------------+                      +--+
+--R               n |  n log(x)    n       n log(x)     n  | n
+--R           - 2a \|%e         + a   + (%e         + 2a )\|a
+--R       log(-------------------------------------------------)
+--R                                 n log(x)
+--R                               %e
+--R     + 
+--R              +-------+    +--+
+--R              | n    n     | n
+--R             \|x  + a   - \|a
+--R       - log(------------------)
+--R              +-------+    +--+
+--R              | n    n     | n
+--R             \|x  + a   + \|a
+--R  /
+--R       +--+
+--R       | n
+--R     n\|a
+--R                                                     Type: Expression Integer
+--E
+
+--S 18
+dd1:=expandLog cc1
+--R
+--R   (4)
+--R               +---------------+                        +--+
+--R             n |  n log(x)    n         n log(x)     n  | n
+--R       log(2a \|%e         + a   + (- %e         - 2a )\|a  )
+--R     + 
+--R            +-------+    +--+         +-------+    +--+
+--R            | n    n     | n          | n    n     | n
+--R       log(\|x  + a   + \|a  ) - log(\|x  + a   - \|a  ) - n log(x) + log(- 1)
+--R  /
+--R       +--+
+--R       | n
+--R     n\|a
+--R                                                     Type: Expression Integer
+--E
+
+--S 19
+explog:=rule(%e^(n*log(x)) == x^n)
+--R
+--R          n log(x)     n
+--R   (5)  %e         == x
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 20
+ee1:=explog dd1
+--R
+--R   (6)
+--R               +-------+                +--+         +-------+    +--+
+--R             n | n    n        n     n  | n          | n    n     | n
+--R       log(2a \|x  + a   + (- x  - 2a )\|a  ) + log(\|x  + a   + \|a  )
+--R     + 
+--R              +-------+    +--+
+--R              | n    n     | n
+--R       - log(\|x  + a   - \|a  ) - n log(x) + log(- 1)
+--R  /
+--R       +--+
+--R       | n
+--R     n\|a
+--R                                                     Type: Expression Integer
+--E
+
+--S 21
+ff1:=complexNormalize ee1
+--R
+--R        n log(a) + 4log(- 1)
+--R   (7)  --------------------
+--R              +----------+
+--R              |  n log(a)
+--R           2n\|%e
+--R                                                     Type: Expression Integer
+--E
+
+--S 22     14:329 Schaums and Axiom differ by a constant
+gg1:=explog ff1
+--R
+--R        n log(a) + 4log(- 1)
+--R   (8)  --------------------
+--R                  +--+
+--R                  | n
+--R               2n\|a
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.330~~~~~$\displaystyle
@@ -140,7 +356,7 @@ $$
 <<*>>=
 )clear all
 
---S 6 of 14
+--S 23
 aa:=integrate(1/(x*(x^n-a^n)),x)
 --R 
 --R
@@ -151,6 +367,79 @@ aa:=integrate(1/(x*(x^n-a^n)),x)
 --R                      n a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 24
+bb:=1/(n*a^n)*log((x^n-a^n)/x^n)
+--R
+--R             n    n
+--R            x  - a
+--R        log(-------)
+--R                n
+--R               x
+--R   (2)  ------------
+--R               n
+--R            n a
+--R                                                     Type: Expression Integer
+--E
+
+--S 25
+cc:=aa-bb
+--R
+--R                                    n    n
+--R              n log(x)    n        x  - a
+--R        log(%e         - a ) - log(-------) - n log(x)
+--R                                       n
+--R                                      x
+--R   (3)  ----------------------------------------------
+--R                                n
+--R                             n a
+--R                                                     Type: Expression Integer
+--E
+
+--S 26
+dd:=expandLog cc
+--R
+--R              n log(x)    n         n         n    n
+--R        log(%e         - a ) + log(x ) - log(x  - a ) - n log(x)
+--R   (4)  --------------------------------------------------------
+--R                                     n
+--R                                  n a
+--R                                                     Type: Expression Integer
+--E
+
+--S 27
+explog:=rule(%e^(n*log(x)) == x^n)
+--R
+--R          n log(x)     n
+--R   (5)  %e         == x
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 28
+ee:=explog dd
+--R
+--R             n
+--R        log(x ) - n log(x)
+--R   (6)  ------------------
+--R                  n
+--R               n a
+--R                                                     Type: Expression Integer
+--E
+
+--S 29
+logpow:=rule(log(a^n) == n*log(a))
+--R
+--R             n
+--R   (7)  log(a ) == n log(a)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 30     14:330 Schaums and Axiom agree
+ff:=logpow ee
+--R
+--R   (8)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.331~~~~~$\displaystyle
@@ -161,7 +450,7 @@ $$
 <<*>>=
 )clear all
 
---S 7 of 14
+--S 31
 aa:=integrate(x^(n-1)/(x^n-a^n),x)
 --R 
 --R
@@ -171,6 +460,42 @@ aa:=integrate(x^(n-1)/(x^n-a^n),x)
 --R                  n
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 32
+bb:=1/n*log(x^n-a^n)
+--R
+--R             n    n
+--R        log(x  - a )
+--R   (2)  ------------
+--R              n
+--R                                                     Type: Expression Integer
+--E
+
+--S 33
+cc:=aa-bb
+--R
+--R              n log(x)    n         n    n
+--R        log(%e         - a ) - log(x  - a )
+--R   (3)  -----------------------------------
+--R                         n
+--R                                                     Type: Expression Integer
+--E
+
+--S 34
+explog:=rule(%e^(n*log(x)) == x^n)
+--R
+--R          n log(x)     n
+--R   (4)  %e         == x
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 35     14:331 Schaums and Axiom agree
+dd:=explog cc
+--R
+--R   (5)  0
+--R                                                     Type: Expression Integer
+--E
+
 @
 
 \section{\cite{1}:14.332~~~~~$\displaystyle
@@ -182,7 +507,7 @@ $$
 <<*>>=
 )clear all
 
---S 8 of 14
+--S 36     14:332 Axiom cannot compute this integral
 aa:=integrate(x^m/(x^n-a^n)^r,x)
 --R 
 --R
@@ -204,7 +529,7 @@ $$
 <<*>>=
 )clear all
 
---S 9 of 14
+--S 37     14:333 Axiom cannot compute this integral
 aa:=integrate(1/(x^m*(x^n-a^n)^r),x)
 --R 
 --R
@@ -225,7 +550,7 @@ $$
 <<*>>=
 )clear all
 
---S 10 of 14
+--S 38
 aa:=integrate(1/(x*sqrt(x^n-a^n)),x)
 --R 
 --R
@@ -252,6 +577,62 @@ aa:=integrate(1/(x*sqrt(x^n-a^n)),x)
 --R                n\|a
 --R                                     Type: Union(List Expression Integer,...)
 --E 
+
+--S 39
+bb:=2/(n*sqrt(a^n))*acos(sqrt(a^n/x^n))
+--R
+--R               +--+
+--R               | n
+--R               |a
+--R        2acos( |-- )
+--R               | n
+--R              \|x
+--R   (2)  ------------
+--R             +--+
+--R             | n
+--R           n\|a
+--R                                                     Type: Expression Integer
+--E
+
+--S 40
+cc1:=aa.1-bb
+--R
+--R   (3)
+--R                    +---------------+                      +----+
+--R        +--+      n |  n log(x)    n       n log(x)     n  |   n
+--R        | n     2a \|%e         - a   + (%e         - 2a )\|- a
+--R       \|a  log(-------------------------------------------------)
+--R                                      n log(x)
+--R                                    %e
+--R     + 
+--R                       +--+
+--R           +----+      | n
+--R           |   n       |a
+--R       - 2\|- a  acos( |-- )
+--R                       | n
+--R                      \|x
+--R  /
+--R       +----+ +--+
+--R       |   n  | n
+--R     n\|- a  \|a
+--R                                                     Type: Expression Integer
+--E
+
+--S 41     14:334 Axiom cannot simplify this expression
+cc2:=aa.2-bb
+--R
+--R               +--+ +---------------+           +--+
+--R               | n  |  n log(x)    n            | n
+--R              \|a  \|%e         - a             |a
+--R        2atan(-----------------------) - 2acos( |-- )
+--R                          n                     | n
+--R                         a                     \|x
+--R   (4)  ---------------------------------------------
+--R                              +--+
+--R                              | n
+--R                            n\|a
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.335~~~~~$\displaystyle
@@ -269,7 +650,7 @@ $$
 <<*>>=
 )clear all
 
---S 11 of 14
+--S 42     14:335 Axiom cannot compute this integral
 aa:=integrate(x^(p-1)/(x^(2*m)+a^(2*m)),x)
 --R 
 --R
@@ -299,7 +680,7 @@ $$
 <<*>>=
 )clear all
 
---S 12 of 14
+--S 43     14:336 Axiom cannot compute this integral
 aa:=integrate(x^(p-1)/(x^(2*m)-a^(2*m)),x)
 --R 
 --R
@@ -333,7 +714,7 @@ $$
 <<*>>=
 )clear all
 
---S 13 of 14
+--S 44     14:337 Axiom cannot compute this integral
 aa:=integrate(x^(p-1)/(x^(2*m+1)+a^(2*m+1)),x)
 --R 
 --R
@@ -369,7 +750,7 @@ $$
 <<*>>=
 )clear all
 
---S 14 of 14
+--S 45     14:338 Axiom cannot compute this integral
 aa:=integrate(x^(p-1)/(x^(2*m+1)-a^(2*m+1)),x)
 --R 
 --R



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Date: Tue, 22 Apr 2008 07:58:44 -0400
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Organization: A constant variable
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Subject: [Axiom-developer] March Fedora 8
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While the March binary still has a back reference to the root user; the 
source file compiled correctly after downloading the gettext package.
My system is happy and I have debugged the test program!

RayR



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Subject: [Axiom-developer] sage interface impression
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After taking a look at the sage web interface I plan to continue with my
own plans.  The sage interface looks very good and well developed but
is not what I have in mind.

I comment that I  think it is unlikely that one interface will be optimal
for everybody.

Arthur



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schaum17.input.pamphlet
  14:339 Schaums and Axiom agree
  14:340 Schaums and Axiom agree
  14:341 Schaums and Axiom agree
  14:342 Schaums and Axiom agree
  14:343 Schaums and Axiom agree by definition
  14:344 Axiom cannot compute this integral
  14:345 Schaums and Axiom agree
  14:346 Axiom cannot compute this integral
  14:347 Schaums and Axiom agreee
  14:348 Schaums and Axiom differ by a constant
  14:349 Schaums and Axiom agree
  14:350 Schaums and Axiom agree
  14:351 Schaums and Axiom agree
  14:352 Schaums and Axiom agree
  14:353 Axiom cannot simplify this expression
  14:354 Schaums and Axiom differ by a constant
  14:355 Axiom cannot simplify this expression
  14:356 Axiom cannot simplify this expression
  14:357 Axiom cannot simplify this expression
  14:358 Axiom cannot simplify this expression
  14:359 Axiom cannot simplify this expression
  14:360 Axiom cannot simplify these equations
  14:361 Schaums and Axiom differ by a constant
  14:362 Axiom cannot simplify this expression
  14:363 Axiom cannot simplify this expression
  14:364 Axiom cannot compute this integral
  14:365 Axiom cannot compute this integral
  14:366 Axiom cannot compute this integral
  14:367 Axiom cannot compute this integral
  14:368 Axiom cannot compute this integral
  
schaum18.input.pamphlet
  14:369 Schaums and Axiom agree
  14:370 Schaums and Axiom agree
  14:371 Schaums and Axiom agree
  14:372 Schaums and Axiom agree
  14:373 Schaums and Axiom agree by definition
  14:374 Axiom cannot compute this integral
  14:375 Axiom cannot simplify these expressions
  14:376 Axiom cannot compute this integral
  14:377 Schaums and Axiom agree
  14:378 Schaums and Axiom differ by a constant
  14:379 Schaums and Axiom agree
  14:380 Axiom cannot simplify this expression
  14:381 Schaums and Axiom agree
  14:382 Axiom cannot simplify this expression
  14:383 Axiom cannot simplify this expression
  14:384 Axiom cannot simplify this expression
  14:385 Axiom cannot simplify this expression
  14:386 Axiom cannot simplify this expression
  14:387 Axiom cannot simplify this expression
  14:388 Axiom cannot simplify this expression
  14:389 Axiom cannot simplify this expression
  14:390 Axiom cannot simplify these expressions
  14:391 Schaums and Axiom agree
  14:392 Axiom cannot simplify these expressions
  14:393 Axiom cannot simplify these expressions
  14:394 Axiom cannot compute this integral
  14:395 Axiom cannot compute this integral
  14:396 Axiom cannot compute this integral
  14:397 Axiom cannot compute this integral
  14:398 Axiom cannot compute this integral

schaum19.input.pamphlet
  14:399 Schaums and Axiom differ by a constant
  14:400 Axiom is unable to simplify this expression
  14:401 Schaums and Axiom agree
  14:402 Schaums and Axiom agree
  14:403 Schaums and Axiom agree
  14:404 Schaums and Axiom differ by a constant
  14:405 Schaums and Axiom differ by a constant
  14:406 Schaums and Axiom differ by a constant
  14:407 Schaums and Axiom agree
  14:408 Schaums and Axiom differ by a constant
  14:409 Schaums and Axiom agree
  14:410 Schaums and Axiom differ by a constant
  14:411 Schaums and Axiom differ by a constant
  14:412 Axiom cannot simplify this expression
  14:413 Schaums and Axiom agree
  14:414 Schaums and Axiom agree
  14:415 Schaums and Axiom differ by a constant
  14:416 Schaums and Axiom differ by a constant
  14:417 Schaums and Axiom agree
  14:418 Schaums and Axiom agree
  14:419 Axiom cannot simplify this expression
  14:420 Axiom cannot simplify these expressions
  14:421 Schaums and Axiom agree
  14:422 Axiom cannot simplify this expression
  14:423 Axiom cannot simplify this expressions
  14:424 Schaums and Axiom differ by a constant
  14:425 Axiom cannot compute this integral
  14:426 Axiom cannot compute this integral
  14:427 Axiom cannot compute this integral
  14:428 Axiom cannot compute this integral
  
schaum20.input.pamphlet
  14:429 Schaums and Axiom agree
  14:430 Schaums and Axiom agree
  14:431 Schaums and Axiom agree
  14:432 Schaums and Axiom agree
  14:433 Schaums and Axiom differ by a constant
  14:435 Axiom cannot compute this integral
  14:436 Axiom cannot compute this integral
  14:437 Schaums and Axiom agree
  14:438 Schaums and Axiom agree
  14:439 Axiom cannot compute this integral

schaum21.input.pamphlet
  14:440 Schaums and Axiom agree
  14:441 Schaums and Axiom agree
  14:442 Schaums and Axiom agree
  14:443 Schaums and Axiom agree
  14:444 Schaums and Axiom differ by a constant
  14:445 Schaums and Axiom agree
  14:446 Axiom cannot compute this integral
  14:447 Axiom cannot compute this integral
  14:448 Schaums and Axiom agree
  14:449 Axiom cannot simplify this expression
  14:450 Axiom cannot compute this integral

schaum22.input.pamphlet
  14:451 Schaums and Axiom differ by a constant
  14:452 Schaums and Axiom agree
  14:453 Schaums and Axiom differ by a constant
  14:454 Axiom cannot simplify this expression
  14:455 Schaums and Axiom agree
  14:456 Axiom cannot compute this integral
  14:457 Axiom cannot compute this integral
  14:458 Schaums and Axiom differ by a constant
  14:459 Schaums and Axiom agree
  14:460 Axiom cannot compute this integral
========================================================================
diff --git a/changelog b/changelog
index 4b454b8..80e94f3 100644
--- a/changelog
+++ b/changelog
@@ -1,3 +1,9 @@
+20080423 tpd src/input/schaum22.input show Schaums-Axiom equivalence
+20080423 tpd src/input/schaum21.input show Schaums-Axiom equivalence
+20080423 tpd src/input/schaum20.input show Schaums-Axiom equivalence
+20080423 tpd src/input/schaum19.input show Schaums-Axiom equivalence
+20080423 tpd src/input/schaum18.input show Schaums-Axiom equivalence
+20080423 tpd src/input/schaum17.input show Schaums-Axiom equivalence
 20080421 tpd src/input/schaum16.input show Schaums-Axiom equivalence
 20080421 tpd src/input/schaum15.input show Schaums-Axiom equivalence
 20080421 tpd src/input/schaum14.input show Schaums-Axiom equivalence
diff --git a/src/input/schaum17.input.pamphlet b/src/input/schaum17.input.pamphlet
index fd40132..a11b623 100644
--- a/src/input/schaum17.input.pamphlet
+++ b/src/input/schaum17.input.pamphlet
@@ -18,7 +18,7 @@ $$
 )set message auto off
 )clear all
 
---S 1 of 30
+--S 1
 aa:=integrate(sin(a*x),x)
 --R 
 --R
@@ -27,6 +27,22 @@ aa:=integrate(sin(a*x),x)
 --R              a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 2
+bb:=-cos(a*x)/a
+--R
+--R          cos(a x)
+--R   (2)  - --------
+--R              a
+--R                                                     Type: Expression Integer
+--E
+
+--S 3      14:339 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.340~~~~~$\displaystyle
@@ -37,7 +53,7 @@ $$
 <<*>>=
 )clear all
 
---S 2 of 30
+--S 4
 aa:=integrate(x*sin(a*x),x)
 --R 
 --R
@@ -47,6 +63,23 @@ aa:=integrate(x*sin(a*x),x)
 --R                   a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 5
+bb:=sin(a*x)/a^2-(x*cos(a*x))/a
+--R
+--R        sin(a x) - a x cos(a x)
+--R   (2)  -----------------------
+--R                    2
+--R                   a
+--R                                                     Type: Expression Integer
+--E
+
+--S 6      14:340 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.341~~~~~$\displaystyle
@@ -57,7 +90,7 @@ $$
 <<*>>=
 )clear all
 
---S 3 of 30
+--S 7
 aa:=integrate(x^2*sin(a*x),x)
 --R 
 --R
@@ -68,6 +101,24 @@ aa:=integrate(x^2*sin(a*x),x)
 --R                         a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 8
+bb:=(2*x)/a^2*sin(a*x)+(2/a^3-x^2/a)*cos(a*x)
+--R
+--R                            2 2
+--R        2a x sin(a x) + (- a x  + 2)cos(a x)
+--R   (2)  ------------------------------------
+--R                          3
+--R                         a
+--R                                                     Type: Expression Integer
+--E
+
+--S 9      14:341 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.342~~~~~$\displaystyle
@@ -79,7 +130,7 @@ $$
 <<*>>=
 )clear all
 
---S 4 of 30
+--S 10
 aa:=integrate(x^3*sin(a*x),x)
 --R 
 --R
@@ -90,6 +141,24 @@ aa:=integrate(x^3*sin(a*x),x)
 --R                              a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 11
+bb:=((3*x^2)/a^2-6/a^4)*sin(a*x)+(6*x/a^3-x^3/a)*cos(a*x)
+--R
+--R           2 2                    3 3
+--R        (3a x  - 6)sin(a x) + (- a x  + 6a x)cos(a x)
+--R   (2)  ---------------------------------------------
+--R                               4
+--R                              a
+--R                                                     Type: Expression Integer
+--E
+
+--S 12     14:342 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.343~~~~~$\displaystyle
@@ -100,7 +169,7 @@ $$
 <<*>>=
 )clear all
 
---S 5 of 30
+--S 13     14:343 Schaums and Axiom agree by definition
 aa:=integrate(sin(x)/x,x)
 --R 
 --R
@@ -117,7 +186,7 @@ $$
 <<*>>=
 )clear all
 
---S 6 of 30
+--S 14     14:344 Axiom cannot compute this integral
 aa:=integrate(sin(a*x)/x^2,x)
 --R 
 --R
@@ -139,7 +208,7 @@ $$
 <<*>>=
 )clear all
 
---S 7 of 30
+--S 15
 aa:=integrate(1/sin(a*x),x)
 --R 
 --R
@@ -150,6 +219,35 @@ aa:=integrate(1/sin(a*x),x)
 --R                a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 16
+bb:=1/a*log(tan((a*x)/2))
+--R
+--R                a x
+--R        log(tan(---))
+--R                 2
+--R   (2)  -------------
+--R              a
+--R                                                     Type: Expression Integer
+--E
+
+--S 17
+cc:=aa-bb
+--R
+--R                  a x           sin(a x)
+--R        - log(tan(---)) + log(------------)
+--R                   2          cos(a x) + 1
+--R   (3)  -----------------------------------
+--R                         a
+--R                                                     Type: Expression Integer
+--E
+
+--S 18     14:345 Schaums and Axiom agree
+dd:=complexNormalize cc
+--R
+--R   (4)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.346~~~~~$\displaystyle
@@ -162,7 +260,7 @@ $$
 <<*>>=
 )clear all
 
---S 8 of 30
+--S 19     14:346 Axiom cannot compute this integral
 aa:=integrate(x/sin(a*x),x)
 --R 
 --R
@@ -182,7 +280,7 @@ $$
 <<*>>=
 )clear all
 
---S 9 of 30
+--S 20
 aa:=integrate(sin(a*x)^2,x)
 --R 
 --R
@@ -191,6 +289,31 @@ aa:=integrate(sin(a*x)^2,x)
 --R                   2a
 --R                                          Type: Union(Expression Integer,...)
 --E
+
+--S 21
+bb:=x/2-sin(2*a*x)/(4*a)
+--R
+--R        - sin(2a x) + 2a x
+--R   (2)  ------------------
+--R                4a
+--R                                                     Type: Expression Integer
+--E
+
+--S 22
+cc:=aa-bb
+--R
+--R        sin(2a x) - 2cos(a x)sin(a x)
+--R   (3)  -----------------------------
+--R                      4a
+--R                                                     Type: Expression Integer
+--E
+
+--S 23     14:347 Schaums and Axiom agreee
+dd:=complexNormalize cc
+--R
+--R   (4)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.348~~~~~$\displaystyle
@@ -201,7 +324,7 @@ $$
 <<*>>=
 )clear all
 
---S 10 of 30
+--S 24
 aa:=integrate(x*sin(a*x)^2,x)
 --R 
 --R
@@ -212,6 +335,38 @@ aa:=integrate(x*sin(a*x)^2,x)
 --R                            4a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 25
+bb:=x^2/4-(x*sin(2*a*x))/(4*a)-cos(2*a*x)/(8*a^2)
+--R
+--R                                         2 2
+--R        - 2a x sin(2a x) - cos(2a x) + 2a x
+--R   (2)  ------------------------------------
+--R                           2
+--R                         8a
+--R                                                     Type: Expression Integer
+--E
+
+--S 26
+cc:=aa-bb
+--R
+--R                                                                      2
+--R        2a x sin(2a x) - 4a x cos(a x)sin(a x) + cos(2a x) - 2cos(a x)
+--R   (3)  ---------------------------------------------------------------
+--R                                        2
+--R                                      8a
+--R                                                     Type: Expression Integer
+--E
+
+--S 27     14:348 Schaums and Axiom differ by a constant
+dd:=complexNormalize cc
+--R
+--R           1
+--R   (4)  - ---
+--R            2
+--R          8a
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.349~~~~~$\displaystyle
@@ -222,7 +377,7 @@ $$
 <<*>>=
 )clear all
 
---S 11 of 30
+--S 28
 aa:=integrate(sin(a*x)^3,x)
 --R 
 --R
@@ -232,6 +387,23 @@ aa:=integrate(sin(a*x)^3,x)
 --R                  3a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 29
+bb:=-cos(a*x)/a+cos(a*x)^3/(3*a)
+--R
+--R                3
+--R        cos(a x)  - 3cos(a x)
+--R   (2)  ---------------------
+--R                  3a
+--R                                                     Type: Expression Integer
+--E
+
+--S 30     14:349 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.350~~~~~$\displaystyle
@@ -242,7 +414,7 @@ $$
 <<*>>=
 )clear all
 
---S 12 of 30
+--S 31
 aa:=integrate(sin(a*x)^4,x)
 --R 
 --R
@@ -252,6 +424,32 @@ aa:=integrate(sin(a*x)^4,x)
 --R                           8a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 32
+bb:=(3*x)/8-sin(2*a*x)/(4*a)+sin(4*a*x)/(32*a)
+--R
+--R        sin(4a x) - 8sin(2a x) + 12a x
+--R   (2)  ------------------------------
+--R                      32a
+--R                                                     Type: Expression Integer
+--E
+
+--S 33
+cc:=aa-bb
+--R
+--R                                             3
+--R        - sin(4a x) + 8sin(2a x) + (8cos(a x)  - 20cos(a x))sin(a x)
+--R   (3)  ------------------------------------------------------------
+--R                                     32a
+--R                                                     Type: Expression Integer
+--E
+
+--S 34     14:350 Schaums and Axiom agree
+dd:=complexNormalize cc
+--R
+--R   (4)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.351~~~~~$\displaystyle
@@ -262,7 +460,7 @@ $$
 <<*>>=
 )clear all
 
---S 13 of 30
+--S 35
 aa:=integrate(1/sin(a*x)^2,x)
 --R 
 --R
@@ -271,6 +469,31 @@ aa:=integrate(1/sin(a*x)^2,x)
 --R          a sin(a x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 36
+bb:=-1/a*cot(a*x)
+--R
+--R          cot(a x)
+--R   (2)  - --------
+--R              a
+--R                                                     Type: Expression Integer
+--E
+
+--S 37
+cc:=aa-bb
+--R
+--R        cot(a x)sin(a x) - cos(a x)
+--R   (3)  ---------------------------
+--R                 a sin(a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 38     14:351 Schaums and Axiom agree
+dd:=complexNormalize cc
+--R
+--R   (4)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.352~~~~~$\displaystyle
@@ -281,7 +504,7 @@ $$
 <<*>>=
 )clear all
 
---S 14 of 30
+--S 39
 aa:=integrate(1/sin(a*x)^3,x)
 --R 
 --R
@@ -293,6 +516,66 @@ aa:=integrate(1/sin(a*x)^3,x)
 --R                     2a cos(a x)  - 2a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 40
+bb:=-cos(a*x)/(2*a*sin(a*x)^2)+1/(2*a)*log(tan((a*x)/2))
+--R
+--R                2        a x
+--R        sin(a x) log(tan(---)) - cos(a x)
+--R                          2
+--R   (2)  ---------------------------------
+--R                              2
+--R                   2a sin(a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 41
+cc:=aa-bb
+--R
+--R   (3)
+--R                  2             2        a x
+--R       (- cos(a x)  + 1)sin(a x) log(tan(---))
+--R                                          2
+--R     + 
+--R                2             2      sin(a x)                      2           3
+--R       (cos(a x)  - 1)sin(a x) log(------------) + cos(a x)sin(a x)  + cos(a x)
+--R                                   cos(a x) + 1
+--R     + 
+--R       - cos(a x)
+--R  /
+--R                 2              2
+--R     (2a cos(a x)  - 2a)sin(a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 42
+dd:=expandLog cc
+--R
+--R   (4)
+--R                  2             2        a x
+--R       (- cos(a x)  + 1)sin(a x) log(tan(---))
+--R                                          2
+--R     + 
+--R                2             2
+--R       (cos(a x)  - 1)sin(a x) log(sin(a x))
+--R     + 
+--R                  2             2                                    2
+--R       (- cos(a x)  + 1)sin(a x) log(cos(a x) + 1) + cos(a x)sin(a x)
+--R     + 
+--R               3
+--R       cos(a x)  - cos(a x)
+--R  /
+--R                 2              2
+--R     (2a cos(a x)  - 2a)sin(a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 43     14:352 Schaums and Axiom agree
+ee:=complexNormalize dd
+--R
+--R   (5)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.353~~~~~$\displaystyle
@@ -303,7 +586,7 @@ $$
 <<*>>=
 )clear all
 
---S 15 of 30
+--S 44
 aa:=integrate(sin(p*x)*sin(q*x),x)
 --R 
 --R
@@ -312,7 +595,30 @@ aa:=integrate(sin(p*x)*sin(q*x),x)
 --R                         2    2
 --R                        q  - p
 --R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 45
+bb:=(sin(p-q)*x)/(2*(p-q))-(sin(p+q)*x)/(2*(p+q))
+--R
+--R        (- q + p)x sin(q + p) + (q + p)x sin(q - p)
+--R   (2)  -------------------------------------------
+--R                           2     2
+--R                         2q  - 2p
+--R                                                     Type: Expression Integer
 --E 
+
+--S 46     14:353 Axiom cannot simplify this expression
+cc:=aa-bb
+--R
+--R   (3)
+--R       2p cos(p x)sin(q x) - 2q cos(q x)sin(p x) + (q - p)x sin(q + p)
+--R     + 
+--R       (- q - p)x sin(q - p)
+--R  /
+--R       2     2
+--R     2q  - 2p
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.354~~~~~$\displaystyle
@@ -323,7 +629,7 @@ $$
 <<*>>=
 )clear all
 
---S 16 of 30
+--S 47
 aa:=integrate(1/(1-sin(a*x)),x)
 --R 
 --R
@@ -331,7 +637,38 @@ aa:=integrate(1/(1-sin(a*x)),x)
 --R   (1)  ---------------------------
 --R        a sin(a x) - a cos(a x) - a
 --R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 48
+bb:=1/a*tan(%pi/4+(a*x)/2)
+--R
+--R            2a x + %pi
+--R        tan(----------)
+--R                 4
+--R   (2)  ---------------
+--R               a
+--R                                                     Type: Expression Integer
 --E 
+
+--S 49
+cc:=aa-bb
+--R
+--R                                       2a x + %pi
+--R        (- sin(a x) + cos(a x) + 1)tan(----------) - 2cos(a x) - 2
+--R                                            4
+--R   (3)  ----------------------------------------------------------
+--R                        a sin(a x) - a cos(a x) - a
+--R                                                     Type: Expression Integer
+--E
+
+--S 50     14:354 Schaums and Axiom differ by a constant
+dd:=complexNormalize cc
+--R
+--R        1
+--R   (4)  -
+--R        a
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.355~~~~~$\displaystyle
@@ -343,7 +680,7 @@ $$
 <<*>>=
 )clear all
 
---S 17 of 30
+--S 51
 aa:=integrate(x/(1-sin(ax)),x)
 --R 
 --R
@@ -353,6 +690,35 @@ aa:=integrate(x/(1-sin(ax)),x)
 --R          2sin(ax) - 2
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 52
+bb:=x/a*tan(%pi/4+(a*x)/2)+2/a^2*log(sin(%pi/4-(a*x)/2))
+--R
+--R                   2a x - %pi             2a x + %pi
+--R        2log(- sin(----------)) + a x tan(----------)
+--R                        4                      4
+--R   (2)  ---------------------------------------------
+--R                               2
+--R                              a
+--R                                                     Type: Expression Integer
+--E
+
+--S 53     14:355 Axiom cannot simplify this expression
+cc:=aa-bb
+--R
+--R   (3)
+--R                                 2a x - %pi
+--R       (- 4sin(ax) + 4)log(- sin(----------))
+--R                                      4
+--R     + 
+--R                                  2a x + %pi     2 2
+--R       (- 2a x sin(ax) + 2a x)tan(----------) - a x
+--R                                       4
+--R  /
+--R       2            2
+--R     2a sin(ax) - 2a
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.356~~~~~$\displaystyle
@@ -363,7 +729,7 @@ $$
 <<*>>=
 )clear all
 
---S 18 of 30
+--S 54
 aa:=integrate(1/(1+sin(ax)),x)
 --R 
 --R
@@ -372,6 +738,46 @@ aa:=integrate(1/(1+sin(ax)),x)
 --R        sin(ax) + 1
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 55
+bb:=-1/a*tan(%pi/4-(a*x)/2)
+--R
+--R            2a x - %pi
+--R        tan(----------)
+--R                 4
+--R   (2)  ---------------
+--R               a
+--R                                                     Type: Expression Integer
+--E
+
+--S 56
+cc:=aa-bb
+--R
+--R                           2a x - %pi
+--R        (- sin(ax) - 1)tan(----------) + a x
+--R                                4
+--R   (3)  ------------------------------------
+--R                    a sin(ax) + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 57
+tanrule:=rule(tan(a/b) == sin(a)/cos(b))
+--R
+--R            a     sin(a)
+--R   (4)  tan(-) == ------
+--R            b     cos(b)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 58     14:356 Axiom cannot simplify this expression
+dd:=tanrule cc
+--R
+--R        (- sin(ax) - 1)sin(2a x - %pi) + a x cos(4)
+--R   (5)  -------------------------------------------
+--R                 a cos(4)sin(ax) + a cos(4)
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.357~~~~~$\displaystyle
@@ -383,7 +789,7 @@ $$
 <<*>>=
 )clear all
 
---S 19 of 30
+--S 59
 aa:=integrate(x/(1+sin(a*x)),x)
 --R 
 --R
@@ -402,6 +808,100 @@ aa:=integrate(x/(1+sin(a*x)),x)
 --R     a sin(a x) + a cos(a x) + a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 60
+bb:=-x/a*tan(%pi/4-(a*x)/2)+2/a^2*log(sin(%pi/4+(a*x)/2))
+--R
+--R                 2a x + %pi             2a x - %pi
+--R        2log(sin(----------)) + a x tan(----------)
+--R                      4                      4
+--R   (2)  -------------------------------------------
+--R                              2
+--R                             a
+--R                                                     Type: Expression Integer
+--E
+
+--S 61
+cc:=aa-bb
+--R
+--R   (3)
+--R                                      sin(a x) + cos(a x) + 1
+--R       (2sin(a x) + 2cos(a x) + 2)log(-----------------------)
+--R                                            cos(a x) + 1
+--R     + 
+--R                                            2a x + %pi
+--R       (- 2sin(a x) - 2cos(a x) - 2)log(sin(----------))
+--R                                                 4
+--R     + 
+--R                                            2
+--R       (- sin(a x) - cos(a x) - 1)log(------------)
+--R                                      cos(a x) + 1
+--R     + 
+--R                                                2a x - %pi
+--R       (- a x sin(a x) - a x cos(a x) - a x)tan(----------) + a x sin(a x)
+--R                                                     4
+--R     + 
+--R       - a x cos(a x) - a x
+--R  /
+--R      2            2            2
+--R     a sin(a x) + a cos(a x) + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 62
+dd:=expandLog cc
+--R
+--R   (4)
+--R       (2sin(a x) + 2cos(a x) + 2)log(sin(a x) + cos(a x) + 1)
+--R     + 
+--R                                            2a x + %pi
+--R       (- 2sin(a x) - 2cos(a x) - 2)log(sin(----------))
+--R                                                 4
+--R     + 
+--R       (- sin(a x) - cos(a x) - 1)log(cos(a x) + 1)
+--R     + 
+--R                                                2a x - %pi
+--R       (- a x sin(a x) - a x cos(a x) - a x)tan(----------)
+--R                                                     4
+--R     + 
+--R       (- log(2) + a x)sin(a x) + (- log(2) - a x)cos(a x) - log(2) - a x
+--R  /
+--R      2            2            2
+--R     a sin(a x) + a cos(a x) + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 63
+tanrule:=rule(tan(a/b) == sin(a)/cos(b))
+--R
+--R            a     sin(a)
+--R   (5)  tan(-) == ------
+--R            b     cos(b)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 64     14:357 Axiom cannot simplify this expression
+ee:=tanrule dd
+--R
+--R   (6)
+--R       (2cos(4)sin(a x) + 2cos(4)cos(a x) + 2cos(4))log(sin(a x) + cos(a x) + 1)
+--R     + 
+--R                                                              2a x + %pi
+--R       (- 2cos(4)sin(a x) - 2cos(4)cos(a x) - 2cos(4))log(sin(----------))
+--R                                                                   4
+--R     + 
+--R       (- cos(4)sin(a x) - cos(4)cos(a x) - cos(4))log(cos(a x) + 1)
+--R     + 
+--R       (- a x sin(a x) - a x cos(a x) - a x)sin(2a x - %pi)
+--R     + 
+--R       (- cos(4)log(2) + a x cos(4))sin(a x)
+--R     + 
+--R       (- cos(4)log(2) - a x cos(4))cos(a x) - cos(4)log(2) - a x cos(4)
+--R  /
+--R      2                  2                  2
+--R     a cos(4)sin(a x) + a cos(4)cos(a x) + a cos(4)
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.358~~~~~$\displaystyle
@@ -413,7 +913,7 @@ $$
 <<*>>=
 )clear all
 
---S 20 of 30
+--S 65
 aa:=integrate(1/(1-sin(a*x))^2,x)
 --R 
 --R
@@ -423,7 +923,76 @@ aa:=integrate(1/(1-sin(a*x))^2,x)
 --R                                                2
 --R        (3a cos(a x) + 6a)sin(a x) + 3a cos(a x)  - 3a cos(a x) - 6a
 --R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 66
+bb:=-1/(2*a)*tan(%pi/4+(a*x)/2)+1/(6*a)*tan(%pi/4+(a*x)/2)^3
+--R
+--R            2a x + %pi 3        2a x + %pi
+--R        tan(----------)  - 3tan(----------)
+--R                 4                   4
+--R   (2)  -----------------------------------
+--R                         6a
+--R                                                     Type: Expression Integer
 --E 
+
+--S 67
+cc:=aa-bb
+--R
+--R   (3)
+--R                                           2                    2a x + %pi 3
+--R       ((- cos(a x) - 2)sin(a x) - cos(a x)  + cos(a x) + 2)tan(----------)
+--R                                                                     4
+--R     + 
+--R                                           2                     2a x + %pi
+--R       ((3cos(a x) + 6)sin(a x) + 3cos(a x)  - 3cos(a x) - 6)tan(----------)
+--R                                                                      4
+--R     + 
+--R                                          2
+--R       (6cos(a x) + 6)sin(a x) + 2cos(a x)  - 8cos(a x) - 10
+--R  /
+--R                                              2
+--R     (6a cos(a x) + 12a)sin(a x) + 6a cos(a x)  - 6a cos(a x) - 12a
+--R                                                     Type: Expression Integer
+--E
+
+--S 68
+tanrule:=rule(tan(a/b) == sin(a)/cos(b))
+--R
+--R            a     sin(a)
+--R   (4)  tan(-) == ------
+--R            b     cos(b)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 69     14:358 Axiom cannot simplify this expression
+dd:=tanrule cc
+--R
+--R   (5)
+--R                                           2                               3
+--R       ((- cos(a x) - 2)sin(a x) - cos(a x)  + cos(a x) + 2)sin(2a x + %pi)
+--R     + 
+--R                   2                  2                   2        2
+--R           (3cos(4) cos(a x) + 6cos(4) )sin(a x) + 3cos(4) cos(a x)
+--R         + 
+--R                    2                  2
+--R           - 3cos(4) cos(a x) - 6cos(4)
+--R      *
+--R         sin(2a x + %pi)
+--R     + 
+--R               3                  3                   3        2
+--R       (6cos(4) cos(a x) + 6cos(4) )sin(a x) + 2cos(4) cos(a x)
+--R     + 
+--R                3                   3
+--R       - 8cos(4) cos(a x) - 10cos(4)
+--R  /
+--R                 3                     3                     3        2
+--R       (6a cos(4) cos(a x) + 12a cos(4) )sin(a x) + 6a cos(4) cos(a x)
+--R     + 
+--R                  3                     3
+--R       - 6a cos(4) cos(a x) - 12a cos(4)
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.359~~~~~$\displaystyle
@@ -435,7 +1004,7 @@ $$
 <<*>>=
 )clear all
 
---S 21 of 30
+--S 70
 aa:=integrate(1/(1+sin(a*x))^2,x)
 --R 
 --R
@@ -445,7 +1014,38 @@ aa:=integrate(1/(1+sin(a*x))^2,x)
 --R                                                2
 --R        (3a cos(a x) + 6a)sin(a x) - 3a cos(a x)  + 3a cos(a x) + 6a
 --R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 71
+bb:=-1/(2*a)*tan(%pi/4-(a*x)/2)-1/(6*a)*tan(%pi/4-(a*x)/2)^3
+--R
+--R            2a x - %pi 3        2a x - %pi
+--R        tan(----------)  + 3tan(----------)
+--R                 4                   4
+--R   (2)  -----------------------------------
+--R                         6a
+--R                                                     Type: Expression Integer
 --E 
+
+--S 72     14:359 Axiom cannot simplify this expression
+cc:=aa-bb
+--R
+--R   (3)
+--R                                           2                    2a x - %pi 3
+--R       ((- cos(a x) - 2)sin(a x) + cos(a x)  - cos(a x) - 2)tan(----------)
+--R                                                                     4
+--R     + 
+--R                                             2                     2a x - %pi
+--R       ((- 3cos(a x) - 6)sin(a x) + 3cos(a x)  - 3cos(a x) - 6)tan(----------)
+--R                                                                        4
+--R     + 
+--R                                            2
+--R       (- 6cos(a x) - 6)sin(a x) + 2cos(a x)  - 8cos(a x) - 10
+--R  /
+--R                                              2
+--R     (6a cos(a x) + 12a)sin(a x) - 6a cos(a x)  + 6a cos(a x) + 12a
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.360~~~~~$\displaystyle
@@ -466,7 +1066,7 @@ $$
 <<*>>=
 )clear all
 
---S 22 of 30
+--S 73
 aa:=integrate(1/(p+q*sin(a*x)),x)
 --R 
 --R
@@ -498,6 +1098,156 @@ aa:=integrate(1/(p+q*sin(a*x)),x)
 --R                        a\|- q  + p
 --R                                     Type: Union(List Expression Integer,...)
 --E 
+
+--S 74
+bb1:=2/(a*sqrt(p^2-q^2))*atan((p*tan((a*x)/2+q))/sqrt(p^2-q^2))
+--R
+--R                    a x + 2q
+--R              p tan(--------)
+--R                        2
+--R        2atan(---------------)
+--R                 +---------+
+--R                 |   2    2
+--R                \|- q  + p
+--R   (2)  ----------------------
+--R               +---------+
+--R               |   2    2
+--R             a\|- q  + p
+--R                                                     Type: Expression Integer
+--E
+
+--S 75
+bb2:=1/(a*sqrt(q^2-p^2))*log((p*tan((a*x)/2+q-sqrt(q^2-p^2)))/(p*tan((a*x)/2+q+sqrt(q^2-p^2))))
+--R
+--R                    +-------+
+--R                    | 2    2
+--R                  2\|q  - p   - a x - 2q
+--R              tan(----------------------)
+--R                             2
+--R        log(- ---------------------------)
+--R                    +-------+
+--R                    | 2    2
+--R                  2\|q  - p   + a x + 2q
+--R              tan(----------------------)
+--R                             2
+--R   (3)  ----------------------------------
+--R                      +-------+
+--R                      | 2    2
+--R                    a\|q  - p
+--R                                                     Type: Expression Integer
+--E
+
+--S 76
+cc1:=aa.1-bb1
+--R
+--R   (4)
+--R          +---------+
+--R          |   2    2
+--R         \|- q  + p
+--R      *
+--R         log
+--R                                                        +-------+
+--R                                  2    2             2  | 2    2
+--R                (p q sin(a x) + (q  - p )cos(a x) + q )\|q  - p
+--R              + 
+--R                      2    3                3    2              3    2
+--R                (- p q  + p )sin(a x) + (- q  + p q)cos(a x) - q  + p q
+--R           /
+--R              q sin(a x) + p
+--R     + 
+--R                               a x + 2q
+--R           +-------+     p tan(--------)
+--R           | 2    2                2
+--R       - 2\|q  - p  atan(---------------)
+--R                            +---------+
+--R                            |   2    2
+--R                           \|- q  + p
+--R  /
+--R       +---------+ +-------+
+--R       |   2    2  | 2    2
+--R     a\|- q  + p  \|q  - p
+--R                                                     Type: Expression Integer
+--E
+
+--S 77
+cc2:=aa.2-bb1
+--R
+--R   (5)
+--R                                         +---------+                a x + 2q
+--R                                         |   2    2           p tan(--------)
+--R           (p sin(a x) + q cos(a x) + q)\|- q  + p                      2
+--R   - 2atan(-----------------------------------------) - 2atan(---------------)
+--R                    2    2             2    2                    +---------+
+--R                  (q  - p )cos(a x) + q  - p                     |   2    2
+--R                                                                \|- q  + p
+--R   ---------------------------------------------------------------------------
+--R                                    +---------+
+--R                                    |   2    2
+--R                                  a\|- q  + p
+--R                                                     Type: Expression Integer
+--E
+
+--S 78
+cc3:=aa.1-bb2
+--R
+--R   (6)
+--R                     +-------+
+--R                     | 2    2
+--R                   2\|q  - p   - a x - 2q
+--R               tan(----------------------)
+--R                              2
+--R       - log(- ---------------------------)
+--R                     +-------+
+--R                     | 2    2
+--R                   2\|q  - p   + a x + 2q
+--R               tan(----------------------)
+--R                              2
+--R     + 
+--R       log
+--R                                                      +-------+
+--R                                2    2             2  | 2    2
+--R              (p q sin(a x) + (q  - p )cos(a x) + q )\|q  - p
+--R            + 
+--R                    2    3                3    2              3    2
+--R              (- p q  + p )sin(a x) + (- q  + p q)cos(a x) - q  + p q
+--R         /
+--R            q sin(a x) + p
+--R  /
+--R       +-------+
+--R       | 2    2
+--R     a\|q  - p
+--R                                                     Type: Expression Integer
+--E
+
+--S 79     14:360 Axiom cannot simplify these equations
+cc4:=aa.2-bb2
+--R
+--R   (7)
+--R                                 +-------+
+--R                                 | 2    2
+--R                               2\|q  - p   - a x - 2q
+--R          +---------+      tan(----------------------)
+--R          |   2    2                      2
+--R       - \|- q  + p  log(- ---------------------------)
+--R                                 +-------+
+--R                                 | 2    2
+--R                               2\|q  - p   + a x + 2q
+--R                           tan(----------------------)
+--R                                          2
+--R     + 
+--R                                                       +---------+
+--R           +-------+                                   |   2    2
+--R           | 2    2      (p sin(a x) + q cos(a x) + q)\|- q  + p
+--R       - 2\|q  - p  atan(-----------------------------------------)
+--R                                  2    2             2    2
+--R                                (q  - p )cos(a x) + q  - p
+--R  /
+--R       +---------+ +-------+
+--R       |   2    2  | 2    2
+--R     a\|- q  + p  \|q  - p
+--R                                                     Type: Expression Integer
+--E
+
 @
 
 \section{\cite{1}:14.361~~~~~$\displaystyle
@@ -509,7 +1259,7 @@ $$
 <<*>>=
 )clear all
 
---S 23 of 30
+--S 80
 aa:=integrate(1/(p+q*sin(a*x))^2,x)
 --R 
 --R
@@ -554,6 +1304,206 @@ aa:=integrate(1/(p+q*sin(a*x))^2,x)
 --R     ]
 --R                                     Type: Union(List Expression Integer,...)
 --E 
+
+--S 81
+t1:=integrate(1/(p+q*sin(a*x)),x)
+--R
+--R   (2)
+--R   [
+--R       log
+--R                                                      +-------+
+--R                                2    2             2  | 2    2
+--R              (p q sin(a x) + (q  - p )cos(a x) + q )\|q  - p
+--R            + 
+--R                    2    3                3    2              3    2
+--R              (- p q  + p )sin(a x) + (- q  + p q)cos(a x) - q  + p q
+--R         /
+--R            q sin(a x) + p
+--R    /
+--R         +-------+
+--R         | 2    2
+--R       a\|q  - p
+--R     ,
+--R                                          +---------+
+--R                                          |   2    2
+--R            (p sin(a x) + q cos(a x) + q)\|- q  + p
+--R      2atan(-----------------------------------------)
+--R                     2    2             2    2
+--R                   (q  - p )cos(a x) + q  - p
+--R    - ------------------------------------------------]
+--R                          +---------+
+--R                          |   2    2
+--R                        a\|- q  + p
+--R                                     Type: Union(List Expression Integer,...)
+--E
+
+--S 82
+bb1:=(q*cos(a*x))/(a*(p^2-q^2)*(p+q*sin(a*x)))+p/(p^2-q^2)*t1.1
+--R
+--R   (3)
+--R                            2
+--R         (- p q sin(a x) - p )
+--R      *
+--R         log
+--R                                                        +-------+
+--R                                  2    2             2  | 2    2
+--R                (p q sin(a x) + (q  - p )cos(a x) + q )\|q  - p
+--R              + 
+--R                      2    3                3    2              3    2
+--R                (- p q  + p )sin(a x) + (- q  + p q)cos(a x) - q  + p q
+--R           /
+--R              q sin(a x) + p
+--R     + 
+--R                    +-------+
+--R                    | 2    2
+--R       - q cos(a x)\|q  - p
+--R  /
+--R                                              +-------+
+--R          3      2                  2      3  | 2    2
+--R     ((a q  - a p q)sin(a x) + a p q  - a p )\|q  - p
+--R                                                     Type: Expression Integer
+--E
+
+--S 83
+bb2:=(q*cos(a*x))/(a*(p^2-q^2)*(p+q*sin(a*x)))+p/(p^2-q^2)*t1.2
+--R
+--R   (4)
+--R                                                               +---------+
+--R                                                               |   2    2
+--R                          2      (p sin(a x) + q cos(a x) + q)\|- q  + p
+--R       (2p q sin(a x) + 2p )atan(-----------------------------------------)
+--R                                          2    2             2    2
+--R                                        (q  - p )cos(a x) + q  - p
+--R     + 
+--R                    +---------+
+--R                    |   2    2
+--R       - q cos(a x)\|- q  + p
+--R  /
+--R                                              +---------+
+--R          3      2                  2      3  |   2    2
+--R     ((a q  - a p q)sin(a x) + a p q  - a p )\|- q  + p
+--R                                                     Type: Expression Integer
+--E
+
+--S 84
+cc1:=aa.1-bb1
+--R
+--R   (5)
+--R          2
+--R         p
+--R      *
+--R         log
+--R                                                        +-------+
+--R                                  2    2             2  | 2    2
+--R                (p q sin(a x) + (q  - p )cos(a x) + q )\|q  - p
+--R              + 
+--R                    2    3              3    2              3    2
+--R                (p q  - p )sin(a x) + (q  - p q)cos(a x) + q  - p q
+--R           /
+--R              q sin(a x) + p
+--R     + 
+--R          2
+--R         p
+--R      *
+--R         log
+--R                                                        +-------+
+--R                                  2    2             2  | 2    2
+--R                (p q sin(a x) + (q  - p )cos(a x) + q )\|q  - p
+--R              + 
+--R                      2    3                3    2              3    2
+--R                (- p q  + p )sin(a x) + (- q  + p q)cos(a x) - q  + p q
+--R           /
+--R              q sin(a x) + p
+--R     + 
+--R           +-------+
+--R           | 2    2
+--R       - q\|q  - p
+--R  /
+--R                     +-------+
+--R           2      3  | 2    2
+--R     (a p q  - a p )\|q  - p
+--R                                                     Type: Expression Integer
+--E
+
+--S 85
+cc2:=aa.2-bb1
+--R
+--R   (6)
+--R            +---------+
+--R          2 |   2    2
+--R         p \|- q  + p
+--R      *
+--R         log
+--R                                                        +-------+
+--R                                  2    2             2  | 2    2
+--R                (p q sin(a x) + (q  - p )cos(a x) + q )\|q  - p
+--R              + 
+--R                      2    3                3    2              3    2
+--R                (- p q  + p )sin(a x) + (- q  + p q)cos(a x) - q  + p q
+--R           /
+--R              q sin(a x) + p
+--R     + 
+--R                                                       +---------+
+--R           +-------+                                   |   2    2
+--R         2 | 2    2      (p sin(a x) + q cos(a x) + q)\|- q  + p
+--R       2p \|q  - p  atan(-----------------------------------------)
+--R                                  2    2             2    2
+--R                                (q  - p )cos(a x) + q  - p
+--R     + 
+--R           +---------+ +-------+
+--R           |   2    2  | 2    2
+--R       - q\|- q  + p  \|q  - p
+--R  /
+--R                     +---------+ +-------+
+--R           2      3  |   2    2  | 2    2
+--R     (a p q  - a p )\|- q  + p  \|q  - p
+--R                                                     Type: Expression Integer
+--E
+
+--S 86
+cc3:=aa.1-bb2
+--R
+--R   (7)
+--R            +---------+
+--R          2 |   2    2
+--R         p \|- q  + p
+--R      *
+--R         log
+--R                                                        +-------+
+--R                                  2    2             2  | 2    2
+--R                (p q sin(a x) + (q  - p )cos(a x) + q )\|q  - p
+--R              + 
+--R                    2    3              3    2              3    2
+--R                (p q  - p )sin(a x) + (q  - p q)cos(a x) + q  - p q
+--R           /
+--R              q sin(a x) + p
+--R     + 
+--R                                                         +---------+
+--R             +-------+                                   |   2    2
+--R           2 | 2    2      (p sin(a x) + q cos(a x) + q)\|- q  + p
+--R       - 2p \|q  - p  atan(-----------------------------------------)
+--R                                    2    2             2    2
+--R                                  (q  - p )cos(a x) + q  - p
+--R     + 
+--R           +---------+ +-------+
+--R           |   2    2  | 2    2
+--R       - q\|- q  + p  \|q  - p
+--R  /
+--R                     +---------+ +-------+
+--R           2      3  |   2    2  | 2    2
+--R     (a p q  - a p )\|- q  + p  \|q  - p
+--R                                                     Type: Expression Integer
+--E
+
+--S 87     14:361 Schaums and Axiom differ by a constant
+cc4:=aa.2-bb2
+--R
+--R                q
+--R   (8)  - -------------
+--R               2      3
+--R          a p q  - a p
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.362~~~~~$\displaystyle
@@ -564,7 +1514,7 @@ $$
 <<*>>=
 )clear all
 
---S 24 of 30
+--S 88
 aa:=integrate(1/(p^2+a^2*sin(a*x)),x)
 --R 
 --R
@@ -597,6 +1547,76 @@ aa:=integrate(1/(p^2+a^2*sin(a*x)),x)
 --R                      a\|p  - a
 --R                                     Type: Union(List Expression Integer,...)
 --E 
+
+--S 89
+bb:=1/(a*p*sqrt(p^2+q^2))*atan((sqrt(p^2+q^2)*tan(a*x))/p)
+--R
+--R                      +-------+
+--R                      | 2    2
+--R             tan(a x)\|q  + p
+--R        atan(------------------)
+--R                      p
+--R   (2)  ------------------------
+--R                  +-------+
+--R                  | 2    2
+--R              a p\|q  + p
+--R                                                     Type: Expression Integer
+--E
+
+--S 90
+cc1:=aa.1-bb
+--R
+--R   (3)
+--R           +-------+
+--R           | 2    2
+--R         p\|q  + p
+--R      *
+--R         log
+--R                                                          +---------+
+--R                  2 2               4    4             4  |   4    4
+--R                (a p sin(a x) + (- p  + a )cos(a x) + a )\|- p  + a
+--R              + 
+--R                  6    4 2              2 4    6             2 4    6
+--R                (p  - a p )sin(a x) + (a p  - a )cos(a x) + a p  - a
+--R           /
+--R               2            2
+--R              a sin(a x) + p
+--R     + 
+--R                                   +-------+
+--R          +---------+              | 2    2
+--R          |   4    4      tan(a x)\|q  + p
+--R       - \|- p  + a  atan(------------------)
+--R                                   p
+--R  /
+--R         +---------+ +-------+
+--R         |   4    4  | 2    2
+--R     a p\|- p  + a  \|q  + p
+--R                                                     Type: Expression Integer
+--E
+
+--S 91     14:362 Axiom cannot simplify this expression
+cc2:=aa.2-bb
+--R
+--R   (4)
+--R                                 +-------+
+--R          +-------+              | 2    2
+--R          | 4    4      tan(a x)\|q  + p
+--R       - \|p  - a  atan(------------------)
+--R                                 p
+--R     + 
+--R                                                       +-------+
+--R          +-------+       2            2            2  | 4    4
+--R          | 2    2      (p sin(a x) + a cos(a x) + a )\|p  - a
+--R       2p\|q  + p  atan(----------------------------------------)
+--R                                 4    4             4    4
+--R                               (p  - a )cos(a x) + p  - a
+--R  /
+--R         +-------+ +-------+
+--R         | 4    4  | 2    2
+--R     a p\|p  - a  \|q  + p
+--R                                                     Type: Expression Integer
+--E
+
 @
 
 \section{\cite{1}:14.363~~~~~$\displaystyle
@@ -616,7 +1636,7 @@ $$
 <<*>>=
 )clear all
 
---S 25 of 30
+--S 92
 aa:=integrate(1/(p^2-q^2*sin(a*x)^2),x)
 --R 
 --R
@@ -658,6 +1678,154 @@ aa:=integrate(1/(p^2-q^2*sin(a*x)^2),x)
 --R     ]
 --R                                     Type: Union(List Expression Integer,...)
 --E 
+
+--S 93
+bb1:=1/(a*p*sqrt(p^2-q^2))*atan((sqrt(p^2-q^2)*tan(a*x))/p)
+--R
+--R                      +---------+
+--R                      |   2    2
+--R             tan(a x)\|- q  + p
+--R        atan(--------------------)
+--R                       p
+--R   (2)  --------------------------
+--R                  +---------+
+--R                  |   2    2
+--R              a p\|- q  + p
+--R                                                     Type: Expression Integer
+--E
+
+--S 94
+bb2:=1/(2*a*p*sqrt(q^2-p^2))*log((sqrt(q^2-p^2)*tan(a*x)+p)/(sqrt(q^2-p^2)*tan(a*x)-p))
+--R
+--R                     +-------+
+--R                     | 2    2
+--R            tan(a x)\|q  - p   + p
+--R        log(----------------------)
+--R                     +-------+
+--R                     | 2    2
+--R            tan(a x)\|q  - p   - p
+--R   (3)  ---------------------------
+--R                    +-------+
+--R                    | 2    2
+--R               2a p\|q  - p
+--R                                                     Type: Expression Integer
+--E
+
+--S 95
+cc1:=aa.1-bb1
+--R
+--R   (4)
+--R          +---------+
+--R          |   2    2
+--R         \|- q  + p
+--R      *
+--R         log
+--R                                                  +-------+
+--R                     2     2         2    2    2  | 2    2
+--R                ((- q  + 2p )cos(a x)  + q  - p )\|q  - p
+--R              + 
+--R                     2     3
+--R                (2p q  - 2p )cos(a x)sin(a x)
+--R           /
+--R               2        2    2    2
+--R              q cos(a x)  - q  + p
+--R     + 
+--R                                  +---------+
+--R           +-------+              |   2    2
+--R           | 2    2      tan(a x)\|- q  + p
+--R       - 2\|q  - p  atan(--------------------)
+--R                                   p
+--R  /
+--R          +---------+ +-------+
+--R          |   2    2  | 2    2
+--R     2a p\|- q  + p  \|q  - p
+--R                                                     Type: Expression Integer
+--E
+
+--S 96
+cc2:=aa.2-bb1
+--R
+--R   (5)
+--R                       +---------+                         +---------+
+--R                       |   2    2                          |   2    2
+--R              tan(a x)\|- q  + p                p sin(a x)\|- q  + p
+--R       - atan(--------------------) - atan(-------------------------------)
+--R                        p                     2     2              2     2
+--R                                           (2q  - 2p )cos(a x) + 2q  - 2p
+--R     + 
+--R                    2    2              2     2
+--R                ((2q  - p )cos(a x) + 2q  - 2p )sin(a x)
+--R       - atan(-------------------------------------------)
+--R                                              +---------+
+--R                         2                    |   2    2
+--R              (p cos(a x)  + 2p cos(a x) + p)\|- q  + p
+--R  /
+--R         +---------+
+--R         |   2    2
+--R     a p\|- q  + p
+--R                                                     Type: Expression Integer
+--E
+
+--S 97
+cc3:=aa.1-bb2
+--R
+--R   (6)
+--R                      +-------+
+--R                      | 2    2
+--R             tan(a x)\|q  - p   + p
+--R       - log(----------------------)
+--R                      +-------+
+--R                      | 2    2
+--R             tan(a x)\|q  - p   - p
+--R     + 
+--R       log
+--R                                                +-------+
+--R                   2     2         2    2    2  | 2    2
+--R              ((- q  + 2p )cos(a x)  + q  - p )\|q  - p
+--R            + 
+--R                   2     3
+--R              (2p q  - 2p )cos(a x)sin(a x)
+--R         /
+--R             2        2    2    2
+--R            q cos(a x)  - q  + p
+--R  /
+--R          +-------+
+--R          | 2    2
+--R     2a p\|q  - p
+--R                                                     Type: Expression Integer
+--E
+
+--S 98     14:363 Axiom cannot simplify this expression
+cc4:=aa.2-bb2
+--R
+--R   (7)
+--R                                  +-------+
+--R          +---------+             | 2    2
+--R          |   2    2     tan(a x)\|q  - p   + p
+--R       - \|- q  + p  log(----------------------)
+--R                                  +-------+
+--R                                  | 2    2
+--R                         tan(a x)\|q  - p   - p
+--R     + 
+--R                                         +---------+
+--R           +-------+                     |   2    2
+--R           | 2    2           p sin(a x)\|- q  + p
+--R       - 2\|q  - p  atan(-------------------------------)
+--R                            2     2              2     2
+--R                         (2q  - 2p )cos(a x) + 2q  - 2p
+--R     + 
+--R           +-------+           2    2              2     2
+--R           | 2    2        ((2q  - p )cos(a x) + 2q  - 2p )sin(a x)
+--R       - 2\|q  - p  atan(-------------------------------------------)
+--R                                                         +---------+
+--R                                    2                    |   2    2
+--R                         (p cos(a x)  + 2p cos(a x) + p)\|- q  + p
+--R  /
+--R          +---------+ +-------+
+--R          |   2    2  | 2    2
+--R     2a p\|- q  + p  \|q  - p
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.364~~~~~$\displaystyle
@@ -669,7 +1837,7 @@ $$
 <<*>>=
 )clear all
 
---S 26 of 30
+--S 99     14:364 Axiom cannot compute this integral
 aa:=integrate(x^m*sin(a*x),x)
 --R 
 --R
@@ -689,7 +1857,7 @@ $$
 <<*>>=
 )clear all
 
---S 26 of 30
+--S 100    14:365 Axiom cannot compute this integral
 aa:=integrate(sin(a*x)/x^n,x)
 --R 
 --R
@@ -710,7 +1878,7 @@ $$
 <<*>>=
 )clear all
 
---S 28 of 30
+--S 101    14:366 Axiom cannot compute this integral
 aa:=integrate(sin(a*x)^n,x)
 --R 
 --R
@@ -731,7 +1899,7 @@ $$
 <<*>>=
 )clear all
 
---S 29 of 30
+--S 102    14:367 Axiom cannot compute this integral
 aa:=integrate(1/(sin(a*x))^n,x)
 --R 
 --R
@@ -739,7 +1907,7 @@ aa:=integrate(1/(sin(a*x))^n,x)
 --R         ++       1
 --I   (1)   |   ---------- d%I
 --R        ++            n
---i             sin(%I a)
+--I             sin(%I a)
 --R                                          Type: Union(Expression Integer,...)
 --E 
 @
@@ -754,7 +1922,7 @@ $$
 <<*>>=
 )clear all
 
---S 30 of 30
+--S 103    14:368 Axiom cannot compute this integral
 aa:=integrate(x/sin(a*x)^n,x)
 --R 
 --R
diff --git a/src/input/schaum18.input.pamphlet b/src/input/schaum18.input.pamphlet
index 3cb4766..95fceae 100644
--- a/src/input/schaum18.input.pamphlet
+++ b/src/input/schaum18.input.pamphlet
@@ -18,7 +18,7 @@ $$
 )set message auto off
 )clear all
 
---S 1 of 30
+--S 1
 aa:=integrate(cos(a*x),x)
 --R 
 --R
@@ -27,6 +27,22 @@ aa:=integrate(cos(a*x),x)
 --R            a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 2
+bb:=sin(a*x)/a
+--R
+--R        sin(a x)
+--R   (2)  --------
+--R            a
+--R                                                     Type: Expression Integer
+--E
+
+--S 3      14:369 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.370~~~~~$\displaystyle
@@ -37,7 +53,7 @@ $$
 <<*>>=
 )clear all
 
---S 2 of 30
+--S 4
 aa:=integrate(x*cos(a*x),x)
 --R 
 --R
@@ -47,6 +63,23 @@ aa:=integrate(x*cos(a*x),x)
 --R                   a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 5
+bb:=cos(a*x)/a^2+(x*sin(a*x))/a
+--R
+--R        a x sin(a x) + cos(a x)
+--R   (2)  -----------------------
+--R                    2
+--R                   a
+--R                                                     Type: Expression Integer
+--E
+
+--S 6      14:370 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.371~~~~~$\displaystyle
@@ -57,7 +90,7 @@ $$
 <<*>>=
 )clear all
 
---S 3 of 30
+--S 7
 aa:=integrate(x^2*cos(a*x),x)
 --R 
 --R
@@ -68,6 +101,24 @@ aa:=integrate(x^2*cos(a*x),x)
 --R                        a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 8
+bb:=(2*x)/a^2*cos(a*x)+(x^2/a-2/a^3)*sin(a*x)
+--R
+--R          2 2
+--R        (a x  - 2)sin(a x) + 2a x cos(a x)
+--R   (2)  ----------------------------------
+--R                         3
+--R                        a
+--R                                                     Type: Expression Integer
+--E
+
+--S 9      14:371 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.372~~~~~$\displaystyle
@@ -79,7 +130,7 @@ $$
 <<*>>=
 )clear all
 
---S 4 of 30
+--S 10
 aa:=integrate(x^3*cos(a*x),x)
 --R 
 --R
@@ -90,6 +141,24 @@ aa:=integrate(x^3*cos(a*x),x)
 --R                             a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 11
+bb:=((3*x^2)/a^2-6/a^4)*cos(a*x)+(x^3/a-(6*x)/a^3)*sin(a*x)
+--R
+--R          3 3                      2 2
+--R        (a x  - 6a x)sin(a x) + (3a x  - 6)cos(a x)
+--R   (2)  -------------------------------------------
+--R                              4
+--R                             a
+--R                                                     Type: Expression Integer
+--E
+
+--S 12     14:372 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.373~~~~~$\displaystyle
@@ -101,7 +170,7 @@ $$
 <<*>>=
 )clear all
 
---S 5 of 30
+--S 13     14:373 Schaums and Axiom agree by definition
 aa:=integrate(cos(x)/x,x)
 --R 
 --R
@@ -118,7 +187,7 @@ $$
 <<*>>=
 )clear all
 
---S 6 of 30
+--S 14     14:374 Axiom cannot compute this integral
 aa:=integrate(cos(a*x)/x^2,x)
 --R 
 --R
@@ -140,7 +209,7 @@ $$
 <<*>>=
 )clear all
 
---S 7 of 30
+--S 15
 aa:=integrate(1/cos(a*x),x)
 --R 
 --R
@@ -151,6 +220,59 @@ aa:=integrate(1/cos(a*x),x)
 --R                                     a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 16
+bb1:=1/a*log(sec(a*x)+tan(a*x))
+--R
+--R        log(tan(a x) + sec(a x))
+--R   (2)  ------------------------
+--R                    a
+--R                                                     Type: Expression Integer
+--E
+
+--S 17
+bb2:=1/a*log(tan(%pi/4+(a*x)/2))
+--R
+--R                2a x + %pi
+--R        log(tan(----------))
+--R                     4
+--R   (3)  --------------------
+--R                  a
+--R                                                     Type: Expression Integer
+--E
+
+--S 18
+cc1:=aa-bb1
+--R
+--R   (4)
+--R                                        sin(a x) + cos(a x) + 1
+--R       - log(tan(a x) + sec(a x)) + log(-----------------------)
+--R                                              cos(a x) + 1
+--R     + 
+--R             sin(a x) - cos(a x) - 1
+--R       - log(-----------------------)
+--R                   cos(a x) + 1
+--R  /
+--R     a
+--R                                                     Type: Expression Integer
+--E
+
+--S 19     14:375 Axiom cannot simplify these expressions
+cc2:=aa-bb2
+--R
+--R   (5)
+--R                 2a x + %pi         sin(a x) + cos(a x) + 1
+--R       - log(tan(----------)) + log(-----------------------)
+--R                      4                   cos(a x) + 1
+--R     + 
+--R             sin(a x) - cos(a x) - 1
+--R       - log(-----------------------)
+--R                   cos(a x) + 1
+--R  /
+--R     a
+--R                                                     Type: Expression Integer
+--E
+
 @
 
 \section{\cite{1}:14.376~~~~~$\displaystyle
@@ -164,7 +286,7 @@ $$
 <<*>>=
 )clear all
 
---S 8 of 30
+--S 20     14:376 Axiom cannot compute this integral
 aa:=integrate(x/cos(a*x),x)
 --R 
 --R
@@ -184,7 +306,7 @@ $$
 <<*>>=
 )clear all
 
---S 9 of 30
+--S 21
 aa:=integrate(cos(a*x)^2,x)
 --R 
 --R
@@ -193,6 +315,40 @@ aa:=integrate(cos(a*x)^2,x)
 --R                  2a
 --R                                          Type: Union(Expression Integer,...)
 --E
+
+--S 22
+bb:=x/2+sin(2*a*x)/(4*a)
+--R
+--R        sin(2a x) + 2a x
+--R   (2)  ----------------
+--R               4a
+--R                                                     Type: Expression Integer
+--E
+
+--S 23
+cc:=aa-bb
+--R
+--R        - sin(2a x) + 2cos(a x)sin(a x)
+--R   (3)  -------------------------------
+--R                       4a
+--R                                                     Type: Expression Integer
+--E
+
+--S 24
+cossinrule:=rule(cos(b)*sin(a) == 1/2*(sin(a-b)+sin(a+b)))
+--R
+--I                           %S sin(b + a) - %S sin(b - a)
+--I   (4)  %S cos(b)sin(a) == -----------------------------
+--R                                         2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 25     14:377 Schaums and Axiom agree
+dd:=cossinrule cc
+--R
+--R   (5)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.378~~~~~$\displaystyle
@@ -203,7 +359,7 @@ $$
 <<*>>=
 )clear all
 
---S 10 of 30
+--S 26
 aa:=integrate(x*cos(a*x)^2,x)
 --R 
 --R
@@ -214,6 +370,87 @@ aa:=integrate(x*cos(a*x)^2,x)
 --R                           4a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 27
+bb:=x^2/4+(x*sin(2*a*x))/(4*a)+cos(2*a*x)/(8*a^2)
+--R
+--R                                       2 2
+--R        2a x sin(2a x) + cos(2a x) + 2a x
+--R   (2)  ----------------------------------
+--R                          2
+--R                        8a
+--R                                                     Type: Expression Integer
+--E
+
+--S 28
+cc:=aa-bb
+--R
+--R                                                                        2
+--R        - 2a x sin(2a x) + 4a x cos(a x)sin(a x) - cos(2a x) + 2cos(a x)
+--R   (3)  -----------------------------------------------------------------
+--R                                         2
+--R                                       8a
+--R                                                     Type: Expression Integer
+--E
+
+--S 29
+cossinrule:=rule(cos(b)*sin(a) == 1/2*(sin(a-b)+sin(a+b)))
+--R
+--I                           %T sin(b + a) - %T sin(b - a)
+--I   (4)  %T cos(b)sin(a) == -----------------------------
+--R                                         2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 30
+dd:=cossinrule cc
+--R
+--R                               2
+--R        - cos(2a x) + 2cos(a x)
+--R   (5)  ------------------------
+--R                     2
+--R                   8a
+--R                                                     Type: Expression Integer
+--E
+
+--S 31
+coscosrule:=rule(cos(a)*cos(b) == 1/2*(cos(a-b)+cos(a+b)))
+--R
+--I                           %U cos(b + a) + %U cos(b - a)
+--I   (6)  %U cos(a)cos(b) == -----------------------------
+--R                                         2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 32
+ee:=coscosrule dd
+--R
+--R                               2
+--R        - cos(2a x) + 2cos(a x)
+--R   (7)  ------------------------
+--R                     2
+--R                   8a
+--R                                                     Type: Expression Integer
+--E
+
+--S 33
+cossqrrule1:=rule(cos(a)^2 == 1/2+1/2*cos(2*a))
+--R
+--R              2    cos(2a) + 1
+--R   (8)  cos(a)  == -----------
+--R                        2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 34     14:378 Schaums and Axiom differ by a constant
+ff:=cossqrrule1 ee
+--R
+--R         1
+--R   (9)  ---
+--R          2
+--R        8a
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.379~~~~~$\displaystyle
@@ -224,7 +461,7 @@ $$
 <<*>>=
 )clear all
 
---S 11 of 30
+--S 35
 aa:=integrate(cos(a*x)^3,x)
 --R 
 --R
@@ -233,7 +470,42 @@ aa:=integrate(cos(a*x)^3,x)
 --R   (1)  -----------------------
 --R                   3a
 --R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 36
+bb:=sin(a*x)/a-sin(a*x)^3/(3*a)
+--R
+--R                  3
+--R        - sin(a x)  + 3sin(a x)
+--R   (2)  -----------------------
+--R                   3a
+--R                                                     Type: Expression Integer
 --E 
+
+--S 37
+cc:=aa-bb
+--R
+--R                3            2
+--R        sin(a x)  + (cos(a x)  - 1)sin(a x)
+--R   (3)  -----------------------------------
+--R                         3a
+--R                                                     Type: Expression Integer
+--E
+
+--S 38
+cossqrrule:=rule(cos(a)^2 == 1-sin(a)^2)
+--R
+--R              2            2
+--R   (4)  cos(a)  == - sin(a)  + 1
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 39     14:379 Schaums and Axiom agree
+dd:=cossqrrule cc
+--R
+--R   (5)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.380~~~~~$\displaystyle
@@ -244,7 +516,7 @@ $$
 <<*>>=
 )clear all
 
---S 12 of 30
+--S 40
 aa:=integrate(cos(a*x)^4,x)
 --R 
 --R
@@ -253,7 +525,26 @@ aa:=integrate(cos(a*x)^4,x)
 --R   (1)  ---------------------------------------
 --R                           8a
 --R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 41
+bb:=(3*x)/8+sin(2*a*x)/(4*a)+sin(4*a*x)/(32*a)
+--R
+--R        sin(4a x) + 8sin(2a x) + 12a x
+--R   (2)  ------------------------------
+--R                      32a
+--R                                                     Type: Expression Integer
 --E 
+
+--S 42     14:380 Axiom cannot simplify this expression
+cc:=aa-bb
+--R
+--R                                             3
+--R        - sin(4a x) - 8sin(2a x) + (8cos(a x)  + 12cos(a x))sin(a x)
+--R   (3)  ------------------------------------------------------------
+--R                                     32a
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.381~~~~~$\displaystyle
@@ -264,7 +555,7 @@ $$
 <<*>>=
 )clear all
 
---S 13 of 30
+--S 43
 aa:=integrate(1/cos(a*x)^2,x)
 --R 
 --R
@@ -272,7 +563,41 @@ aa:=integrate(1/cos(a*x)^2,x)
 --R   (1)  ----------
 --R        a cos(a x)
 --R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 44
+bb:=tan(a*x)/a
+--R
+--R        tan(a x)
+--R   (2)  --------
+--R            a
+--R                                                     Type: Expression Integer
 --E 
+
+--S 45
+cc:=aa-bb
+--R
+--R        - cos(a x)tan(a x) + sin(a x)
+--R   (3)  -----------------------------
+--R                  a cos(a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 46
+tanrule:=rule(tan(a) == sin(a)/cos(a))
+--R
+--R                  sin(a)
+--R   (4)  tan(a) == ------
+--R                  cos(a)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 47     14:381 Schaums and Axiom agree
+dd:=tanrule cc
+--R
+--R   (5)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.382~~~~~$\displaystyle
@@ -284,7 +609,7 @@ $$
 <<*>>=
 )clear all
 
---S 14 of 30
+--S 48
 aa:=integrate(1/cos(a*x)^3,x)
 --R 
 --R
@@ -300,7 +625,35 @@ aa:=integrate(1/cos(a*x)^3,x)
 --R                2
 --R     2a cos(a x)
 --R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 49
+bb:=sin(a*x)/(2*a*cos(a*x)^2)+1/(2*a)*log(tan(%pi/4+(a*x)/2))
+--R
+--R                2        2a x + %pi
+--R        cos(a x) log(tan(----------)) + sin(a x)
+--R                              4
+--R   (2)  ----------------------------------------
+--R                                 2
+--R                      2a cos(a x)
+--R                                                     Type: Expression Integer
 --E 
+
+--S 50     14:382 Axiom cannot simplify this expression
+cc:=aa-bb
+--R
+--R   (3)
+--R                 2a x + %pi         sin(a x) + cos(a x) + 1
+--R       - log(tan(----------)) + log(-----------------------)
+--R                      4                   cos(a x) + 1
+--R     + 
+--R             sin(a x) - cos(a x) - 1
+--R       - log(-----------------------)
+--R                   cos(a x) + 1
+--R  /
+--R     2a
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.383~~~~~$\displaystyle
@@ -311,7 +664,7 @@ $$
 <<*>>=
 )clear all
 
---S 15 of 30
+--S 51
 aa:=integrate(cos(p*x)*cos(q*x),x)
 --R 
 --R
@@ -320,7 +673,35 @@ aa:=integrate(cos(p*x)*cos(q*x),x)
 --R                         2    2
 --R                        q  - p
 --R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 52
+bb:=(sin(a-p)*x)/(2*(a-p))+(sin(a+p)*x)/(2*(a+p))
+--R
+--R        (p - a)x sin(p + a) + (p + a)x sin(p - a)
+--R   (2)  -----------------------------------------
+--R                          2     2
+--R                        2p  - 2a
+--R                                                     Type: Expression Integer
 --E 
+
+--S 53     14:383 Axiom cannot simplify this expression
+cc:=aa-bb
+--R
+--R   (3)
+--R          2     2                           3     2
+--R       (2p  - 2a )q cos(p x)sin(q x) + (- 2p  + 2a p)cos(q x)sin(p x)
+--R     + 
+--R                  2    3      2
+--R       ((- p + a)q  + p  - a p )x sin(p + a)
+--R     + 
+--R                  2    3      2
+--R       ((- p - a)q  + p  + a p )x sin(p - a)
+--R  /
+--R        2     2  2     4     2 2
+--R     (2p  - 2a )q  - 2p  + 2a p
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.384~~~~~$\displaystyle
@@ -331,7 +712,7 @@ $$
 <<*>>=
 )clear all
 
---S 16 of 30
+--S 54
 aa:=integrate(1/(1-cos(a*x)),x)
 --R 
 --R
@@ -340,6 +721,24 @@ aa:=integrate(1/(1-cos(a*x)),x)
 --R          a sin(a x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 55
+bb:=-1/a*cot(a*x)/2
+--R
+--R          cot(a x)
+--R   (2)  - --------
+--R             2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 56     14:384 Axiom cannot simplify this expression
+cc:=aa-bb
+--R
+--R        cot(a x)sin(a x) - 2cos(a x) - 2
+--R   (3)  --------------------------------
+--R                   2a sin(a x)
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.385~~~~~$\displaystyle
@@ -351,7 +750,7 @@ $$
 <<*>>=
 )clear all
 
---S 17 of 30
+--S 57
 aa:=integrate(x/(1-cos(ax)),x)
 --R 
 --R
@@ -361,6 +760,30 @@ aa:=integrate(x/(1-cos(ax)),x)
 --R          2cos(ax) - 2
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 58
+bb:=-x/a*cot(a*x)/2+2/a^2*log(sin((a*x)/2))
+--R
+--R                 a x
+--R        4log(sin(---)) - a x cot(a x)
+--R                  2
+--R   (2)  -----------------------------
+--R                       2
+--R                     2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 59     14:385 Axiom cannot simplify this expression
+cc:=aa-bb
+--R
+--R                                a x                                    2 2
+--R        (- 4cos(ax) + 4)log(sin(---)) + (a x cos(ax) - a x)cot(a x) - a x
+--R                                 2
+--R   (3)  ------------------------------------------------------------------
+--R                                   2            2
+--R                                 2a cos(ax) - 2a
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.386~~~~~$\displaystyle
@@ -371,7 +794,7 @@ $$
 <<*>>=
 )clear all
 
---S 18 of 30
+--S 60
 aa:=integrate(1/(1+cos(ax)),x)
 --R 
 --R
@@ -379,7 +802,25 @@ aa:=integrate(1/(1+cos(ax)),x)
 --R   (1)  -----------
 --R        cos(ax) + 1
 --R                                          Type: Union(Expression Integer,...)
---E 
+--E
+
+--S 61
+bb:=1/a*tan(a*x)/2
+--R
+--R        tan(a x)
+--R   (2)  --------
+--R           2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 62     14:386 Axiom cannot simplify this expression
+cc:=aa-bb
+--R
+--R        (- cos(ax) - 1)tan(a x) + 2a x
+--R   (3)  ------------------------------
+--R                2a cos(ax) + 2a
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.387~~~~~$\displaystyle
@@ -391,7 +832,7 @@ $$
 <<*>>=
 )clear all
 
---S 19 of 30
+--S 63
 aa:=integrate(x/(1+cos(a*x)),x)
 --R 
 --R
@@ -403,6 +844,35 @@ aa:=integrate(x/(1+cos(a*x)),x)
 --R                         a cos(a x) + a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 64
+bb:=x/a*tan((a*x)/2)+2/a^2*log(cos((a*x)/2))
+--R
+--R                 a x             a x
+--R        2log(cos(---)) + a x tan(---)
+--R                  2               2
+--R   (2)  -----------------------------
+--R                       2
+--R                      a
+--R                                                     Type: Expression Integer
+--E
+
+--S 65     14:387 Axiom cannot simplify this expression
+cc:=aa-bb
+--R
+--R   (3)
+--R                                a x                               2
+--R       (- 2cos(a x) - 2)log(cos(---)) + (- cos(a x) - 1)log(------------)
+--R                                 2                          cos(a x) + 1
+--R     + 
+--R                                 a x
+--R       (- a x cos(a x) - a x)tan(---) + a x sin(a x)
+--R                                  2
+--R  /
+--R      2            2
+--R     a cos(a x) + a
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.388~~~~~$\displaystyle
@@ -414,7 +884,7 @@ $$
 <<*>>=
 )clear all
 
---S 20 of 30
+--S 66
 aa:=integrate(1/(1-cos(a*x))^2,x)
 --R 
 --R
@@ -423,7 +893,32 @@ aa:=integrate(1/(1-cos(a*x))^2,x)
 --R   (1)  --------------------------
 --R        (3a cos(a x) - 3a)sin(a x)
 --R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 67
+bb:=-1/(2*a)*cot((a*x)/2)-1/(6*a)*cot((a*x)/2)^3
+--R
+--R              a x 3        a x
+--R        - cot(---)  - 3cot(---)
+--R               2            2
+--R   (2)  -----------------------
+--R                   6a
+--R                                                     Type: Expression Integer
 --E 
+
+--S 68     14:388 Axiom cannot simplify this expression
+cc:=aa-bb
+--R
+--R   (3)
+--R                          a x 3                      a x                      2
+--R       ((cos(a x) - 1)cot(---)  + (3cos(a x) - 3)cot(---))sin(a x) - 2cos(a x)
+--R                           2                          2
+--R     + 
+--R       2cos(a x) + 4
+--R  /
+--R     (6a cos(a x) - 6a)sin(a x)
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.389~~~~~$\displaystyle
@@ -435,7 +930,7 @@ $$
 <<*>>=
 )clear all
 
---S 21 of 30
+--S 69
 aa:=integrate(1/(1+cos(a*x))^2,x)
 --R 
 --R
@@ -445,6 +940,34 @@ aa:=integrate(1/(1+cos(a*x))^2,x)
 --R        3a cos(a x)  + 6a cos(a x) + 3a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 70
+bb:=1/(2*a)*tan((a*x)/2)+1/(6*a)*tan((a*x)/2)^2
+--R
+--R            a x 2        a x
+--R        tan(---)  + 3tan(---)
+--R             2            2
+--R   (2)  ---------------------
+--R                  6a
+--R                                                     Type: Expression Integer
+--E
+
+--S 71     14:389 Axiom cannot simplify this expression
+cc:=aa-bb
+--R
+--R   (3)
+--R                  2                     a x 2
+--R       (- cos(a x)  - 2cos(a x) - 1)tan(---)
+--R                                         2
+--R     + 
+--R                   2                     a x
+--R       (- 3cos(a x)  - 6cos(a x) - 3)tan(---) + (2cos(a x) + 4)sin(a x)
+--R                                          2
+--R  /
+--R                2
+--R     6a cos(a x)  + 12a cos(a x) + 6a
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.390~~~~~$\displaystyle
@@ -466,7 +989,7 @@ $$
 <<*>>=
 )clear all
 
---S 22 of 30
+--S 72
 aa:=integrate(1/(p+q*cos(a*x)),x)
 --R 
 --R
@@ -491,6 +1014,128 @@ aa:=integrate(1/(p+q*cos(a*x)),x)
 --R             a\|- q  + p
 --R                                     Type: Union(List Expression Integer,...)
 --E 
+
+--S 73
+bb1:=2/(a*sqrt(p^2-q^2))*atan(sqrt((p-q)/(p+q)))*tan(1/2*a*x)
+--R
+--R                       +-------+
+--R             a x       |- q + p
+--R        2tan(---)atan( |------- )
+--R              2       \| q + p
+--R   (2)  -------------------------
+--R                +---------+
+--R                |   2    2
+--R              a\|- q  + p
+--R                                                     Type: Expression Integer
+--E
+
+--S 74
+bb2:=a/(a*sqrt(q^2-p^2))*log((tan(1/2*a*x)+sqrt((q+p)/(q-p)))/(tan(1/2*a*x)-sqrt((q+p)/(q-p))))
+--R
+--R               +-----+
+--R               |q + p        a x
+--R            -  |-----  - tan(---)
+--R              \|q - p         2
+--R        log(---------------------)
+--R              +-----+
+--R              |q + p        a x
+--R              |-----  - tan(---)
+--R             \|q - p         2
+--R   (3)  --------------------------
+--R                 +-------+
+--R                 | 2    2
+--R                \|q  - p
+--R                                                     Type: Expression Integer
+--E
+
+--S 75
+cc1:=aa.1-bb1
+--R
+--R   (4)
+--R                                          +-------+
+--R        +---------+                       | 2    2        2    2
+--R        |   2    2     (- p cos(a x) - q)\|q  - p   + (- q  + p )sin(a x)
+--R       \|- q  + p  log(--------------------------------------------------)
+--R                                         q cos(a x) + p
+--R     + 
+--R                   +-------+      +-------+
+--R              a x  | 2    2       |- q + p
+--R       - 2tan(---)\|q  - p  atan( |------- )
+--R               2                 \| q + p
+--R  /
+--R       +---------+ +-------+
+--R       |   2    2  | 2    2
+--R     a\|- q  + p  \|q  - p
+--R                                                     Type: Expression Integer
+--E
+
+--S 76
+cc2:=aa.2-bb1
+--R
+--R                                                       +---------+
+--R                         +-------+                     |   2    2
+--R               a x       |- q + p             sin(a x)\|- q  + p
+--R        - 2tan(---)atan( |------- ) + 2atan(-----------------------)
+--R                2       \| q + p            (q + p)cos(a x) + q + p
+--R   (5)  ------------------------------------------------------------
+--R                                  +---------+
+--R                                  |   2    2
+--R                                a\|- q  + p
+--R                                                     Type: Expression Integer
+--E
+
+--S 77
+cc3:=aa.1-bb2
+--R
+--R   (6)
+--R                  +-----+
+--R                  |q + p        a x
+--R               -  |-----  - tan(---)
+--R                 \|q - p         2
+--R       - a log(---------------------)
+--R                 +-----+
+--R                 |q + p        a x
+--R                 |-----  - tan(---)
+--R                \|q - p         2
+--R     + 
+--R                              +-------+
+--R                              | 2    2        2    2
+--R           (- p cos(a x) - q)\|q  - p   + (- q  + p )sin(a x)
+--R       log(--------------------------------------------------)
+--R                             q cos(a x) + p
+--R  /
+--R       +-------+
+--R       | 2    2
+--R     a\|q  - p
+--R                                                     Type: Expression Integer
+--E
+
+--S 78     14:390 Axiom cannot simplify these expressions
+cc4:=aa.2-bb2
+--R
+--R   (7)
+--R                             +-----+
+--R                             |q + p        a x
+--R           +---------+    -  |-----  - tan(---)
+--R           |   2    2       \|q - p         2
+--R       - a\|- q  + p  log(---------------------)
+--R                            +-----+
+--R                            |q + p        a x
+--R                            |-----  - tan(---)
+--R                           \|q - p         2
+--R     + 
+--R                                  +---------+
+--R         +-------+                |   2    2
+--R         | 2    2        sin(a x)\|- q  + p
+--R       2\|q  - p  atan(-----------------------)
+--R                       (q + p)cos(a x) + q + p
+--R  /
+--R       +---------+ +-------+
+--R       |   2    2  | 2    2
+--R     a\|- q  + p  \|q  - p
+--R                                                     Type: Expression Integer
+--E
+
 @
 
 \section{\cite{1}:14.391~~~~~$\displaystyle
@@ -502,7 +1147,7 @@ $$
 <<*>>=
 )clear all
 
---S 23 of 30
+--S 79
 aa:=integrate(1/(p+q*cos(a*x))^2,x)
 --R 
 --R
@@ -542,6 +1187,143 @@ aa:=integrate(1/(p+q*cos(a*x))^2,x)
 --R     ]
 --R                                     Type: Union(List Expression Integer,...)
 --E 
+
+--S 80
+t1:=integrate(1/(p+q*cos(a*x)),x)
+--R
+--R   (2)
+--R                           +-------+
+--R                           | 2    2        2    2
+--R        (- p cos(a x) - q)\|q  - p   + (- q  + p )sin(a x)
+--R    log(--------------------------------------------------)
+--R                          q cos(a x) + p
+--R   [-------------------------------------------------------,
+--R                            +-------+
+--R                            | 2    2
+--R                          a\|q  - p
+--R                     +---------+
+--R                     |   2    2
+--R            sin(a x)\|- q  + p
+--R    2atan(-----------------------)
+--R          (q + p)cos(a x) + q + p
+--R    ------------------------------]
+--R               +---------+
+--R               |   2    2
+--R             a\|- q  + p
+--R                                     Type: Union(List Expression Integer,...)
+--E
+
+--S 81
+bb1:=(q*sin(a*x))/(a*(q^2-p^2)*(p+q*cos(a*x)))-p/(q^2-p^2)*t1.1
+--R
+--R   (3)
+--R                            2
+--R         (- p q cos(a x) - p )
+--R      *
+--R                                +-------+
+--R                                | 2    2        2    2
+--R             (- p cos(a x) - q)\|q  - p   + (- q  + p )sin(a x)
+--R         log(--------------------------------------------------)
+--R                               q cos(a x) + p
+--R     + 
+--R                  +-------+
+--R                  | 2    2
+--R       q sin(a x)\|q  - p
+--R  /
+--R                                              +-------+
+--R          3      2                  2      3  | 2    2
+--R     ((a q  - a p q)cos(a x) + a p q  - a p )\|q  - p
+--R                                                     Type: Expression Integer
+--E
+
+--S 82
+bb2:=(q*sin(a*x))/(a*(q^2-p^2)*(p+q*cos(a*x)))-p/(q^2-p^2)*t1.2
+--R
+--R   (4)
+--R                                          +---------+
+--R                                          |   2    2                 +---------+
+--R                        2        sin(a x)\|- q  + p                  |   2    2
+--R   (- 2p q cos(a x) - 2p )atan(-----------------------) + q sin(a x)\|- q  + p
+--R                               (q + p)cos(a x) + q + p
+--R   -----------------------------------------------------------------------------
+--R                                                         +---------+
+--R                     3      2                  2      3  |   2    2
+--R                ((a q  - a p q)cos(a x) + a p q  - a p )\|- q  + p
+--R                                                     Type: Expression Integer
+--E
+
+--S 83
+cc1:=aa.1-bb1
+--R
+--R   (5)
+--R                                +-------+
+--R                                | 2    2      2    2
+--R             (- p cos(a x) - q)\|q  - p   + (q  - p )sin(a x)
+--R       p log(------------------------------------------------)
+--R                              q cos(a x) + p
+--R     + 
+--R                                +-------+
+--R                                | 2    2        2    2
+--R             (- p cos(a x) - q)\|q  - p   + (- q  + p )sin(a x)
+--R       p log(--------------------------------------------------)
+--R                               q cos(a x) + p
+--R  /
+--R                   +-------+
+--R         2      2  | 2    2
+--R     (a q  - a p )\|q  - p
+--R                                                     Type: Expression Integer
+--E
+
+--S 84
+cc2:=aa.2-bb1
+--R
+--R   (6)
+--R                                           +-------+
+--R         +---------+                       | 2    2        2    2
+--R         |   2    2     (- p cos(a x) - q)\|q  - p   + (- q  + p )sin(a x)
+--R       p\|- q  + p  log(--------------------------------------------------)
+--R                                          q cos(a x) + p
+--R     + 
+--R                                     +---------+
+--R            +-------+                |   2    2
+--R            | 2    2        sin(a x)\|- q  + p
+--R       - 2p\|q  - p  atan(-----------------------)
+--R                          (q + p)cos(a x) + q + p
+--R  /
+--R                   +---------+ +-------+
+--R         2      2  |   2    2  | 2    2
+--R     (a q  - a p )\|- q  + p  \|q  - p
+--R                                                     Type: Expression Integer
+--E
+
+--S 85
+cc3:=aa.1-bb2
+--R
+--R   (7)
+--R                                           +-------+
+--R         +---------+                       | 2    2      2    2
+--R         |   2    2     (- p cos(a x) - q)\|q  - p   + (q  - p )sin(a x)
+--R       p\|- q  + p  log(------------------------------------------------)
+--R                                         q cos(a x) + p
+--R     + 
+--R                                   +---------+
+--R          +-------+                |   2    2
+--R          | 2    2        sin(a x)\|- q  + p
+--R       2p\|q  - p  atan(-----------------------)
+--R                        (q + p)cos(a x) + q + p
+--R  /
+--R                   +---------+ +-------+
+--R         2      2  |   2    2  | 2    2
+--R     (a q  - a p )\|- q  + p  \|q  - p
+--R                                                     Type: Expression Integer
+--E
+
+--S 86     14:391 Schaums and Axiom agree
+cc4:=aa.2-bb2
+--R
+--R   (8)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.392~~~~~$\displaystyle
@@ -552,7 +1334,7 @@ $$
 <<*>>=
 )clear all
 
---S 24 of 30
+--S 87
 aa:=integrate(1/(p^2+a^2*cos(a*x)),x)
 --R 
 --R
@@ -579,6 +1361,63 @@ aa:=integrate(1/(p^2+a^2*cos(a*x)),x)
 --R                a\|p  - a
 --R                                     Type: Union(List Expression Integer,...)
 --E 
+
+--S 88
+bb:=1/(a*p*sqrt(p^2+q^2))*atan((p*tan(a*x))/sqrt(p^2+q^2))
+--R
+--R             p tan(a x)
+--R        atan(----------)
+--R              +-------+
+--R              | 2    2
+--R             \|q  + p
+--R   (2)  ----------------
+--R              +-------+
+--R              | 2    2
+--R          a p\|q  + p
+--R                                                     Type: Expression Integer
+--E
+
+--S 89
+cc1:=aa.1-bb
+--R
+--R   (3)
+--R                                          +---------+
+--R         +-------+        2            2  |   4    4      4    4
+--R         | 2    2     (- p cos(a x) - a )\|- p  + a   + (p  - a )sin(a x)
+--R       p\|q  + p  log(---------------------------------------------------)
+--R                                         2            2
+--R                                        a cos(a x) + p
+--R     + 
+--R          +---------+
+--R          |   4    4      p tan(a x)
+--R       - \|- p  + a  atan(----------)
+--R                           +-------+
+--R                           | 2    2
+--R                          \|q  + p
+--R  /
+--R         +---------+ +-------+
+--R         |   4    4  | 2    2
+--R     a p\|- p  + a  \|q  + p
+--R                                                     Type: Expression Integer
+--E
+
+--S 90     14:392 Axiom cannot simplify these expressions
+cc2:=aa.2-bb
+--R
+--R   (4)
+--R                                  +-------+
+--R      +-------+                   | 4    4          +-------+
+--R      | 2    2           sin(a x)\|p  - a           | 4    4      p tan(a x)
+--R   2p\|q  + p  atan(---------------------------) - \|p  - a  atan(----------)
+--R                      2    2             2    2                    +-------+
+--R                    (p  + a )cos(a x) + p  + a                     | 2    2
+--R                                                                  \|q  + p
+--R   --------------------------------------------------------------------------
+--R                                 +-------+ +-------+
+--R                                 | 4    4  | 2    2
+--R                             a p\|p  - a  \|q  + p
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.393~~~~~$\displaystyle
@@ -598,7 +1437,7 @@ $$
 <<*>>=
 )clear all
 
---S 25 of 30
+--S 91
 aa:=integrate(1/(p^2-q^2*cos(a*x)^2),x)
 --R 
 --R
@@ -633,6 +1472,152 @@ aa:=integrate(1/(p^2-q^2*cos(a*x)^2),x)
 --R     ]
 --R                                     Type: Union(List Expression Integer,...)
 --E 
+
+--S 92
+bb1:=1/(a*p*sqrt(p^2-a^2))*atan((p*tan(a*x))/sqrt(p^2-q^2))
+--R
+--R              p tan(a x)
+--R        atan(------------)
+--R              +---------+
+--R              |   2    2
+--R             \|- q  + p
+--R   (2)  ------------------
+--R               +-------+
+--R               | 2    2
+--R           a p\|p  - a
+--R                                                     Type: Expression Integer
+--E
+
+--S 93
+bb2:=1/(2*a*p*sqrt(q^2-p^2))*log((p*tan(a*x)-sqrt(q^2-p^2))/(p*tan(a*x)+sqrt(q^2-p^2)))
+--R
+--R               +-------+
+--R               | 2    2
+--R            - \|q  - p   + p tan(a x)
+--R        log(-------------------------)
+--R              +-------+
+--R              | 2    2
+--R             \|q  - p   + p tan(a x)
+--R   (3)  ------------------------------
+--R                     +-------+
+--R                     | 2    2
+--R                2a p\|q  - p
+--R                                                     Type: Expression Integer
+--E
+
+--S 94
+cc1:=aa.1-bb1
+--R
+--R   (4)
+--R          +-------+
+--R          | 2    2
+--R         \|p  - a
+--R      *
+--R         log
+--R                                           +-------+
+--R                   2     2         2    2  | 2    2
+--R                ((q  - 2p )cos(a x)  + p )\|q  - p
+--R              + 
+--R                       2     3
+--R                (- 2p q  + 2p )cos(a x)sin(a x)
+--R           /
+--R               2        2    2
+--R              q cos(a x)  - p
+--R     + 
+--R           +-------+
+--R           | 2    2       p tan(a x)
+--R       - 2\|q  - p  atan(------------)
+--R                          +---------+
+--R                          |   2    2
+--R                         \|- q  + p
+--R  /
+--R          +-------+ +-------+
+--R          | 2    2  | 2    2
+--R     2a p\|p  - a  \|q  - p
+--R                                                     Type: Expression Integer
+--E
+
+--S 95
+cc2:=aa.2-bb1
+--R
+--R   (5)
+--R                               +---------+
+--R        +-------+              |   2    2      +---------+
+--R        | 2    2      sin(a x)\|- q  + p       |   2    2       p tan(a x)
+--R       \|p  - a  atan(--------------------) - \|- q  + p  atan(------------)
+--R                        2p cos(a x) + 2p                        +---------+
+--R                                                                |   2    2
+--R                                                               \|- q  + p
+--R     + 
+--R        +-------+             2    2              2
+--R        | 2    2           ((q  + p )cos(a x) + 2p )sin(a x)
+--R       \|p  - a  atan(-------------------------------------------)
+--R                                                      +---------+
+--R                                 2                    |   2    2
+--R                      (p cos(a x)  + 2p cos(a x) + p)\|- q  + p
+--R  /
+--R         +---------+ +-------+
+--R         |   2    2  | 2    2
+--R     a p\|- q  + p  \|p  - a
+--R                                                     Type: Expression Integer
+--E
+
+--S 96
+cc3:=aa.1-bb2
+--R
+--R   (6)
+--R       log
+--R                                     +-------+
+--R             2     2         2    2  | 2    2           2     3
+--R          ((q  - 2p )cos(a x)  + p )\|q  - p   + (- 2p q  + 2p )cos(a x)sin(a x)
+--R          ----------------------------------------------------------------------
+--R                                      2        2    2
+--R                                     q cos(a x)  - p
+--R     + 
+--R                +-------+
+--R                | 2    2
+--R             - \|q  - p   + p tan(a x)
+--R       - log(-------------------------)
+--R               +-------+
+--R               | 2    2
+--R              \|q  - p   + p tan(a x)
+--R  /
+--R          +-------+
+--R          | 2    2
+--R     2a p\|q  - p
+--R                                                     Type: Expression Integer
+--E
+
+--S 97     14:393 Axiom cannot simplify these expressions
+cc4:=aa.2-bb2
+--R
+--R   (7)
+--R                            +-------+
+--R          +---------+       | 2    2
+--R          |   2    2     - \|q  - p   + p tan(a x)
+--R       - \|- q  + p  log(-------------------------)
+--R                           +-------+
+--R                           | 2    2
+--R                          \|q  - p   + p tan(a x)
+--R     + 
+--R                                +---------+
+--R         +-------+              |   2    2
+--R         | 2    2      sin(a x)\|- q  + p
+--R       2\|q  - p  atan(--------------------)
+--R                         2p cos(a x) + 2p
+--R     + 
+--R         +-------+             2    2              2
+--R         | 2    2           ((q  + p )cos(a x) + 2p )sin(a x)
+--R       2\|q  - p  atan(-------------------------------------------)
+--R                                                       +---------+
+--R                                  2                    |   2    2
+--R                       (p cos(a x)  + 2p cos(a x) + p)\|- q  + p
+--R  /
+--R          +---------+ +-------+
+--R          |   2    2  | 2    2
+--R     2a p\|- q  + p  \|q  - p
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.394~~~~~$\displaystyle
@@ -644,7 +1629,7 @@ $$
 <<*>>=
 )clear all
 
---S 26 of 30
+--S 98     14:394 Axiom cannot compute this integral
 aa:=integrate(x^m*cos(a*x),x)
 --R 
 --R
@@ -664,7 +1649,7 @@ $$
 <<*>>=
 )clear all
 
---S 26 of 30
+--S 99     14:395 Axiom cannot compute this integral
 aa:=integrate(cos(a*x)/x^n,x)
 --R 
 --R
@@ -685,7 +1670,7 @@ $$
 <<*>>=
 )clear all
 
---S 28 of 30
+--S 100    14:396 Axiom cannot compute this integral
 aa:=integrate(cos(a*x)^n,x)
 --R 
 --R
@@ -706,7 +1691,7 @@ $$
 <<*>>=
 )clear all
 
---S 29 of 30
+--S 101    14:397 Axiom cannot compute this integral
 aa:=integrate(1/(cos(a*x))^n,x)
 --R 
 --R
@@ -729,7 +1714,7 @@ $$
 <<*>>=
 )clear all
 
---S 30 of 30
+--S 102    14:398 Axiom cannot compute this integral
 aa:=integrate(x/cos(a*x)^n,x)
 --R 
 --R
diff --git a/src/input/schaum19.input.pamphlet b/src/input/schaum19.input.pamphlet
index 37e89ee..bf580f0 100644
--- a/src/input/schaum19.input.pamphlet
+++ b/src/input/schaum19.input.pamphlet
@@ -18,7 +18,7 @@ $$
 )set message auto off
 )clear all
 
---S 1 of 36
+--S 1
 aa:=integrate(sin(a*x)*cos(a*x),x)
 --R 
 --R
@@ -28,6 +28,43 @@ aa:=integrate(sin(a*x)*cos(a*x),x)
 --R              2a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 2
+bb:=sin(a*x)^2/(2*a)
+--R
+--R                2
+--R        sin(a x)
+--R   (2)  ---------
+--R            2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 3
+cc:=aa-bb
+--R
+--R                  2           2
+--R        - sin(a x)  - cos(a x)
+--R   (3)  -----------------------
+--R                   2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 4
+cossqrrule:=rule(cos(a)^2 == 1-sin(a)^2)
+--R
+--R              2            2
+--R   (4)  cos(a)  == - sin(a)  + 1
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 5      14:399 Schaums and Axiom differ by a constant
+dd:=cossqrrule cc
+--R
+--R           1
+--R   (5)  - --
+--R          2a
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.400~~~~~$\displaystyle
@@ -38,7 +75,7 @@ $$
 <<*>>=
 )clear all
 
---S 2 of 36
+--S 6
 aa:=integrate(sin(p*x)*cos(q*x),x)
 --R 
 --R
@@ -48,6 +85,29 @@ aa:=integrate(sin(p*x)*cos(q*x),x)
 --R                        q  - p
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 7
+bb:=-(cos(p-q)*x)/(2*(p-q))-(cos(p+q)*x)/(2*(p+q))
+--R
+--R        (- q + p)x cos(q + p) + (q + p)x cos(q - p)
+--R   (2)  -------------------------------------------
+--R                           2     2
+--R                         2q  - 2p
+--R                                                     Type: Expression Integer
+--E
+
+--S 8      14:400 Axiom is unable to simplify this expression
+cc:=aa-bb
+--R
+--R   (3)
+--R       2q sin(p x)sin(q x) + 2p cos(p x)cos(q x) + (q - p)x cos(q + p)
+--R     + 
+--R       (- q - p)x cos(q - p)
+--R  /
+--R       2     2
+--R     2q  - 2p
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.401~~~~~$\displaystyle
@@ -58,7 +118,7 @@ $$
 <<*>>=
 )clear all
 
---S 3 of 36
+--S 9
 aa:=integrate(sin(a*x)^n*cos(a*x),x)
 --R 
 --R
@@ -68,6 +128,51 @@ aa:=integrate(sin(a*x)^n*cos(a*x),x)
 --R                 a n + a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 10
+bb:=sin(a*x)^(n+1)/((n+1)*a)
+--R
+--R                n + 1
+--R        sin(a x)
+--R   (2)  -------------
+--R           a n + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 11
+cc:=aa-bb
+--R
+--R                  n log(sin(a x))           n + 1
+--R        sin(a x)%e                - sin(a x)
+--R   (3)  -----------------------------------------
+--R                         a n + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 12
+explog:=rule(%e^(n*log(x)) == x^n)
+--R
+--R          n log(x)     n
+--R   (4)  %e         == x
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 13
+dd:=explog cc
+--R
+--R                  n + 1                   n
+--R        - sin(a x)      + sin(a x)sin(a x)
+--R   (5)  -----------------------------------
+--R                      a n + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 14     14:401 Schaums and Axiom agree
+ee:=complexNormalize dd
+--R
+--R   (6)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.402~~~~~$\displaystyle
@@ -78,7 +183,7 @@ $$
 <<*>>=
 )clear all
 
---S 4 of 36
+--S 15
 aa:=integrate(cos(a*x)^n*sin(a*x),x)
 --R 
 --R
@@ -87,7 +192,52 @@ aa:=integrate(cos(a*x)^n*sin(a*x),x)
 --R   (1)  - -------------------------
 --R                   a n + a
 --R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 16
+bb:=-cos(a*x)^(n+1)/((n+1)*a)
+--R
+--R                  n + 1
+--R          cos(a x)
+--R   (2)  - -------------
+--R             a n + a
+--R                                                     Type: Expression Integer
 --E 
+
+--S 17
+cc:=aa-bb
+--R
+--R                    n log(cos(a x))           n + 1
+--R        - cos(a x)%e                + cos(a x)
+--R   (3)  -------------------------------------------
+--R                          a n + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 18
+explog:=rule(%e^(n*log(x)) == x^n)
+--R
+--R          n log(x)     n
+--R   (4)  %e         == x
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 19
+dd:=explog cc
+--R
+--R                n + 1                   n
+--R        cos(a x)      - cos(a x)cos(a x)
+--R   (5)  ---------------------------------
+--R                     a n + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 20     14:402 Schaums and Axiom agree
+ee:=complexNormalize dd
+--R
+--R   (6)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.403~~~~~$\displaystyle
@@ -98,7 +248,7 @@ $$
 <<*>>=
 )clear all
 
---S 5 of 36
+--S 21
 aa:=integrate(sin(a*x)^2*cos(a*x)^2,x)
 --R 
 --R
@@ -108,6 +258,32 @@ aa:=integrate(sin(a*x)^2*cos(a*x)^2,x)
 --R                           8a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 22
+bb:=x/8-sin(4*a*x)/(32*a)
+--R
+--R        - sin(4a x) + 4a x
+--R   (2)  ------------------
+--R                32a
+--R                                                     Type: Expression Integer
+--E
+
+--S 23
+cc:=aa-bb
+--R
+--R                                3
+--R        sin(4a x) + (- 8cos(a x)  + 4cos(a x))sin(a x)
+--R   (3)  ----------------------------------------------
+--R                              32a
+--R                                                     Type: Expression Integer
+--E
+
+--S 24     14:403 Schaums and Axiom agree
+dd:=complexNormalize cc
+--R
+--R   (4)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.404~~~~~$\displaystyle
@@ -118,7 +294,7 @@ $$
 <<*>>=
 )clear all
 
---S 6 of 36
+--S 25
 aa:=integrate(1/(sin(a*x)*cos(a*x)),x)
 --R 
 --R
@@ -129,6 +305,55 @@ aa:=integrate(1/(sin(a*x)*cos(a*x)),x)
 --R                           a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 26
+bb:=1/a*log(tan(a*x))
+--R
+--R        log(tan(a x))
+--R   (2)  -------------
+--R              a
+--R                                                     Type: Expression Integer
+--E
+
+--S 27
+cc:=aa-bb
+--R
+--R                                sin(a x)              2cos(a x)
+--R        - log(tan(a x)) + log(------------) - log(- ------------)
+--R                              cos(a x) + 1          cos(a x) + 1
+--R   (3)  ---------------------------------------------------------
+--R                                    a
+--R                                                     Type: Expression Integer
+--E
+
+--S 28
+tanrule:=rule(tan(a) == sin(a)/cos(a))
+--R
+--R                  sin(a)
+--R   (4)  tan(a) == ------
+--R                  cos(a)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 29
+dd:=tanrule cc
+--R
+--R              sin(a x)          sin(a x)              2cos(a x)
+--R        - log(--------) + log(------------) - log(- ------------)
+--R              cos(a x)        cos(a x) + 1          cos(a x) + 1
+--R   (5)  ---------------------------------------------------------
+--R                                    a
+--R                                                     Type: Expression Integer
+--E
+
+--S 30     14:404 Schaums and Axiom differ by a constant
+ee:=expandLog dd
+--R
+--R          log(- 2)
+--R   (6)  - --------
+--R              a
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.405~~~~~$\displaystyle
@@ -139,7 +364,7 @@ $$
 <<*>>=
 )clear all
 
---S 7 of 36
+--S 31
 aa:=integrate(1/(sin(a*x)^2*cos(a*x)),x)
 --R 
 --R
@@ -155,6 +380,85 @@ aa:=integrate(1/(sin(a*x)^2*cos(a*x)),x)
 --R     a sin(a x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 32
+bb:=1/a*log(tan(%pi/4+(a*x)/2))-1/(a*sin(a*x))
+--R
+--R                        2a x + %pi
+--R        sin(a x)log(tan(----------)) - 1
+--R                             4
+--R   (2)  --------------------------------
+--R                   a sin(a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 33
+cc:=aa-bb
+--R
+--R   (3)
+--R                 2a x + %pi         sin(a x) + cos(a x) + 1
+--R       - log(tan(----------)) + log(-----------------------)
+--R                      4                   cos(a x) + 1
+--R     + 
+--R             sin(a x) - cos(a x) - 1
+--R       - log(-----------------------)
+--R                   cos(a x) + 1
+--R  /
+--R     a
+--R                                                     Type: Expression Integer
+--E
+
+--S 34
+tanrule:=rule(tan(a) == sin(a)/cos(a))
+--R
+--R                  sin(a)
+--R   (4)  tan(a) == ------
+--R                  cos(a)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 35
+dd:=tanrule cc
+--R
+--R   (5)
+--R           sin(a x) + cos(a x) + 1        sin(a x) - cos(a x) - 1
+--R       log(-----------------------) - log(-----------------------)
+--R                 cos(a x) + 1                   cos(a x) + 1
+--R     + 
+--R                 2a x + %pi
+--R             sin(----------)
+--R                      4
+--R       - log(---------------)
+--R                 2a x + %pi
+--R             cos(----------)
+--R                      4
+--R  /
+--R     a
+--R                                                     Type: Expression Integer
+--E
+
+--S 36
+ee:=expandLog dd
+--R
+--R   (6)
+--R       log(sin(a x) + cos(a x) + 1) - log(sin(a x) - cos(a x) - 1)
+--R     + 
+--R                 2a x + %pi             2a x + %pi
+--R       - log(sin(----------)) + log(cos(----------))
+--R                      4                      4
+--R  /
+--R     a
+--R                                                     Type: Expression Integer
+--E
+
+--S 37     14:405 Schaums and Axiom differ by a constant
+ff:=complexNormalize %
+--R
+--R        log(- 1)
+--R   (7)  --------
+--R            a
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.406~~~~~$\displaystyle
@@ -165,7 +469,7 @@ $$
 <<*>>=
 )clear all
 
---S 8 of 36
+--S 38
 aa:=integrate(1/(sin(a*x)*cos(a*x)^2),x)
 --R 
 --R
@@ -176,6 +480,72 @@ aa:=integrate(1/(sin(a*x)*cos(a*x)^2),x)
 --R                       a cos(a x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 39
+bb:=1/a*log(tan((a*x)/2))+1/(a*cos(a*x))
+--R
+--R                        a x
+--R        cos(a x)log(tan(---)) + 1
+--R                         2
+--R   (2)  -------------------------
+--R                a cos(a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 40
+cc:=aa-bb
+--R
+--R                  a x           sin(a x)
+--R        - log(tan(---)) + log(------------) + 1
+--R                   2          cos(a x) + 1
+--R   (3)  ---------------------------------------
+--R                           a
+--R                                                     Type: Expression Integer
+--E
+
+--S 41
+tanrule:=rule(tan(a) == sin(a)/cos(a))
+--R
+--R                  sin(a)
+--R   (4)  tan(a) == ------
+--R                  cos(a)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 42
+dd:=tanrule cc
+--R
+--R                                    a x
+--R                                sin(---)
+--R              sin(a x)               2
+--R        log(------------) - log(--------) + 1
+--R            cos(a x) + 1            a x
+--R                                cos(---)
+--R                                     2
+--R   (5)  -------------------------------------
+--R                          a
+--R                                                     Type: Expression Integer
+--E
+
+--S 43
+ee:=expandLog dd
+--R
+--R                                a x                                 a x
+--R        log(sin(a x)) - log(sin(---)) - log(cos(a x) + 1) + log(cos(---)) + 1
+--R                                 2                                   2
+--R   (6)  ---------------------------------------------------------------------
+--R                                          a
+--R                                                     Type: Expression Integer
+--E
+
+--S 44     14:406 Schaums and Axiom differ by a constant
+ff:=complexNormalize ee
+--R
+--R        1
+--R   (7)  -
+--R        a
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.407~~~~~$\displaystyle
@@ -186,7 +556,7 @@ $$
 <<*>>=
 )clear all
 
---S 9 of 36
+--S 45
 aa:=integrate(1/(sin(a*x)^2*cos(a*x)^2),x)
 --R 
 --R
@@ -196,6 +566,51 @@ aa:=integrate(1/(sin(a*x)^2*cos(a*x)^2),x)
 --R        a cos(a x)sin(a x)
 --R                                          Type: Union(Expression Integer,...)
 --E
+
+--S 46
+bb:=-(2*cot(2*a*x))/a
+--R
+--R          2cot(2a x)
+--R   (2)  - ----------
+--R               a
+--R                                                     Type: Expression Integer
+--E
+
+--S 47
+cc:=aa-bb
+--R
+--R                                              2
+--R        2cos(a x)cot(2a x)sin(a x) - 2cos(a x)  + 1
+--R   (3)  -------------------------------------------
+--R                     a cos(a x)sin(a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 48
+cotrule:=rule(cot(a) == cos(a)/sin(a))
+--R
+--R                  cos(a)
+--R   (4)  cot(a) == ------
+--R                  sin(a)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 49
+dd:=cotrule cc
+--R
+--R                    2
+--R        (- 2cos(a x)  + 1)sin(2a x) + 2cos(a x)cos(2a x)sin(a x)
+--R   (5)  --------------------------------------------------------
+--R                       a cos(a x)sin(a x)sin(2a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 50     14:407 Schaums and Axiom agree
+ee:=complexNormalize dd
+--R
+--R   (6)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.408~~~~~$\displaystyle
@@ -206,7 +621,7 @@ $$
 <<*>>=
 )clear all
 
---S 10 of 36
+--S 51
 aa:=integrate(sin(a*x)^2/cos(a*x),x)
 --R 
 --R
@@ -217,6 +632,85 @@ aa:=integrate(sin(a*x)^2/cos(a*x),x)
 --R                                           a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 52
+bb:=-sin(a*x)/a+1/a*log(tan((a*x)/2+%pi/4))
+--R
+--R                2a x + %pi
+--R        log(tan(----------)) - sin(a x)
+--R                     4
+--R   (2)  -------------------------------
+--R                       a
+--R                                                     Type: Expression Integer
+--E
+
+--S 53
+cc:=aa-bb
+--R
+--R   (3)
+--R                 2a x + %pi         sin(a x) + cos(a x) + 1
+--R       - log(tan(----------)) + log(-----------------------)
+--R                      4                   cos(a x) + 1
+--R     + 
+--R             sin(a x) - cos(a x) - 1
+--R       - log(-----------------------)
+--R                   cos(a x) + 1
+--R  /
+--R     a
+--R                                                     Type: Expression Integer
+--E
+
+--S 54
+tanrule:=rule(tan(a) == sin(a)/cos(a))
+--R
+--R                  sin(a)
+--R   (4)  tan(a) == ------
+--R                  cos(a)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 55
+dd:=tanrule cc
+--R
+--R   (5)
+--R           sin(a x) + cos(a x) + 1        sin(a x) - cos(a x) - 1
+--R       log(-----------------------) - log(-----------------------)
+--R                 cos(a x) + 1                   cos(a x) + 1
+--R     + 
+--R                 2a x + %pi
+--R             sin(----------)
+--R                      4
+--R       - log(---------------)
+--R                 2a x + %pi
+--R             cos(----------)
+--R                      4
+--R  /
+--R     a
+--R                                                     Type: Expression Integer
+--E
+
+--S 56
+ee:=expandLog dd
+--R
+--R   (6)
+--R       log(sin(a x) + cos(a x) + 1) - log(sin(a x) - cos(a x) - 1)
+--R     + 
+--R                 2a x + %pi             2a x + %pi
+--R       - log(sin(----------)) + log(cos(----------))
+--R                      4                      4
+--R  /
+--R     a
+--R                                                     Type: Expression Integer
+--E
+
+--S 57     14:408 Schaums and Axiom differ by a constant
+ff:=complexNormalize ee
+--R
+--R        log(- 1)
+--R   (7)  --------
+--R            a
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.409~~~~~$\displaystyle
@@ -227,7 +721,7 @@ $$
 <<*>>=
 )clear all
 
---S 11 of 36
+--S 58
 aa:=integrate(cos(a*x)^2/sin(a*x),x)
 --R 
 --R
@@ -238,6 +732,70 @@ aa:=integrate(cos(a*x)^2/sin(a*x),x)
 --R                      a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 59
+bb:=cos(a*x)/a+1/a*log(tan((a*x)/2))
+--R
+--R                a x
+--R        log(tan(---)) + cos(a x)
+--R                 2
+--R   (2)  ------------------------
+--R                    a
+--R                                                     Type: Expression Integer
+--E
+
+--S 60
+cc:=aa-bb
+--R
+--R                  a x           sin(a x)
+--R        - log(tan(---)) + log(------------)
+--R                   2          cos(a x) + 1
+--R   (3)  -----------------------------------
+--R                         a
+--R                                                     Type: Expression Integer
+--E
+
+--S 61
+tanrule:=rule(tan(a) == sin(a)/cos(a))
+--R
+--R                  sin(a)
+--R   (4)  tan(a) == ------
+--R                  cos(a)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 62
+dd:=tanrule cc
+--R
+--R                                    a x
+--R                                sin(---)
+--R              sin(a x)               2
+--R        log(------------) - log(--------)
+--R            cos(a x) + 1            a x
+--R                                cos(---)
+--R                                     2
+--R   (5)  ---------------------------------
+--R                        a
+--R                                                     Type: Expression Integer
+--E
+
+--S 63
+ee:=expandLog dd
+--R
+--R                                a x                                 a x
+--R        log(sin(a x)) - log(sin(---)) - log(cos(a x) + 1) + log(cos(---))
+--R                                 2                                   2
+--R   (6)  -----------------------------------------------------------------
+--R                                        a
+--R                                                     Type: Expression Integer
+--E
+
+--S 64     14:409 Schaums and Axiom agree
+ff:=complexNormalize ee
+--R
+--R   (7)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.410~~~~~$\displaystyle
@@ -249,7 +807,7 @@ $$
 <<*>>=
 )clear all
 
---S 12 of 36
+--S 65
 aa:=integrate(1/(cos(a*x)*(1+sin(a*x))),x)
 --R 
 --R
@@ -266,9 +824,88 @@ aa:=integrate(1/(cos(a*x)*(1+sin(a*x))),x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
 
+--S 66
+bb:=-1/(2*a*(1+sin(a*x)))+1/(2*a)*log(tan((a*x)/2+%pi/4))
+--R
+--R                              2a x + %pi
+--R        (sin(a x) + 1)log(tan(----------)) - 1
+--R                                   4
+--R   (2)  --------------------------------------
+--R                   2a sin(a x) + 2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 67
+cc:=aa-bb
+--R
+--R   (3)
+--R                 2a x + %pi         sin(a x) + cos(a x) + 1
+--R       - log(tan(----------)) + log(-----------------------)
+--R                      4                   cos(a x) + 1
+--R     + 
+--R             sin(a x) - cos(a x) - 1
+--R       - log(-----------------------) + 1
+--R                   cos(a x) + 1
+--R  /
+--R     2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 68
+tanrule:=rule(tan(a) == sin(a)/cos(a))
+--R
+--R                  sin(a)
+--R   (4)  tan(a) == ------
+--R                  cos(a)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 69
+dd:=tanrule cc
+--R
+--R   (5)
+--R           sin(a x) + cos(a x) + 1        sin(a x) - cos(a x) - 1
+--R       log(-----------------------) - log(-----------------------)
+--R                 cos(a x) + 1                   cos(a x) + 1
+--R     + 
+--R                 2a x + %pi
+--R             sin(----------)
+--R                      4
+--R       - log(---------------) + 1
+--R                 2a x + %pi
+--R             cos(----------)
+--R                      4
+--R  /
+--R     2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 70
+ee:=expandLog dd
+--R
+--R   (6)
+--R       log(sin(a x) + cos(a x) + 1) - log(sin(a x) - cos(a x) - 1)
+--R     + 
+--R                 2a x + %pi             2a x + %pi
+--R       - log(sin(----------)) + log(cos(----------)) + 1
+--R                      4                      4
+--R  /
+--R     2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 71
+ff:=complexNormalize ee
+--R
+--R        log(- 1) + 1
+--R   (7)  ------------
+--R             2a
+--R                                                     Type: Expression Integer
+--E
+
 )clear all 
 
---S 13 of 36
+--S 72
 aa:=integrate(1/(cos(a*x)*(1-sin(a*x))),x)
 --R 
 --R
@@ -284,6 +921,86 @@ aa:=integrate(1/(cos(a*x)*(1-sin(a*x))),x)
 --R     2a sin(a x) - 2a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 73
+bb:=1/(2*a*(1-sin(a*x)))+1/(2*a)*log(tan((a*x)/2+%pi/4))
+--R
+--R                              2a x + %pi
+--R        (sin(a x) - 1)log(tan(----------)) - 1
+--R                                   4
+--R   (2)  --------------------------------------
+--R                   2a sin(a x) - 2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 74
+cc:=aa-bb
+--R
+--R   (3)
+--R                 2a x + %pi         sin(a x) + cos(a x) + 1
+--R       - log(tan(----------)) + log(-----------------------)
+--R                      4                   cos(a x) + 1
+--R     + 
+--R             sin(a x) - cos(a x) - 1
+--R       - log(-----------------------) - 1
+--R                   cos(a x) + 1
+--R  /
+--R     2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 75
+tanrule:=rule(tan(a) == sin(a)/cos(a))
+--R
+--R                  sin(a)
+--R   (4)  tan(a) == ------
+--R                  cos(a)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 76
+dd:=tanrule cc
+--R
+--R   (5)
+--R           sin(a x) + cos(a x) + 1        sin(a x) - cos(a x) - 1
+--R       log(-----------------------) - log(-----------------------)
+--R                 cos(a x) + 1                   cos(a x) + 1
+--R     + 
+--R                 2a x + %pi
+--R             sin(----------)
+--R                      4
+--R       - log(---------------) - 1
+--R                 2a x + %pi
+--R             cos(----------)
+--R                      4
+--R  /
+--R     2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 77
+ee:=expandLog dd
+--R
+--R   (6)
+--R       log(sin(a x) + cos(a x) + 1) - log(sin(a x) - cos(a x) - 1)
+--R     + 
+--R                 2a x + %pi             2a x + %pi
+--R       - log(sin(----------)) + log(cos(----------)) - 1
+--R                      4                      4
+--R  /
+--R     2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 78     14:410 Schaums and Axiom differ by a constant
+ff:=complexNormalize ee
+--R
+--R        log(- 1) - 1
+--R   (7)  ------------
+--R             2a
+--R                                                     Type: Expression Integer
+--E
+
 @
 
 \section{\cite{1}:14.411~~~~~$\displaystyle
@@ -294,7 +1011,7 @@ $$
 <<*>>=
 )clear all
 
---S 14 of 36
+--S 79
 aa:=integrate(1/(sin(a*x)*(1+cos(a*x))),x)
 --R 
 --R
@@ -306,9 +1023,76 @@ aa:=integrate(1/(sin(a*x)*(1+cos(a*x))),x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
 
+--S 80
+bb:=1/(2*a*(1+cos(a*x)))+1/(2*a)*log(tan((a*x)/2))
+--R
+--R                              a x
+--R        (cos(a x) + 1)log(tan(---)) + 1
+--R                               2
+--R   (2)  -------------------------------
+--R                2a cos(a x) + 2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 81
+cc:=aa-bb
+--R
+--R                   a x            sin(a x)
+--R        - 2log(tan(---)) + 2log(------------) - 1
+--R                    2           cos(a x) + 1
+--R   (3)  -----------------------------------------
+--R                            4a
+--R                                                     Type: Expression Integer
+--E
+
+--S 82
+tanrule:=rule(tan(a) == sin(a)/cos(a))
+--R
+--R                  sin(a)
+--R   (4)  tan(a) == ------
+--R                  cos(a)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 83
+dd:=tanrule cc
+--R
+--R                                      a x
+--R                                  sin(---)
+--R               sin(a x)                2
+--R        2log(------------) - 2log(--------) - 1
+--R             cos(a x) + 1             a x
+--R                                  cos(---)
+--R                                       2
+--R   (5)  ---------------------------------------
+--R                           4a
+--R                                                     Type: Expression Integer
+--E
+
+--S 84
+ee:=expandLog dd
+--R
+--R   (6)
+--R                             a x                                   a x
+--R   2log(sin(a x)) - 2log(sin(---)) - 2log(cos(a x) + 1) + 2log(cos(---)) - 1
+--R                              2                                     2
+--R   -------------------------------------------------------------------------
+--R                                       4a
+--R                                                     Type: Expression Integer
+--E
+
+--S 85
+ff:=complexNormalize ee
+--R
+--R           1
+--R   (7)  - --
+--R          4a
+--R                                                     Type: Expression Integer
+--E
+
 )clear all
 
---S 15 of 36
+--S 86
 aa:=integrate(1/(sin(a*x)*(1-cos(a*x))),x)
 --R 
 --R
@@ -319,6 +1103,73 @@ aa:=integrate(1/(sin(a*x)*(1-cos(a*x))),x)
 --R                        4a cos(a x) - 4a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 87
+bb:=-1/(2*a*(1-cos(a*x)))+1/(2*a)*log(tan((a*x)/2))
+--R
+--R                              a x
+--R        (cos(a x) - 1)log(tan(---)) + 1
+--R                               2
+--R   (2)  -------------------------------
+--R                2a cos(a x) - 2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 88
+cc:=aa-bb
+--R
+--R                   a x            sin(a x)
+--R        - 2log(tan(---)) + 2log(------------) + 1
+--R                    2           cos(a x) + 1
+--R   (3)  -----------------------------------------
+--R                            4a
+--R                                                     Type: Expression Integer
+--E
+
+--S 89
+tanrule:=rule(tan(a) == sin(a)/cos(a))
+--R
+--R                  sin(a)
+--R   (4)  tan(a) == ------
+--R                  cos(a)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 90
+dd:=tanrule cc
+--R
+--R                                      a x
+--R                                  sin(---)
+--R               sin(a x)                2
+--R        2log(------------) - 2log(--------) + 1
+--R             cos(a x) + 1             a x
+--R                                  cos(---)
+--R                                       2
+--R   (5)  ---------------------------------------
+--R                           4a
+--R                                                     Type: Expression Integer
+--E
+
+--S 91
+ee:=expandLog dd
+--R
+--R   (6)
+--R                             a x                                   a x
+--R   2log(sin(a x)) - 2log(sin(---)) - 2log(cos(a x) + 1) + 2log(cos(---)) + 1
+--R                              2                                     2
+--R   -------------------------------------------------------------------------
+--R                                       4a
+--R                                                     Type: Expression Integer
+--E
+
+--S 92     14:411 Schaums and Axiom differ by a constant
+ff:=complexNormalize ee
+--R
+--R         1
+--R   (7)  --
+--R        4a
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.412~~~~~$\displaystyle
@@ -329,7 +1180,7 @@ $$
 <<*>>=
 )clear all
 
---S 16 of 36
+--S 93
 aa:=integrate(1/(sin(a*x)+cos(a*x)),x)
 --R 
 --R
@@ -342,9 +1193,37 @@ aa:=integrate(1/(sin(a*x)+cos(a*x)),x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
 
+--S 94
+bb:=1/(a*sqrt(2))*log(tan((a*x)/2+%pi/8))
+--R
+--R         +-+        4a x + %pi
+--R        \|2 log(tan(----------))
+--R                         8
+--R   (2)  ------------------------
+--R                   2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 95
+cc:=aa-bb
+--R
+--R   (3)
+--R          +-+        4a x + %pi
+--R       - \|2 log(tan(----------))
+--R                          8
+--R     + 
+--R                   +-+                  +-+                 +-+
+--R        +-+    (- \|2  + 1)sin(a x) + (\|2  - 1)cos(a x) + \|2  - 2
+--R       \|2 log(----------------------------------------------------)
+--R                                sin(a x) + cos(a x)
+--R  /
+--R     2a
+--R                                                     Type: Expression Integer
+--E
+
 )clear all
 
---S 17 of 36
+--S 96
 aa:=integrate(1/(sin(a*x)-cos(a*x)),x)
 --R 
 --R
@@ -356,6 +1235,35 @@ aa:=integrate(1/(sin(a*x)-cos(a*x)),x)
 --R                                       2a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 97
+bb:=1/(a*sqrt(2))*log(tan((a*x)/2-%pi/8))
+--R
+--R         +-+        4a x - %pi
+--R        \|2 log(tan(----------))
+--R                         8
+--R   (2)  ------------------------
+--R                   2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 98     14:412 Axiom cannot simplify this expression
+cc:=aa-bb
+--R
+--R   (3)
+--R          +-+        4a x - %pi
+--R       - \|2 log(tan(----------))
+--R                          8
+--R     + 
+--R                   +-+                    +-+                 +-+
+--R        +-+    (- \|2  + 1)sin(a x) + (- \|2  + 1)cos(a x) - \|2  + 2
+--R       \|2 log(------------------------------------------------------)
+--R                                 sin(a x) - cos(a x)
+--R  /
+--R     2a
+--R                                                     Type: Expression Integer
+--E
+
 @
 
 \section{\cite{1}:14.413~~~~~$\displaystyle
@@ -366,7 +1274,7 @@ $$
 <<*>>=
 )clear all
 
---S 18 of 36
+--S 99
 aa:=integrate(sin(a*x)/(sin(a*x)+cos(a*x)),x)
 --R 
 --R
@@ -378,9 +1286,48 @@ aa:=integrate(sin(a*x)/(sin(a*x)+cos(a*x)),x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
 
+--S 100
+bb:=x/2-1/(2*a)*log(sin(a*x)+cos(a*x))
+--R
+--R        - log(sin(a x) + cos(a x)) + a x
+--R   (2)  --------------------------------
+--R                       2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 101
+cc:=aa-bb
+--R
+--R   (3)
+--R                                        2             - 2sin(a x) - 2cos(a x)
+--R   log(sin(a x) + cos(a x)) + log(------------) - log(-----------------------)
+--R                                  cos(a x) + 1              cos(a x) + 1
+--R   ---------------------------------------------------------------------------
+--R                                        2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 102
+dd:=expandLog cc
+--R
+--R        log(sin(a x) + cos(a x)) - log(- sin(a x) - cos(a x))
+--R   (4)  -----------------------------------------------------
+--R                                  2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 103
+ee:=complexNormalize dd
+--R
+--R        log(- 1)
+--R   (5)  --------
+--R           2a
+--R                                                     Type: Expression Integer
+--E
+
 )clear all 
 
---S 19 of 36
+--S 104
 aa:=integrate(sin(a*x)/(sin(a*x)-cos(a*x)),x)
 --R 
 --R
@@ -391,6 +1338,34 @@ aa:=integrate(sin(a*x)/(sin(a*x)-cos(a*x)),x)
 --R                                 2a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 105
+bb:=x/2+1/(2*a)*log(sin(a*x)-cos(a*x))
+--R
+--R        log(sin(a x) - cos(a x)) + a x
+--R   (2)  ------------------------------
+--R                      2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 106
+cc:=aa-bb
+--R
+--R   (3)
+--R                                    2sin(a x) - 2cos(a x)              2
+--R   - log(sin(a x) - cos(a x)) + log(---------------------) - log(------------)
+--R                                         cos(a x) + 1            cos(a x) + 1
+--R   ---------------------------------------------------------------------------
+--R                                        2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 107    14:413 Schaums and Axiom agree
+dd:=expandLog cc
+--R
+--R   (4)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.414~~~~~$\displaystyle
@@ -401,7 +1376,7 @@ $$
 <<*>>=
 )clear all
 
---S 20 of 36
+--S 108
 aa:=integrate(cos(a*x)/(sin(a*x)+cos(a*x)),x)
 --R 
 --R
@@ -413,9 +1388,48 @@ aa:=integrate(cos(a*x)/(sin(a*x)+cos(a*x)),x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
 
+--S 109
+bb:=x/2+1/(2*a)*log(sin(a*x)+cos(a*x))
+--R
+--R        log(sin(a x) + cos(a x)) + a x
+--R   (2)  ------------------------------
+--R                      2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 110
+cc:=aa-bb
+--R
+--R   (3)
+--R                                          2             - 2sin(a x) - 2cos(a x)
+--R   - log(sin(a x) + cos(a x)) - log(------------) + log(-----------------------)
+--R                                    cos(a x) + 1              cos(a x) + 1
+--R   -----------------------------------------------------------------------------
+--R                                         2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 111
+dd:=expandLog cc
+--R
+--R        - log(sin(a x) + cos(a x)) + log(- sin(a x) - cos(a x))
+--R   (4)  -------------------------------------------------------
+--R                                   2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 112
+ee:=complexNormalize dd
+--R
+--R          log(- 1)
+--R   (5)  - --------
+--R             2a
+--R                                                     Type: Expression Integer
+--E
+
 )clear all
 
---S 21 of 36
+--S 113
 aa:=integrate(cos(a*x)/(sin(a*x)-cos(a*x)),x)
 --R 
 --R
@@ -426,6 +1440,34 @@ aa:=integrate(cos(a*x)/(sin(a*x)-cos(a*x)),x)
 --R                                 2a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 114
+bb:=-x/2+1/(2*a)*log(sin(a*x)-cos(a*x))
+--R
+--R        log(sin(a x) - cos(a x)) - a x
+--R   (2)  ------------------------------
+--R                      2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 115
+cc:=aa-bb
+--R
+--R   (3)
+--R                                    2sin(a x) - 2cos(a x)              2
+--R   - log(sin(a x) - cos(a x)) + log(---------------------) - log(------------)
+--R                                         cos(a x) + 1            cos(a x) + 1
+--R   ---------------------------------------------------------------------------
+--R                                        2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 116    14:414 Schaums and Axiom agree
+dd:=expandLog cc
+--R
+--R   (4)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.415~~~~~$\displaystyle
@@ -436,7 +1478,7 @@ $$
 <<*>>=
 )clear all
 
---S 22 of 36
+--S 117
 aa:=integrate(sin(a*x)/(p+q*cos(a*x)),x)
 --R 
 --R
@@ -447,6 +1489,44 @@ aa:=integrate(sin(a*x)/(p+q*cos(a*x)),x)
 --R                            a q
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 118
+bb:=-1/(a*q)*log(p+q*cos(a*x))
+--R
+--R          log(q cos(a x) + p)
+--R   (2)  - -------------------
+--R                  a q
+--R                                                     Type: Expression Integer
+--E
+
+--S 119
+cc:=aa-bb
+--R
+--R                                        2             - 2q cos(a x) - 2p
+--R        log(q cos(a x) + p) + log(------------) - log(------------------)
+--R                                  cos(a x) + 1           cos(a x) + 1
+--R   (3)  -----------------------------------------------------------------
+--R                                       a q
+--R                                                     Type: Expression Integer
+--E
+
+--S 120
+dd:=expandLog cc
+--R
+--R        log(q cos(a x) + p) - log(- q cos(a x) - p)
+--R   (4)  -------------------------------------------
+--R                            a q
+--R                                                     Type: Expression Integer
+--E
+
+--S 121    14:415 Schaums and Axiom differ by a constant
+ee:=complexNormalize dd
+--R
+--R        log(- 1)
+--R   (5)  --------
+--R           a q
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.416~~~~~$\displaystyle
@@ -457,7 +1537,7 @@ $$
 <<*>>=
 )clear all
 
---S 23 of 36
+--S 122
 aa:=integrate(cos(a*x)/(p+q*sin(a*x)),x)
 --R 
 --R
@@ -468,6 +1548,33 @@ aa:=integrate(cos(a*x)/(p+q*sin(a*x)),x)
 --R                           a q
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 123
+bb:=1/(a*q)*log(p+q*sin(a*x))
+--R
+--R        log(q sin(a x) + p)
+--R   (2)  -------------------
+--R                a q
+--R                                                     Type: Expression Integer
+--E
+
+--S 124
+cc:=aa-bb
+--R
+--R                                    2q sin(a x) + 2p              2
+--R        - log(q sin(a x) + p) + log(----------------) - log(------------)
+--R                                      cos(a x) + 1          cos(a x) + 1
+--R   (3)  -----------------------------------------------------------------
+--R                                       a q
+--R                                                     Type: Expression Integer
+--E
+
+--S 125    14:416 Schaums and Axiom differ by a constant
+dd:=expandLog cc
+--R
+--R   (4)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.417~~~~~$\displaystyle
@@ -478,7 +1585,7 @@ $$
 <<*>>=
 )clear all
 
---S 24 of 36
+--S 126
 aa:=integrate(sin(a*x)/(p+q*cos(a*x))^n,x)
 --R 
 --R
@@ -488,6 +1595,53 @@ aa:=integrate(sin(a*x)/(p+q*cos(a*x))^n,x)
 --R        (a n - a)q %e
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 127
+bb:=1/(a*q*(n-1)*(p+q*cos(a*x))^(n-1))
+--R
+--R                        1
+--R   (2)  --------------------------------
+--R                                   n - 1
+--R        (a n - a)q (q cos(a x) + p)
+--R                                                     Type: Expression Integer
+--E
+
+--S 128
+cc:=aa-bb
+--R
+--R            n log(q cos(a x) + p)                                   n - 1
+--R        - %e                      + (q cos(a x) + p)(q cos(a x) + p)
+--R   (3)  -----------------------------------------------------------------
+--R                                        n - 1  n log(q cos(a x) + p)
+--R             (a n - a)q (q cos(a x) + p)     %e
+--R                                                     Type: Expression Integer
+--E
+
+--S 129
+explog:=rule(%e^(n*log(x)) == x^n)
+--R
+--R          n log(x)     n
+--R   (4)  %e         == x
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 130
+dd:=explog cc
+--R
+--R                          n                                   n - 1
+--R        - (q cos(a x) + p)  + (q cos(a x) + p)(q cos(a x) + p)
+--R   (5)  -----------------------------------------------------------
+--R                                        n - 1                n
+--R             (a n - a)q (q cos(a x) + p)     (q cos(a x) + p)
+--R                                                     Type: Expression Integer
+--E
+
+--S 131    14:417 Schaums and Axiom agree
+ee:=complexNormalize dd
+--R
+--R   (6)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.418~~~~~$\displaystyle
@@ -498,7 +1652,7 @@ $$
 <<*>>=
 )clear all
 
---S 25 of 36
+--S 132
 aa:=integrate(cos(a*x)/(p+q*sin(a*x))^n,x)
 --R 
 --R
@@ -508,6 +1662,53 @@ aa:=integrate(cos(a*x)/(p+q*sin(a*x))^n,x)
 --R        (a n - a)q %e
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 133
+bb:=-1/(a*q*(n-1)*(p+q*sin(a*x))^(n-1))
+--R
+--R                          1
+--R   (2)  - --------------------------------
+--R                                     n - 1
+--R          (a n - a)q (q sin(a x) + p)
+--R                                                     Type: Expression Integer
+--E
+
+--S 134
+cc:=aa-bb
+--R
+--R          n log(q sin(a x) + p)                                     n - 1
+--R        %e                      + (- q sin(a x) - p)(q sin(a x) + p)
+--R   (3)  -----------------------------------------------------------------
+--R                                        n - 1  n log(q sin(a x) + p)
+--R             (a n - a)q (q sin(a x) + p)     %e
+--R                                                     Type: Expression Integer
+--E
+
+--S 135
+explog:=rule(%e^(n*log(x)) == x^n)
+--R
+--R          n log(x)     n
+--R   (4)  %e         == x
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 136
+dd:=explog cc
+--R
+--R                        n                                     n - 1
+--R        (q sin(a x) + p)  + (- q sin(a x) - p)(q sin(a x) + p)
+--R   (5)  -----------------------------------------------------------
+--R                                        n - 1                n
+--R             (a n - a)q (q sin(a x) + p)     (q sin(a x) + p)
+--R                                                     Type: Expression Integer
+--E
+
+--S 137    14:418 Schaums and Axiom agree
+ee:=complexNormalize dd
+--R
+--R   (6)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.419~~~~~$\displaystyle
@@ -518,7 +1719,7 @@ $$
 <<*>>=
 )clear all
 
---S 26 of 36
+--S 138
 aa:=integrate(1/(p*sin(a*x)+q*cos(a*x)),x)
 --R 
 --R
@@ -538,6 +1739,47 @@ aa:=integrate(1/(p*sin(a*x)+q*cos(a*x)),x)
 --R     a\|q  + p
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 139
+bb:=1/(a*sqrt(p^2+q^2))*log(tan((a*x+atan(q/p))/2))
+--R
+--R                     q
+--R                atan(-) + a x
+--R                     p
+--R        log(tan(-------------))
+--R                      2
+--R   (2)  -----------------------
+--R                +-------+
+--R                | 2    2
+--R              a\|q  + p
+--R                                                     Type: Expression Integer
+--E
+
+--S 140    14:419 Axiom cannot simplify this expression
+cc:=aa-bb
+--R
+--R   (3)
+--R                      q
+--R                 atan(-) + a x
+--R                      p
+--R       - log(tan(-------------))
+--R                       2
+--R     + 
+--R       log
+--R                                                    +-------+
+--R                               2            2    2  | 2    2
+--R              (p q sin(a x) - p cos(a x) - q  - p )\|q  + p
+--R            + 
+--R                  3    2                 2    3               2    3
+--R              (- q  - p q)sin(a x) + (p q  + p )cos(a x) + p q  + p
+--R         /
+--R            p sin(a x) + q cos(a x)
+--R  /
+--R       +-------+
+--R       | 2    2
+--R     a\|q  + p
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.420~~~~~$\displaystyle
@@ -559,7 +1801,7 @@ $$
 <<*>>=
 )clear all
 
---S 27 of 36
+--S 141
 aa:=integrate(1/(p*sin(a*x)+q*cos(a*x)+r),x)
 --R 
 --R
@@ -600,6 +1842,174 @@ aa:=integrate(1/(p*sin(a*x)+q*cos(a*x)+r),x)
 --R                        a\|r  - q  - p
 --R                                     Type: Union(List Expression Integer,...)
 --E 
+
+--S 142
+bb1:=2/(a*sqrt(r^2-p^2-q^2))*atan((p+(r-q)*tan((a*x)/2))/sqrt(r^2-p^2-q^2))
+--R
+--R                         a x
+--R              (r - q)tan(---) + p
+--R                          2
+--R        2atan(-------------------)
+--R                 +------------+
+--R                 | 2    2    2
+--R                \|r  - q  - p
+--R   (2)  --------------------------
+--R               +------------+
+--R               | 2    2    2
+--R             a\|r  - q  - p
+--R                                                     Type: Expression Integer
+--E
+
+--S 143
+bb2:=1/(a*sqrt(p^2+q^2-r^2))*log((p-sqrt(p^2+q^2-r^2)+(r-q)*tan((a*x)/2))/(p+sqrt(p^2+q^2-r^2)+(r-q)*tan((a*x)/2)))
+--R
+--R               +--------------+
+--R               |   2    2    2               a x
+--R            - \|- r  + q  + p   + (r - q)tan(---) + p
+--R                                              2
+--R        log(-----------------------------------------)
+--R              +--------------+
+--R              |   2    2    2               a x
+--R             \|- r  + q  + p   + (r - q)tan(---) + p
+--R                                             2
+--R   (3)  ----------------------------------------------
+--R                        +--------------+
+--R                        |   2    2    2
+--R                      a\|- r  + q  + p
+--R                                                     Type: Expression Integer
+--E
+
+--S 144
+cc1:=aa.1-bb1
+--R
+--R   (4)
+--R          +------------+
+--R          | 2    2    2
+--R         \|r  - q  - p
+--R      *
+--R         log
+--R                                              2          2                   2
+--R                    (p r - p q)sin(a x) + (- r  + q r + p )cos(a x) - q r + q
+--R                  + 
+--R                     2
+--R                    p
+--R               *
+--R                   +--------------+
+--R                   |   2    2    2
+--R                  \|- r  + q  + p
+--R              + 
+--R                  3      2       2    2      3    2
+--R                (r  - q r  + (- q  - p )r + q  + p q)sin(a x)
+--R              + 
+--R                    2      2    3               2      2    3
+--R                (p r  - p q  - p )cos(a x) + p r  - p q  - p
+--R           /
+--R              p sin(a x) + q cos(a x) + r
+--R     + 
+--R                                           a x
+--R           +--------------+     (r - q)tan(---) + p
+--R           |   2    2    2                  2
+--R       - 2\|- r  + q  + p  atan(-------------------)
+--R                                   +------------+
+--R                                   | 2    2    2
+--R                                  \|r  - q  - p
+--R  /
+--R       +--------------+ +------------+
+--R       |   2    2    2  | 2    2    2
+--R     a\|- r  + q  + p  \|r  - q  - p
+--R                                                     Type: Expression Integer
+--E
+
+--S 145
+cc2:=aa.2-bb1
+--R
+--R   (5)
+--R                                                +------------+
+--R                                                | 2    2    2
+--R             ((r - q)sin(a x) + p cos(a x) + p)\|r  - q  - p
+--R       2atan(-------------------------------------------------)
+--R                     2    2    2             2    2    2
+--R                   (r  - q  - p )cos(a x) + r  - q  - p
+--R     + 
+--R                          a x
+--R               (r - q)tan(---) + p
+--R                           2
+--R       - 2atan(-------------------)
+--R                  +------------+
+--R                  | 2    2    2
+--R                 \|r  - q  - p
+--R  /
+--R       +------------+
+--R       | 2    2    2
+--R     a\|r  - q  - p
+--R                                                     Type: Expression Integer
+--E
+
+--S 146
+cc3:=aa.1-bb2
+--R
+--R   (6)
+--R       log
+--R                                              2          2                   2
+--R                    (p r - p q)sin(a x) + (- r  + q r + p )cos(a x) - q r + q
+--R                  + 
+--R                     2
+--R                    p
+--R             *
+--R                 +--------------+
+--R                 |   2    2    2
+--R                \|- r  + q  + p
+--R            + 
+--R                3      2       2    2      3    2
+--R              (r  - q r  + (- q  - p )r + q  + p q)sin(a x)
+--R            + 
+--R                  2      2    3               2      2    3
+--R              (p r  - p q  - p )cos(a x) + p r  - p q  - p
+--R         /
+--R            p sin(a x) + q cos(a x) + r
+--R     + 
+--R                +--------------+
+--R                |   2    2    2               a x
+--R             - \|- r  + q  + p   + (r - q)tan(---) + p
+--R                                               2
+--R       - log(-----------------------------------------)
+--R               +--------------+
+--R               |   2    2    2               a x
+--R              \|- r  + q  + p   + (r - q)tan(---) + p
+--R                                              2
+--R  /
+--R       +--------------+
+--R       |   2    2    2
+--R     a\|- r  + q  + p
+--R                                                     Type: Expression Integer
+--E
+
+--S 147    14:420 Axiom cannot simplify these expressions
+cc4:=aa.2-bb2
+--R
+--R   (7)
+--R                               +--------------+
+--R                               |   2    2    2               a x
+--R          +------------+    - \|- r  + q  + p   + (r - q)tan(---) + p
+--R          | 2    2    2                                       2
+--R       - \|r  - q  - p  log(-----------------------------------------)
+--R                              +--------------+
+--R                              |   2    2    2               a x
+--R                             \|- r  + q  + p   + (r - q)tan(---) + p
+--R                                                             2
+--R     + 
+--R                                                               +------------+
+--R       +--------------+                                        | 2    2    2
+--R       |   2    2    2      ((r - q)sin(a x) + p cos(a x) + p)\|r  - q  - p
+--R     2\|- r  + q  + p  atan(-------------------------------------------------)
+--R                                    2    2    2             2    2    2
+--R                                  (r  - q  - p )cos(a x) + r  - q  - p
+--R  /
+--R       +--------------+ +------------+
+--R       |   2    2    2  | 2    2    2
+--R     a\|- r  + q  + p  \|r  - q  - p
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.421~~~~~$\displaystyle
@@ -610,7 +2020,7 @@ $$
 <<*>>=
 )clear all
 
---S 28 of 36
+--S 148
 aa:=integrate(1/(p*sin(a*x)+q*(1+cos(a*x))),x)
 --R 
 --R
@@ -620,7 +2030,76 @@ aa:=integrate(1/(p*sin(a*x)+q*(1+cos(a*x))),x)
 --R   (1)  --------------------------------
 --R                       a p
 --R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 149
+bb:=1/(a*p)*log(q+p*tan((a*x)/2))
+--R
+--R                  a x
+--R        log(p tan(---) + q)
+--R                   2
+--R   (2)  -------------------
+--R                a p
+--R                                                     Type: Expression Integer
 --E 
+
+--S 150
+cc:=aa-bb
+--R
+--R                    a x             p sin(a x) + q cos(a x) + q
+--R        - log(p tan(---) + q) + log(---------------------------)
+--R                     2                      cos(a x) + 1
+--R   (3)  --------------------------------------------------------
+--R                                   a p
+--R                                                     Type: Expression Integer
+--E
+
+--S 151
+tanrule:=rule(tan(a) == sin(a)/cos(a))
+--R
+--R                  sin(a)
+--R   (4)  tan(a) == ------
+--R                  cos(a)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 152
+dd:=tanrule cc
+--R
+--R                                                     a x          a x
+--R                                               p sin(---) + q cos(---)
+--R            p sin(a x) + q cos(a x) + q               2            2
+--R        log(---------------------------) - log(-----------------------)
+--R                    cos(a x) + 1                           a x
+--R                                                       cos(---)
+--R                                                            2
+--R   (5)  ---------------------------------------------------------------
+--R                                      a p
+--R                                                     Type: Expression Integer
+--E
+
+--S 153
+ee:=expandLog dd
+--R
+--R   (6)
+--R                                                    a x          a x
+--R       log(p sin(a x) + q cos(a x) + q) - log(p sin(---) + q cos(---))
+--R                                                     2            2
+--R     + 
+--R                                     a x
+--R       - log(cos(a x) + 1) + log(cos(---))
+--R                                      2
+--R  /
+--R     a p
+--R                                                     Type: Expression Integer
+--E
+
+--S 154    14:421 Schaums and Axiom agree
+ff:=complexNormalize ee
+--R
+--R   (7)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.422~~~~~$\displaystyle
@@ -632,7 +2111,7 @@ $$
 <<*>>=
 )clear all
 
---S 29 of 36
+--S 155
 aa:=integrate(1/(p*sin(a*x)+q*cos(a*x)+sqrt(p^2+q^2)),x)
 --R 
 --R
@@ -665,9 +2144,88 @@ aa:=integrate(1/(p*sin(a*x)+q*cos(a*x)+sqrt(p^2+q^2)),x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
 
+--S 156
+bb:=-1/(a*sqrt(p^2+q^2))*tan(%pi/4-(a*x+atan(q/p))/2)
+--R
+--R                  q
+--R            2atan(-) + 2a x - %pi
+--R                  p
+--R        tan(---------------------)
+--R                      4
+--R   (2)  --------------------------
+--R                  +-------+
+--R                  | 2    2
+--R                a\|q  + p
+--R                                                     Type: Expression Integer
+--E
+
+--S 157
+cc:=aa-bb
+--R
+--R   (3)
+--R                   6      2 4      4 2    6
+--R               (64q  + 80p q  + 24p q  + p )sin(a x)
+--R             + 
+--R                       5      3 3     5                  5      3 3     5
+--R               (- 32p q  - 32p q  - 6p q)cos(a x) - 32p q  - 32p q  - 6p q
+--R          *
+--R              +-------+
+--R              | 2    2
+--R             \|q  + p
+--R         + 
+--R                 7       2 5      4 3     6
+--R           (- 64q  - 112p q  - 56p q  - 7p q)sin(a x)
+--R         + 
+--R               6      3 4      5 2    7                 6      3 4      5 2    7
+--R         (32p q  + 48p q  + 18p q  + p )cos(a x) + 32p q  + 48p q  + 18p q  + p
+--R      *
+--R                   q
+--R             2atan(-) + 2a x - %pi
+--R                   p
+--R         tan(---------------------)
+--R                       4
+--R     + 
+--R              6      2 4      4 2     6               6      2 4      4 2     6
+--R         ((64q  + 96p q  + 36p q  + 2p )cos(a x) + 64q  + 96p q  + 36p q  + 2p )
+--R      *
+--R          +-------+
+--R          | 2    2
+--R         \|q  + p
+--R     + 
+--R             7       2 5      4 3      6                7       2 5      4 3
+--R       (- 64q  - 128p q  - 76p q  - 12p q)cos(a x) - 64q  - 128p q  - 76p q
+--R     + 
+--R            6
+--R       - 12p q
+--R  /
+--R                 7         2 5        4 3       6
+--R           (64a q  + 112a p q  + 56a p q  + 7a p q)sin(a x)
+--R         + 
+--R                     6        3 4        5 2      7                   6
+--R           (- 32a p q  - 48a p q  - 18a p q  - a p )cos(a x) - 32a p q
+--R         + 
+--R                  3 4        5 2      7
+--R           - 48a p q  - 18a p q  - a p
+--R      *
+--R          +-------+
+--R          | 2    2
+--R         \|q  + p
+--R     + 
+--R               8         2 6         4 4        6 2      8
+--R       (- 64a q  - 144a p q  - 104a p q  - 25a p q  - a p )sin(a x)
+--R     + 
+--R               7        3 5        5 3       7                    7        3 5
+--R       (32a p q  + 64a p q  + 38a p q  + 6a p q)cos(a x) + 32a p q  + 64a p q
+--R     + 
+--R            5 3       7
+--R       38a p q  + 6a p q
+--R                                                     Type: Expression Integer
+--E
+
+
 )clear all
 
---S 30 of 36
+--S 158
 aa:=integrate(1/(p*sin(a*x)+q*cos(a*x)-sqrt(p^2+q^2)),x)
 --R 
 --R
@@ -699,6 +2257,84 @@ aa:=integrate(1/(p*sin(a*x)+q*cos(a*x)-sqrt(p^2+q^2)),x)
 --R       - 18a p q  - a p
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 159
+bb:=-1/(a*sqrt(p^2+q^2))*tan(%pi/4+(a*x+atan(q/p))/2)
+--R
+--R                    q
+--R              2atan(-) + 2a x + %pi
+--R                    p
+--R          tan(---------------------)
+--R                        4
+--R   (2)  - --------------------------
+--R                    +-------+
+--R                    | 2    2
+--R                  a\|q  + p
+--R                                                     Type: Expression Integer
+--E
+
+--S 160    14:422 Axiom cannot simplify this expression
+cc:=aa-bb
+--R
+--R   (3)
+--R                   6      2 4      4 2    6
+--R               (64q  + 80p q  + 24p q  + p )sin(a x)
+--R             + 
+--R                       5      3 3     5                  5      3 3     5
+--R               (- 32p q  - 32p q  - 6p q)cos(a x) - 32p q  - 32p q  - 6p q
+--R          *
+--R              +-------+
+--R              | 2    2
+--R             \|q  + p
+--R         + 
+--R               7       2 5      4 3     6
+--R           (64q  + 112p q  + 56p q  + 7p q)sin(a x)
+--R         + 
+--R                   6      3 4      5 2    7                 6      3 4      5 2
+--R           (- 32p q  - 48p q  - 18p q  - p )cos(a x) - 32p q  - 48p q  - 18p q
+--R         + 
+--R              7
+--R           - p
+--R      *
+--R                   q
+--R             2atan(-) + 2a x + %pi
+--R                   p
+--R         tan(---------------------)
+--R                       4
+--R     + 
+--R              6      2 4      4 2     6               6      2 4      4 2     6
+--R         ((64q  + 96p q  + 36p q  + 2p )cos(a x) + 64q  + 96p q  + 36p q  + 2p )
+--R      *
+--R          +-------+
+--R          | 2    2
+--R         \|q  + p
+--R     + 
+--R         7       2 5      4 3      6                7       2 5      4 3      6
+--R     (64q  + 128p q  + 76p q  + 12p q)cos(a x) + 64q  + 128p q  + 76p q  + 12p q
+--R  /
+--R                 7         2 5        4 3       6
+--R           (64a q  + 112a p q  + 56a p q  + 7a p q)sin(a x)
+--R         + 
+--R                     6        3 4        5 2      7                   6
+--R           (- 32a p q  - 48a p q  - 18a p q  - a p )cos(a x) - 32a p q
+--R         + 
+--R                  3 4        5 2      7
+--R           - 48a p q  - 18a p q  - a p
+--R      *
+--R          +-------+
+--R          | 2    2
+--R         \|q  + p
+--R     + 
+--R             8         2 6         4 4        6 2      8
+--R       (64a q  + 144a p q  + 104a p q  + 25a p q  + a p )sin(a x)
+--R     + 
+--R                 7        3 5        5 3       7                    7        3 5
+--R       (- 32a p q  - 64a p q  - 38a p q  - 6a p q)cos(a x) - 32a p q  - 64a p q
+--R     + 
+--R              5 3       7
+--R       - 38a p q  - 6a p q
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.423~~~~~$\displaystyle
@@ -709,7 +2345,7 @@ $$
 <<*>>=
 )clear all
 
---S 31 of 36
+--S 161
 aa:=integrate(1/(p^2*sin(a*x)^2+q^2*cos(a*x)^2),x)
 --R 
 --R
@@ -722,6 +2358,37 @@ aa:=integrate(1/(p^2*sin(a*x)^2+q^2*cos(a*x)^2),x)
 --R                                        a p q
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 162
+bb:=1/(a*p*q)*atan((p*tan(a*x))/q)
+--R
+--R             p tan(a x)
+--R        atan(----------)
+--R                  q
+--R   (2)  ----------------
+--R              a p q
+--R                                                     Type: Expression Integer
+--E
+
+--S 163    14:423 Axiom cannot simplify this expressions
+cc:=aa-bb
+--R
+--R   (3)
+--R                                     2     2              2
+--R              p tan(a x)          ((q  - 2p )cos(a x) - 2p )sin(a x)
+--R       - atan(----------) - atan(-----------------------------------)
+--R                   q                         2
+--R                                 p q cos(a x)  + 2p q cos(a x) + p q
+--R     + 
+--R               q sin(a x)
+--R       atan(----------------)
+--R            2p cos(a x) + 2p
+--R  /
+--R     a p q
+--R                                                     Type: Expression Integer
+--E
+
+
 @
 
 \section{\cite{1}:14.424~~~~~$\displaystyle
@@ -732,7 +2399,7 @@ $$
 <<*>>=
 )clear all
 
---S 32 of 36
+--S 164
 aa:=integrate(1/(p^2*sin(a*x)^2-q^2*cos(a*x)^2),x)
 --R 
 --R
@@ -742,7 +2409,77 @@ aa:=integrate(1/(p^2*sin(a*x)^2-q^2*cos(a*x)^2),x)
 --R   (1)  -----------------------------------------------------------------
 --R                                      2a p q
 --R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 165
+bb:=1/(2*a*p*q)*log((p*tan(a*x)-q)/(p*tan(a*x)+q))
+--R
+--R            p tan(a x) - q
+--R        log(--------------)
+--R            p tan(a x) + q
+--R   (2)  -------------------
+--R               2a p q
+--R                                                     Type: Expression Integer
 --E 
+
+--S 166
+cc:=aa-bb
+--R
+--R   (3)
+--R           2p sin(a x) - 2q cos(a x)        p tan(a x) - q
+--R       log(-------------------------) - log(--------------)
+--R                  cos(a x) + 1              p tan(a x) + q
+--R     + 
+--R             - 2p sin(a x) - 2q cos(a x)
+--R       - log(---------------------------)
+--R                     cos(a x) + 1
+--R  /
+--R     2a p q
+--R                                                     Type: Expression Integer
+--E
+
+--S 167
+tanrule:=rule(tan(a) == sin(a)/cos(a))
+--R
+--R                  sin(a)
+--R   (4)  tan(a) == ------
+--R                  cos(a)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 168
+dd:=tanrule cc
+--R
+--R   (5)
+--R           2p sin(a x) - 2q cos(a x)        p sin(a x) - q cos(a x)
+--R       log(-------------------------) - log(-----------------------)
+--R                  cos(a x) + 1              p sin(a x) + q cos(a x)
+--R     + 
+--R             - 2p sin(a x) - 2q cos(a x)
+--R       - log(---------------------------)
+--R                     cos(a x) + 1
+--R  /
+--R     2a p q
+--R                                                     Type: Expression Integer
+--E
+
+--S 169
+ee:=expandLog dd
+--R
+--R        log(p sin(a x) + q cos(a x)) - log(- p sin(a x) - q cos(a x))
+--R   (6)  -------------------------------------------------------------
+--R                                    2a p q
+--R                                                     Type: Expression Integer
+--E
+
+--S 170    14:424 Schaums and Axiom differ by a constant
+ff:=complexNormalize ee
+--R
+--R        log(- 1)
+--R   (7)  --------
+--R         2a p q
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.425~~~~~$\displaystyle
@@ -763,7 +2500,7 @@ $$
 <<*>>=
 )clear all
 
---S 33 of 36
+--S 171    14:425 Axiom cannot compute this integral
 aa:=integrate(sin(a*x)^m*cos(a*x)^n,x)
 --R 
 --R
@@ -797,7 +2534,7 @@ $$
 <<*>>=
 )clear all
 
---S 34 of 36
+--S 172    14:426 Axiom cannot compute this integral
 aa:=integrate(sin(a*x)^m/cos(a*x)^n,x)
 --R 
 --R
@@ -832,7 +2569,7 @@ $$
 <<*>>=
 )clear all
 
---S 35 of 36
+--S 173    14:427 Axiom cannot compute this integral
 aa:=integrate(cos(a*x)^m/sin(a*x)^n,x)
 --R 
 --R
@@ -863,7 +2600,7 @@ $$
 <<*>>=
 )clear all
 
---S 36 of 36
+--S 174    14:428 Axiom cannot compute this integral
 aa:=integrate(1/(sin(a*x)^m*cos(a*x)^n),x)
 --R 
 --R
diff --git a/src/input/schaum20.input.pamphlet b/src/input/schaum20.input.pamphlet
index a25209e..e6981a6 100644
--- a/src/input/schaum20.input.pamphlet
+++ b/src/input/schaum20.input.pamphlet
@@ -19,7 +19,7 @@ $$
 )set message auto off
 )clear all
 
---S 1 of 11
+--S 1
 aa:=integrate(tan(a*x),x)
 --R 
 --R
@@ -29,6 +29,81 @@ aa:=integrate(tan(a*x),x)
 --R                2a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 2
+bb1:=-1/a*log(cos(a*x))
+--R
+--R          log(cos(a x))
+--R   (2)  - -------------
+--R                a
+--R                                                     Type: Expression Integer
+--E
+
+--S 3
+bb2:=1/a*log(sec(a*x))
+--R
+--R        log(sec(a x))
+--R   (3)  -------------
+--R              a
+--R                                                     Type: Expression Integer
+--E
+
+--S 4
+cc1:=aa-bb1
+--R
+--R                    2
+--R        log(tan(a x)  + 1) + 2log(cos(a x))
+--R   (4)  -----------------------------------
+--R                         2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 5
+tanrule:=rule(tan(a) == sin(a)/cos(a))
+--R
+--R                  sin(a)
+--R   (5)  tan(a) == ------
+--R                  cos(a)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 6
+dd1:=tanrule cc1
+--R
+--R                    2           2
+--R            sin(a x)  + cos(a x)
+--R        log(---------------------) + 2log(cos(a x))
+--R                          2
+--R                  cos(a x)
+--R   (6)  -------------------------------------------
+--R                             2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 7
+ee1:=expandLog dd1
+--R
+--R                    2           2
+--R        log(sin(a x)  + cos(a x) )
+--R   (7)  --------------------------
+--R                    2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 8
+sincossqrrule:=rule(sin(a)^2+cos(a)^2 == 1)
+--R
+--R              2         2
+--I   (8)  sin(a)  + cos(a)  + %K == %K + 1
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 9      14:429 Schaums and Axiom agree
+ff1:=sincossqrrule ee1
+--R
+--R   (9)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.430~~~~~$\displaystyle
@@ -39,7 +114,7 @@ $$
 <<*>>=
 )clear all
 
---S 2 of 11
+--S 10
 aa:=integrate(tan(a*x)^2,x)
 --R 
 --R
@@ -48,6 +123,22 @@ aa:=integrate(tan(a*x)^2,x)
 --R               a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 11
+bb:=tan(a*x)/a-x
+--R
+--R        tan(a x) - a x
+--R   (2)  --------------
+--R               a
+--R                                                     Type: Expression Integer
+--E
+
+--S 12     14:430 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.431~~~~~$\displaystyle
@@ -58,7 +149,7 @@ $$
 <<*>>=
 )clear all
 
---S 3 of 11
+--S 13
 aa:=integrate(tan(a*x)^3,x)
 --R 
 --R
@@ -68,6 +159,73 @@ aa:=integrate(tan(a*x)^3,x)
 --R                       2a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 14
+bb:=tan(a*x)^2/(2*a)+1/a*log(cos(a*x))
+--R
+--R                                 2
+--R        2log(cos(a x)) + tan(a x)
+--R   (2)  --------------------------
+--R                    2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 15
+cc:=aa-bb
+--R
+--R                      2
+--R        - log(tan(a x)  + 1) - 2log(cos(a x))
+--R   (3)  -------------------------------------
+--R                          2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 16
+tanrule:=rule(tan(a) == sin(a)/cos(a))
+--R
+--R                  sin(a)
+--R   (4)  tan(a) == ------
+--R                  cos(a)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 17
+dd:=tanrule cc
+--R
+--R                      2           2
+--R              sin(a x)  + cos(a x)
+--R        - log(---------------------) - 2log(cos(a x))
+--R                            2
+--R                    cos(a x)
+--R   (5)  ---------------------------------------------
+--R                              2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 18
+ee:=expandLog dd
+--R
+--R                      2           2
+--R          log(sin(a x)  + cos(a x) )
+--R   (6)  - --------------------------
+--R                      2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 19
+sincossqrrule:=rule(sin(a)^2+cos(a)^2 == 1)
+--R
+--R              2         2
+--I   (7)  sin(a)  + cos(a)  + %L == %L + 1
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 20     14:431 Schaums and Axiom agree
+ff:=sincossqrrule ee
+--R
+--R   (8)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.432~~~~~$\displaystyle
@@ -78,7 +236,7 @@ $$
 <<*>>=
 )clear all
 
---S 4 of 11
+--S 21
 aa:=integrate(tan(a*x)^n*sec(a*x)^2,x)
 --R 
 --R
@@ -90,6 +248,74 @@ aa:=integrate(tan(a*x)^n*sec(a*x)^2,x)
 --R            (a n + a)cos(a x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 22
+bb:=tan(a*x)^(n+1)/((n+1)*a)
+--R
+--R                n + 1
+--R        tan(a x)
+--R   (2)  -------------
+--R           a n + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 23
+cc:=aa-bb
+--R
+--R                        sin(a x)
+--R                  n log(--------)
+--R                        cos(a x)                    n + 1
+--R        sin(a x)%e                - cos(a x)tan(a x)
+--R   (3)  -------------------------------------------------
+--R                        (a n + a)cos(a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 24
+explog:=rule(%e^(n*log(x)) == x^n)
+--R
+--R          n log(x)     n
+--R   (4)  %e         == x
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 25
+dd:=explog cc
+--R
+--R                          n + 1            sin(a x) n
+--R        - cos(a x)tan(a x)      + sin(a x)(--------)
+--R                                           cos(a x)
+--R   (5)  ---------------------------------------------
+--R                      (a n + a)cos(a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 26
+tanrule:=rule(tan(a) == sin(a)/cos(a))
+--R
+--R                  sin(a)
+--R   (6)  tan(a) == ------
+--R                  cos(a)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 27
+ee:=tanrule dd
+--R
+--R                   sin(a x) n + 1            sin(a x) n
+--R        - cos(a x)(--------)      + sin(a x)(--------)
+--R                   cos(a x)                  cos(a x)
+--R   (7)  -----------------------------------------------
+--R                       (a n + a)cos(a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 28     14:432 Schaums and Axiom agree
+ff:=complexNormalize ee
+--R
+--R   (8)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.433~~~~~$\displaystyle
@@ -100,7 +326,7 @@ $$
 <<*>>=
 )clear all
 
---S 5 of 11
+--S 29
 aa:=integrate(sec(a*x)^2/tan(a*x),x)
 --R 
 --R
@@ -111,6 +337,44 @@ aa:=integrate(sec(a*x)^2/tan(a*x),x)
 --R                           a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 30
+bb:=1/a*log(tan(a*x))
+--R
+--R        log(tan(a x))
+--R   (2)  -------------
+--R              a
+--R                                                     Type: Expression Integer
+--E
+
+--S 31
+cc:=aa-bb
+--R
+--R                                sin(a x)              2cos(a x)
+--R        - log(tan(a x)) + log(------------) - log(- ------------)
+--R                              cos(a x) + 1          cos(a x) + 1
+--R   (3)  ---------------------------------------------------------
+--R                                    a
+--R                                                     Type: Expression Integer
+--E
+
+--S 32
+dd:=expandLog cc
+--R
+--R        - log(tan(a x)) + log(sin(a x)) - log(cos(a x)) - log(- 2)
+--R   (4)  ----------------------------------------------------------
+--R                                     a
+--R                                                     Type: Expression Integer
+--E
+
+--S 33     14:433 Schaums and Axiom differ by a constant
+ee:=complexNormalize dd
+--R
+--R          log(- 2)
+--R   (5)  - --------
+--R              a
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.434~~~~~$\displaystyle
@@ -121,7 +385,7 @@ $$
 <<*>>=
 )clear all
 
---S 6 of 11
+--S 34
 aa:=integrate(1/tan(a*x),x)
 --R 
 --R
@@ -131,6 +395,32 @@ aa:=integrate(1/tan(a*x),x)
 --R                          2a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 35
+bb:=1/a*log(sin(a*x))
+--R
+--R        log(sin(a x))
+--R   (2)  -------------
+--R              a
+--R                                                     Type: Expression Integer
+--E
+
+--S 36
+cc:=aa-bb
+--R
+--R                      2
+--R        - log(tan(a x)  + 1) + 2log(tan(a x)) - 2log(sin(a x))
+--R   (3)  ------------------------------------------------------
+--R                                  2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 37
+complexNormalize cc
+--R
+--R   (4)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.435~~~~~$\displaystyle
@@ -142,7 +432,7 @@ $$
 <<*>>=
 )clear all
 
---S 7 of 11
+--S 38     14:435 Axiom cannot compute this integral
 aa:=integrate(x*tan(a*x),x)
 --R 
 --R
@@ -163,7 +453,7 @@ $$
 <<*>>=
 )clear all
 
---S 8 of 11
+--S 39     14:436 Axiom cannot compute this integral
 aa:=integrate(tan(a*x)/x,x)
 --R 
 --R
@@ -183,7 +473,7 @@ $$
 <<*>>=
 )clear all
 
---S 9 of 11
+--S 40
 aa:=integrate(x*tan(a*x)^2,x)
 --R 
 --R
@@ -194,6 +484,77 @@ aa:=integrate(x*tan(a*x)^2,x)
 --R                            2a
 --R                                          Type: Union(Expression Integer,...)
 --E
+
+--S 41
+bb:=(x*tan(a*x))/a+1/a^2*log(cos(a*x))-x^2/2
+--R
+--R                                          2 2
+--R        2log(cos(a x)) + 2a x tan(a x) - a x
+--R   (2)  -------------------------------------
+--R                           2
+--R                         2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 42
+cc:=aa-bb
+--R
+--R                      2
+--R        - log(tan(a x)  + 1) - 2log(cos(a x))
+--R   (3)  -------------------------------------
+--R                           2
+--R                         2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 43
+tanrule:=rule(tan(a) == sin(a)/cos(a))
+--R
+--R                  sin(a)
+--R   (4)  tan(a) == ------
+--R                  cos(a)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 44
+dd:=tanrule cc
+--R
+--R                      2           2
+--R              sin(a x)  + cos(a x)
+--R        - log(---------------------) - 2log(cos(a x))
+--R                            2
+--R                    cos(a x)
+--R   (5)  ---------------------------------------------
+--R                               2
+--R                             2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 45
+ee:=expandLog dd
+--R
+--R                      2           2
+--R          log(sin(a x)  + cos(a x) )
+--R   (6)  - --------------------------
+--R                        2
+--R                      2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 46
+sincossqrrule:=rule(sin(a)^2+cos(a)^2 == 1)
+--R
+--R              2         2
+--I   (7)  sin(a)  + cos(a)  + %R == %R + 1
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 47     14:437 Schaums and Axiom agree
+ff:=sincossqrrule ee
+--R
+--R   (8)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.438~~~~~$\displaystyle
@@ -204,7 +565,7 @@ $$
 <<*>>=
 )clear all
 
---S 10 of 11
+--S 48
 aa:=integrate(1/(p+q*tan(a*x)),x)
 --R 
 --R
@@ -215,6 +576,84 @@ aa:=integrate(1/(p+q*tan(a*x)),x)
 --R                              2a q  + 2a p
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 49
+bb:=(p*x)/(p^2+q^2)+q/(a*(p^2+q^2))*log(q*sin(a*x)+p*cos(a*x))
+--R
+--R        q log(q sin(a x) + p cos(a x)) + a p x
+--R   (2)  --------------------------------------
+--R                         2      2
+--R                      a q  + a p
+--R                                                     Type: Expression Integer
+--E
+
+--S 50
+cc:=aa-bb
+--R
+--R   (3)
+--R                       2
+--R       - q log(tan(a x)  + 1) + 2q log(q tan(a x) + p)
+--R     + 
+--R       - 2q log(q sin(a x) + p cos(a x))
+--R  /
+--R         2       2
+--R     2a q  + 2a p
+--R                                                     Type: Expression Integer
+--E
+
+--S 51
+tanrule:=rule(tan(a) == sin(a)/cos(a))
+--R
+--R                  sin(a)
+--R   (4)  tan(a) == ------
+--R                  cos(a)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 52
+dd:=tanrule cc
+--R
+--R   (5)
+--R                       2           2
+--R               sin(a x)  + cos(a x)
+--R       - q log(---------------------) - 2q log(q sin(a x) + p cos(a x))
+--R                             2
+--R                     cos(a x)
+--R     + 
+--R              q sin(a x) + p cos(a x)
+--R       2q log(-----------------------)
+--R                      cos(a x)
+--R  /
+--R         2       2
+--R     2a q  + 2a p
+--R                                                     Type: Expression Integer
+--E
+
+--S 53
+ee:=expandLog dd
+--R
+--R                        2           2
+--R          q log(sin(a x)  + cos(a x) )
+--R   (6)  - ----------------------------
+--R                      2       2
+--R                  2a q  + 2a p
+--R                                                     Type: Expression Integer
+--E
+
+--S 54
+sincossqrrule:=rule(sin(a)^2+cos(a)^2 == 1)
+--R
+--R              2         2
+--I   (7)  sin(a)  + cos(a)  + %S == %S + 1
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 55     14:438 Schaums and Axiom agree
+ff:=sincossqrrule ee
+--R
+--R   (8)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.439~~~~~$\displaystyle
@@ -225,7 +664,7 @@ $$
 <<*>>=
 )clear all
 
---S 11 of 11
+--S 56     14:439 Axiom cannot compute this integral
 aa:=integrate(tan(a*x)^n,x)
 --R 
 --R
diff --git a/src/input/schaum21.input.pamphlet b/src/input/schaum21.input.pamphlet
index 6e02ffe..4d6a8be 100644
--- a/src/input/schaum21.input.pamphlet
+++ b/src/input/schaum21.input.pamphlet
@@ -18,7 +18,7 @@ $$
 )set message auto off
 )clear all
 
---S 1 of 11
+--S 1
 aa:=integrate(cot(a*x),x)
 --R 
 --R
@@ -29,6 +29,42 @@ aa:=integrate(cot(a*x),x)
 --R                           2a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 2
+bb:=1/a*log(sin(a*x))
+--R
+--R        log(sin(a x))
+--R   (2)  -------------
+--R              a
+--R                                                     Type: Expression Integer
+--E
+
+--S 3
+cc:=aa-bb
+--R
+--R               sin(2a x)                                 2
+--R        2log(-------------) - 2log(sin(a x)) - log(-------------)
+--R             cos(2a x) + 1                         cos(2a x) + 1
+--R   (3)  ---------------------------------------------------------
+--R                                    2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 4
+dd:=expandLog cc
+--R
+--R        2log(sin(2a x)) - 2log(sin(a x)) - log(cos(2a x) + 1) - log(2)
+--R   (4)  --------------------------------------------------------------
+--R                                      2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 5      14:440 Schaums and Axiom agree
+ee:=complexNormalize dd
+--R
+--R   (5)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.441~~~~~$\displaystyle
@@ -39,7 +75,7 @@ $$
 <<*>>=
 )clear all
 
---S 2 of 11
+--S 6
 aa:=integrate(cot(a*x)^2,x)
 --R 
 --R
@@ -48,6 +84,49 @@ aa:=integrate(cot(a*x)^2,x)
 --R                  a sin(2a x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 7
+bb:=-cot(a*x)/a-x
+--R
+--R        - cot(a x) - a x
+--R   (2)  ----------------
+--R                a
+--R                                                     Type: Expression Integer
+--E
+
+--S 8
+cc:=aa-bb
+--R
+--R        cot(a x)sin(2a x) - cos(2a x) - 1
+--R   (3)  ---------------------------------
+--R                   a sin(2a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 9
+cotrule:=rule(cot(a) == cos(a)/sin(a))
+--R
+--R                  cos(a)
+--R   (4)  cot(a) == ------
+--R                  sin(a)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 10
+dd:=cotrule cc
+--R
+--R        cos(a x)sin(2a x) + (- cos(2a x) - 1)sin(a x)
+--R   (5)  ---------------------------------------------
+--R                     a sin(a x)sin(2a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 11     14:441 Schaums and Axiom agree
+ee:=complexNormalize dd
+--R
+--R   (6)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.442~~~~~$\displaystyle
@@ -58,7 +137,7 @@ $$
 <<*>>=
 )clear all
 
---S 3 of 11
+--S 12
 aa:=integrate(cot(a*x)^3,x)
 --R 
 --R
@@ -72,6 +151,97 @@ aa:=integrate(cot(a*x)^3,x)
 --R     2a cos(2a x) - 2a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 13
+bb:=-cot(a*x)^2/(2*a)-1/a*log(sin(a*x))
+--R
+--R                                   2
+--R        - 2log(sin(a x)) - cot(a x)
+--R   (2)  ----------------------------
+--R                     2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 14
+cc:=aa-bb
+--R
+--R   (3)
+--R                               sin(2a x)
+--R       (- 2cos(2a x) + 2)log(-------------) + (2cos(2a x) - 2)log(sin(a x))
+--R                             cos(2a x) + 1
+--R     + 
+--R                                2                                 2
+--R       (cos(2a x) - 1)log(-------------) + (cos(2a x) - 1)cot(a x)  + cos(2a x)
+--R                          cos(2a x) + 1
+--R     + 
+--R       1
+--R  /
+--R     2a cos(2a x) - 2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 15
+cotrule:=rule(cot(a) == cos(a)/sin(a))
+--R
+--R                  cos(a)
+--R   (4)  cot(a) == ------
+--R                  sin(a)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 16
+dd:=cotrule cc
+--R
+--R   (5)
+--R                                 2      sin(2a x)
+--R       (- 2cos(2a x) + 2)sin(a x) log(-------------)
+--R                                      cos(2a x) + 1
+--R     + 
+--R                               2
+--R       (2cos(2a x) - 2)sin(a x) log(sin(a x))
+--R     + 
+--R                              2          2                                 2
+--R       (cos(2a x) - 1)sin(a x) log(-------------) + (cos(2a x) + 1)sin(a x)
+--R                                   cos(2a x) + 1
+--R     + 
+--R               2                    2
+--R       cos(a x) cos(2a x) - cos(a x)
+--R  /
+--R                                2
+--R     (2a cos(2a x) - 2a)sin(a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 17
+ee:=expandLog dd
+--R
+--R   (6)
+--R                                 2
+--R       (- 2cos(2a x) + 2)sin(a x) log(sin(2a x))
+--R     + 
+--R                               2
+--R       (2cos(2a x) - 2)sin(a x) log(sin(a x))
+--R     + 
+--R                              2
+--R       (cos(2a x) - 1)sin(a x) log(cos(2a x) + 1)
+--R     + 
+--R                                                   2           2
+--R       ((log(2) + 1)cos(2a x) - log(2) + 1)sin(a x)  + cos(a x) cos(2a x)
+--R     + 
+--R                 2
+--R       - cos(a x)
+--R  /
+--R                                2
+--R     (2a cos(2a x) - 2a)sin(a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 18     14:442 Schaums and Axiom agree
+ff:=complexNormalize ee
+--R
+--R   (7)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.443~~~~~$\displaystyle
@@ -82,7 +252,7 @@ $$
 <<*>>=
 )clear all
 
---S 4 of 11
+--S 19
 aa:=integrate(cot(a*x)^n*csc(a*x)^2,x)
 --R 
 --R
@@ -94,6 +264,74 @@ aa:=integrate(cot(a*x)^n*csc(a*x)^2,x)
 --R              (a n + a)sin(a x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 20
+bb:=-cot(a*x)^(n+1)/((n+1)*a)
+--R
+--R                  n + 1
+--R          cot(a x)
+--R   (2)  - -------------
+--R             a n + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 21
+cc:=aa-bb
+--R
+--R                          cos(a x)
+--R                    n log(--------)
+--R                          sin(a x)                    n + 1
+--R        - cos(a x)%e                + sin(a x)cot(a x)
+--R   (3)  ---------------------------------------------------
+--R                         (a n + a)sin(a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 22
+explog:=rule(%e^(n*log(x)) == x^n)
+--R
+--R          n log(x)     n
+--R   (4)  %e         == x
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 23
+dd:=explog cc
+--R
+--R                        n + 1            cos(a x) n
+--R        sin(a x)cot(a x)      - cos(a x)(--------)
+--R                                         sin(a x)
+--R   (5)  -------------------------------------------
+--R                     (a n + a)sin(a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 24
+cotrule:=rule(cot(a) == cos(a)/sin(a))
+--R
+--R                  cos(a)
+--R   (6)  cot(a) == ------
+--R                  sin(a)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 25
+ee:=cotrule dd
+--R
+--R                 cos(a x) n + 1            cos(a x) n
+--R        sin(a x)(--------)      - cos(a x)(--------)
+--R                 sin(a x)                  sin(a x)
+--R   (7)  ---------------------------------------------
+--R                      (a n + a)sin(a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 26     14:443 Schaums and Axiom agree
+ff:=complexNormalize ee
+--R
+--R   (8)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.444~~~~~$\displaystyle
@@ -104,7 +342,7 @@ $$
 <<*>>=
 )clear all
 
---S 5 of 11
+--S 27
 aa:=integrate(csc(a*x)^2/cot(a*x),x)
 --R 
 --R
@@ -115,6 +353,55 @@ aa:=integrate(csc(a*x)^2/cot(a*x),x)
 --R                           a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 28
+bb:=-1/a*log(cot(a*x))
+--R
+--R          log(cot(a x))
+--R   (2)  - -------------
+--R                a
+--R                                                     Type: Expression Integer
+--E
+
+--S 29
+cc:=aa-bb
+--R
+--R              sin(a x)                              2cos(a x)
+--R        log(------------) + log(cot(a x)) - log(- ------------)
+--R            cos(a x) + 1                          cos(a x) + 1
+--R   (3)  -------------------------------------------------------
+--R                                   a
+--R                                                     Type: Expression Integer
+--E
+
+--S 30
+cotrule:=rule(cot(a) == cos(a)/sin(a))
+--R
+--R                  cos(a)
+--R   (4)  cot(a) == ------
+--R                  sin(a)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 31
+dd:=cotrule cc
+--R
+--R              sin(a x)          cos(a x)            2cos(a x)
+--R        log(------------) + log(--------) - log(- ------------)
+--R            cos(a x) + 1        sin(a x)          cos(a x) + 1
+--R   (5)  -------------------------------------------------------
+--R                                   a
+--R                                                     Type: Expression Integer
+--E
+
+--S 32     14:444 Schaums and Axiom differ by a constant
+ee:=expandLog dd
+--R
+--R          log(- 2)
+--R   (6)  - --------
+--R              a
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.445~~~~~$\displaystyle
@@ -125,7 +412,7 @@ $$
 <<*>>=
 )clear all
 
---S 6 of 11
+--S 33
 aa:=integrate(1/cot(a*x),x)
 --R 
 --R
@@ -136,6 +423,42 @@ aa:=integrate(1/cot(a*x),x)
 --R                2a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 34
+bb:=-1/a*log(cos(a*x))
+--R
+--R          log(cos(a x))
+--R   (2)  - -------------
+--R                a
+--R                                                     Type: Expression Integer
+--E
+
+--S 35
+cc:=aa-bb
+--R
+--R                                   2
+--R        2log(cos(a x)) + log(-------------)
+--R                             cos(2a x) + 1
+--R   (3)  -----------------------------------
+--R                         2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 36
+dd:=expandLog cc
+--R
+--R        - log(cos(2a x) + 1) + 2log(cos(a x)) + log(2)
+--R   (4)  ----------------------------------------------
+--R                              2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 37     14:445 Schaums and Axiom agree
+ee:=complexNormalize dd
+--R
+--R   (5)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.446~~~~~$\displaystyle
@@ -148,7 +471,7 @@ $$
 <<*>>=
 )clear all
 
---S 7 of 11
+--S 38     14:446 Axiom cannot compute this integral
 aa:=integrate(x*cot(a*x),x)
 --R 
 --R
@@ -169,7 +492,7 @@ $$
 <<*>>=
 )clear all
 
---S 8 of 11
+--S 39     14:447 Axiom cannot compute this integral
 aa:=integrate(cot(a*x)/x,x)
 --R 
 --R
@@ -189,7 +512,7 @@ $$
 <<*>>=
 )clear all
 
---S 9 of 11
+--S 40
 aa:=integrate(x*cot(a*x)^2,x)
 --R 
 --R
@@ -205,6 +528,58 @@ aa:=integrate(x*cot(a*x)^2,x)
 --R     2a sin(2a x)
 --R                                          Type: Union(Expression Integer,...)
 --E
+
+--S 41
+bb:=-(x*cot(a*x))/a+1/a^2*log(sin(a*x))-x^2/2
+--R
+--R                                          2 2
+--R        2log(sin(a x)) - 2a x cot(a x) - a x
+--R   (2)  -------------------------------------
+--R                           2
+--R                         2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 42
+cc:=aa-bb
+--R
+--R   (3)
+--R                       sin(2a x)
+--R       2sin(2a x)log(-------------) - 2sin(2a x)log(sin(a x))
+--R                     cos(2a x) + 1
+--R     + 
+--R                            2
+--R       - sin(2a x)log(-------------) + 2a x cot(a x)sin(2a x) - 2a x cos(2a x)
+--R                      cos(2a x) + 1
+--R     + 
+--R       - 2a x
+--R  /
+--R       2
+--R     2a sin(2a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 43
+dd:=expandLog cc
+--R
+--R   (4)
+--R       2sin(2a x)log(sin(2a x)) - 2sin(2a x)log(sin(a x))
+--R     + 
+--R       - sin(2a x)log(cos(2a x) + 1) + (2a x cot(a x) - log(2))sin(2a x)
+--R     + 
+--R       - 2a x cos(2a x) - 2a x
+--R  /
+--R       2
+--R     2a sin(2a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 44     14:448 Schaums and Axiom agree
+ee:=complexNormalize dd
+--R
+--R   (5)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.449~~~~~$\displaystyle
@@ -215,7 +590,7 @@ $$
 <<*>>=
 )clear all
 
---S 10 of 11
+--S 45
 aa:=integrate(1/(p+q*cot(a*x)),x)
 --R 
 --R
@@ -228,6 +603,34 @@ aa:=integrate(1/(p+q*cot(a*x)),x)
 --R                                2a q  + 2a p
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 46
+bb:=(p*x)/(p^2+q^2)-q/(a*(p^2+q^2))*log(p*sin(a*x)+q*cos(a*x))
+--R
+--R        - q log(p sin(a x) + q cos(a x)) + a p x
+--R   (2)  ----------------------------------------
+--R                          2      2
+--R                       a q  + a p
+--R                                                     Type: Expression Integer
+--E
+
+--S 47     14:449 Axiom cannot simplify this expression
+cc:=aa-bb
+--R
+--R   (3)
+--R                p sin(2a x) + q cos(2a x) + q
+--R       - 2q log(-----------------------------) + 2q log(p sin(a x) + q cos(a x))
+--R                        cos(2a x) + 1
+--R     + 
+--R                   2
+--R       q log(-------------)
+--R             cos(2a x) + 1
+--R  /
+--R         2       2
+--R     2a q  + 2a p
+--R                                                     Type: Expression Integer
+--E
+
 @
 
 \section{\cite{1}:14.450~~~~~$\displaystyle
@@ -238,7 +641,7 @@ $$
 <<*>>=
 )clear all
 
---S 11 of 11
+--S 48     14:450 Axiom cannot compute this integral
 aa:=integrate(cot(a*x)^n,x)
 --R 
 --R
diff --git a/src/input/schaum22.input.pamphlet b/src/input/schaum22.input.pamphlet
index 66befb9..173338a 100644
--- a/src/input/schaum22.input.pamphlet
+++ b/src/input/schaum22.input.pamphlet
@@ -19,7 +19,7 @@ $$
 )set message auto off
 )clear all
 
---S 1 of 10
+--S 1
 aa:=integrate(sec(a*x),x)
 --R 
 --R
@@ -30,6 +30,172 @@ aa:=integrate(sec(a*x),x)
 --R                                     a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 2
+bb1:=1/a*log(sec(a*x)+tan(a*x))
+--R
+--R        log(tan(a x) + sec(a x))
+--R   (2)  ------------------------
+--R                    a
+--R                                                     Type: Expression Integer
+--E
+
+--S 3
+bb2:=1/a*log(tan((a*x)/2+%pi/4))
+--R
+--R                2a x + %pi
+--R        log(tan(----------))
+--R                     4
+--R   (3)  --------------------
+--R                  a
+--R                                                     Type: Expression Integer
+--E
+
+--S 4
+cc1:=aa-bb1
+--R
+--R   (4)
+--R                                        sin(a x) + cos(a x) + 1
+--R       - log(tan(a x) + sec(a x)) + log(-----------------------)
+--R                                              cos(a x) + 1
+--R     + 
+--R             sin(a x) - cos(a x) - 1
+--R       - log(-----------------------)
+--R                   cos(a x) + 1
+--R  /
+--R     a
+--R                                                     Type: Expression Integer
+--E
+
+--S 5
+tanrule:=rule(tan(a) == sin(a)/cos(a))
+--R
+--R                  sin(a)
+--R   (5)  tan(a) == ------
+--R                  cos(a)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 6
+dd1:=tanrule cc1
+--R
+--R   (6)
+--R             sin(a x) + cos(a x)sec(a x)        sin(a x) + cos(a x) + 1
+--R       - log(---------------------------) + log(-----------------------)
+--R                       cos(a x)                       cos(a x) + 1
+--R     + 
+--R             sin(a x) - cos(a x) - 1
+--R       - log(-----------------------)
+--R                   cos(a x) + 1
+--R  /
+--R     a
+--R                                                     Type: Expression Integer
+--E
+
+--S 7
+secrule:=rule(sec(a) == 1/cos(a))
+--R
+--R                     1
+--R   (7)  sec(a) == ------
+--R                  cos(a)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 8
+ee1:=secrule dd1
+--R
+--R   (8)
+--R             sin(a x) + 1        sin(a x) + cos(a x) + 1
+--R       - log(------------) + log(-----------------------)
+--R               cos(a x)                cos(a x) + 1
+--R     + 
+--R             sin(a x) - cos(a x) - 1
+--R       - log(-----------------------)
+--R                   cos(a x) + 1
+--R  /
+--R     a
+--R                                                     Type: Expression Integer
+--E
+
+--S 9
+ff1:=expandLog ee1
+--R
+--R   (9)
+--R       log(sin(a x) + cos(a x) + 1) - log(sin(a x) + 1)
+--R     + 
+--R       - log(sin(a x) - cos(a x) - 1) + log(cos(a x))
+--R  /
+--R     a
+--R                                                     Type: Expression Integer
+--E
+
+--S 10
+gg1:=complexNormalize ff1
+--R
+--R         log(- 1)
+--R   (10)  --------
+--R             a
+--R                                                     Type: Expression Integer
+--E
+
+--S 11
+cc2:=aa-bb2
+--R
+--R   (11)
+--R                 2a x + %pi         sin(a x) + cos(a x) + 1
+--R       - log(tan(----------)) + log(-----------------------)
+--R                      4                   cos(a x) + 1
+--R     + 
+--R             sin(a x) - cos(a x) - 1
+--R       - log(-----------------------)
+--R                   cos(a x) + 1
+--R  /
+--R     a
+--R                                                     Type: Expression Integer
+--E
+
+--S 12
+dd2:=tanrule cc2
+--R
+--R   (12)
+--R           sin(a x) + cos(a x) + 1        sin(a x) - cos(a x) - 1
+--R       log(-----------------------) - log(-----------------------)
+--R                 cos(a x) + 1                   cos(a x) + 1
+--R     + 
+--R                 2a x + %pi
+--R             sin(----------)
+--R                      4
+--R       - log(---------------)
+--R                 2a x + %pi
+--R             cos(----------)
+--R                      4
+--R  /
+--R     a
+--R                                                     Type: Expression Integer
+--E
+
+--S 13
+ee2:=expandLog dd2
+--R
+--R   (13)
+--R       log(sin(a x) + cos(a x) + 1) - log(sin(a x) - cos(a x) - 1)
+--R     + 
+--R                 2a x + %pi             2a x + %pi
+--R       - log(sin(----------)) + log(cos(----------))
+--R                      4                      4
+--R  /
+--R     a
+--R                                                     Type: Expression Integer
+--E
+
+--S 14     14:451 Schaums and Axiom differ by a constant
+ff2:=complexNormalize ee2
+--R
+--R         log(- 1)
+--R   (14)  --------
+--R             a
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.452~~~~~$\displaystyle
@@ -40,7 +206,7 @@ $$
 <<*>>=
 )clear all
 
---S 2 of 10
+--S 15
 aa:=integrate(sec(a*x)^2,x)
 --R 
 --R
@@ -49,6 +215,40 @@ aa:=integrate(sec(a*x)^2,x)
 --R        a cos(a x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 16
+bb:=tan(a*x)/a
+--R
+--R        tan(a x)
+--R   (2)  --------
+--R            a
+--R                                                     Type: Expression Integer
+--E
+
+--S 17
+cc:=aa-bb
+--R
+--R        - cos(a x)tan(a x) + sin(a x)
+--R   (3)  -----------------------------
+--R                  a cos(a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 18
+tanrule:=rule(tan(a) == sin(a)/cos(a))
+--R
+--R                  sin(a)
+--R   (4)  tan(a) == ------
+--R                  cos(a)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 19     14:452 Schaums and Axiom agree
+dd:=tanrule cc
+--R
+--R   (5)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.453~~~~~$\displaystyle
@@ -59,7 +259,7 @@ $$
 <<*>>=
 )clear all
 
---S 3 of 10
+--S 20
 aa:=integrate(sec(a*x)^3,x)
 --R 
 --R
@@ -76,6 +276,113 @@ aa:=integrate(sec(a*x)^3,x)
 --R     2a cos(a x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 21
+bb:=(sec(a*x)*tan(a*x))/(2*a)+1/(2*a)*log(sec(a*x)+tan(a*x))
+--R
+--R        log(tan(a x) + sec(a x)) + sec(a x)tan(a x)
+--R   (2)  -------------------------------------------
+--R                             2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 22
+cc:=aa-bb
+--R
+--R   (3)
+--R                 2
+--R       - cos(a x) log(tan(a x) + sec(a x))
+--R     + 
+--R               2    sin(a x) + cos(a x) + 1
+--R       cos(a x) log(-----------------------)
+--R                          cos(a x) + 1
+--R     + 
+--R                 2    sin(a x) - cos(a x) - 1            2
+--R       - cos(a x) log(-----------------------) - cos(a x) sec(a x)tan(a x)
+--R                            cos(a x) + 1
+--R     + 
+--R       sin(a x)
+--R  /
+--R                2
+--R     2a cos(a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 23
+tanrule:=rule(tan(a) == sin(a)/cos(a))
+--R
+--R                  sin(a)
+--R   (4)  tan(a) == ------
+--R                  cos(a)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 24
+dd:=tanrule cc
+--R
+--R   (5)
+--R                 2    sin(a x) + cos(a x)sec(a x)
+--R       - cos(a x) log(---------------------------)
+--R                                cos(a x)
+--R     + 
+--R               2    sin(a x) + cos(a x) + 1
+--R       cos(a x) log(-----------------------)
+--R                          cos(a x) + 1
+--R     + 
+--R               2    sin(a x) - cos(a x) - 1
+--R     - cos(a x) log(-----------------------) + (- cos(a x)sec(a x) + 1)sin(a x)
+--R                          cos(a x) + 1
+--R  /
+--R                2
+--R     2a cos(a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 25
+secrule:=rule(sec(a) == 1/cos(a))
+--R
+--R                     1
+--R   (6)  sec(a) == ------
+--R                  cos(a)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 26
+ee:=secrule dd
+--R
+--R   (7)
+--R             sin(a x) + 1        sin(a x) + cos(a x) + 1
+--R       - log(------------) + log(-----------------------)
+--R               cos(a x)                cos(a x) + 1
+--R     + 
+--R             sin(a x) - cos(a x) - 1
+--R       - log(-----------------------)
+--R                   cos(a x) + 1
+--R  /
+--R     2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 27
+ff:=expandLog ee
+--R
+--R   (8)
+--R       log(sin(a x) + cos(a x) + 1) - log(sin(a x) + 1)
+--R     + 
+--R       - log(sin(a x) - cos(a x) - 1) + log(cos(a x))
+--R  /
+--R     2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 28     14:453 Schaums and Axiom differ by a constant
+gg:=complexNormalize ff
+--R
+--R        log(- 1)
+--R   (9)  --------
+--R           2a
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.454~~~~~$\displaystyle
@@ -86,7 +393,7 @@ $$
 <<*>>=
 )clear all
 
---S 4 of 10
+--S 29
 aa:=integrate(sec(a*x)^n*tan(a*x),x)
 --R
 --R                    1
@@ -100,6 +407,31 @@ aa:=integrate(sec(a*x)^n*tan(a*x),x)
 --R                a n
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 30
+bb:=sec(a*x)^n/(n*a)
+--R
+--R                n
+--R        sec(a x)
+--R   (2)  ---------
+--R           a n
+--R                                                     Type: Expression Integer
+--E
+
+--S 31     14:454 Axiom cannot simplify this expression
+cc:=aa-bb
+--R
+--R                    1
+--R          n log(---------)
+--R                        2
+--R                cos(a x)
+--R          ----------------
+--R                  2                  n
+--R        %e                 - sec(a x)
+--R   (3)  ------------------------------
+--R                      a n
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.455~~~~~$\displaystyle
@@ -110,7 +442,7 @@ $$
 <<*>>=
 )clear all
 
---S 5 of 10
+--S 32
 aa:=integrate(1/sec(a*x),x)
 --R 
 --R
@@ -118,7 +450,23 @@ aa:=integrate(1/sec(a*x),x)
 --R   (1)  --------
 --R            a
 --R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 33
+bb:=sin(a*x)/a
+--R
+--R        sin(a x)
+--R   (2)  --------
+--R            a
+--R                                                     Type: Expression Integer
 --E 
+
+--S 34     14:455 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.456~~~~~$\displaystyle
@@ -130,7 +478,7 @@ $$
 <<*>>=
 )clear all
 
---S 6 of 10
+--S 35     14:456 Axiom cannot compute this integral
 aa:=integrate(x*sec(a*x),x)
 --R 
 --R
@@ -151,7 +499,7 @@ $$
 <<*>>=
 )clear all
 
---S 7 of 10
+--S 36     14:457 Axiom cannot compute this integral
 aa:=integrate(sec(a*x)/x,x)
 --R 
 --R
@@ -171,7 +519,7 @@ $$
 <<*>>=
 )clear all
 
---S 8 of 10
+--S 37
 aa:=integrate(x*sec(a*x)^2,x)
 --R 
 --R
@@ -184,6 +532,64 @@ aa:=integrate(x*sec(a*x)^2,x)
 --R                                  a cos(a x)
 --R                                          Type: Union(Expression Integer,...)
 --E
+
+--S 38
+bb:=x/a*tan(a*x)+1/a^2*log(cos(a*x))
+--R
+--R        log(cos(a x)) + a x tan(a x)
+--R   (2)  ----------------------------
+--R                      2
+--R                     a
+--R                                                     Type: Expression Integer
+--E
+
+--S 39
+cc:=aa-bb
+--R
+--R   (3)
+--R                                                   2
+--R       - cos(a x)log(cos(a x)) - cos(a x)log(------------)
+--R                                             cos(a x) + 1
+--R     + 
+--R                       2cos(a x)
+--R       cos(a x)log(- ------------) - a x cos(a x)tan(a x) + a x sin(a x)
+--R                     cos(a x) + 1
+--R  /
+--R      2
+--R     a cos(a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 40
+tanrule:=rule(tan(a) == sin(a)/cos(a))
+--R
+--R                  sin(a)
+--R   (4)  tan(a) == ------
+--R                  cos(a)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 41
+dd:=tanrule cc
+--R
+--R                                    2                 2cos(a x)
+--R        - log(cos(a x)) - log(------------) + log(- ------------)
+--R                              cos(a x) + 1          cos(a x) + 1
+--R   (5)  ---------------------------------------------------------
+--R                                     2
+--R                                    a
+--R                                                     Type: Expression Integer
+--E
+
+--S 42     14:458 Schaums and Axiom differ by a constant
+ee:=expandLog dd
+--R
+--R        - log(2) + log(- 2)
+--R   (6)  -------------------
+--R                  2
+--R                 a
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.459~~~~~$\displaystyle
@@ -194,7 +600,7 @@ $$
 <<*>>=
 )clear all
 
---S 9 of 10
+--S 43
 aa:=integrate(1/(q+p*sec(a*x)),x)
 --R 
 --R
@@ -218,7 +624,136 @@ aa:=integrate(1/(q+p*sec(a*x)),x)
 --R                           |   2    2
 --R                       a q\|- q  + p
 --R                                     Type: Union(List Expression Integer,...)
+--E
+
+--S 44
+t1:=integrate(1/(p+q*cos(a*x)),x)
+--R
+--R   (2)
+--R                           +-------+
+--R                           | 2    2        2    2
+--R        (- p cos(a x) - q)\|q  - p   + (- q  + p )sin(a x)
+--R    log(--------------------------------------------------)
+--R                          q cos(a x) + p
+--R   [-------------------------------------------------------,
+--R                            +-------+
+--R                            | 2    2
+--R                          a\|q  - p
+--R                     +---------+
+--R                     |   2    2
+--R            sin(a x)\|- q  + p
+--R    2atan(-----------------------)
+--R          (q + p)cos(a x) + q + p
+--R    ------------------------------]
+--R               +---------+
+--R               |   2    2
+--R             a\|- q  + p
+--R                                     Type: Union(List Expression Integer,...)
 --E 
+
+--S 45
+bb1:=x/q-p/q*t1.1
+--R
+--R   (3)
+--R                              +-------+
+--R                              | 2    2        2    2                 +-------+
+--R           (- p cos(a x) - q)\|q  - p   + (- q  + p )sin(a x)        | 2    2
+--R   - p log(--------------------------------------------------) + a x\|q  - p
+--R                             q cos(a x) + p
+--R   ---------------------------------------------------------------------------
+--R                                      +-------+
+--R                                      | 2    2
+--R                                  a q\|q  - p
+--R                                                     Type: Expression Integer
+--E
+
+--S 46
+bb2:=x/q-p/q*t1.2
+--R
+--R                             +---------+
+--R                             |   2    2          +---------+
+--R                    sin(a x)\|- q  + p           |   2    2
+--R        - 2p atan(-----------------------) + a x\|- q  + p
+--R                  (q + p)cos(a x) + q + p
+--R   (4)  ----------------------------------------------------
+--R                               +---------+
+--R                               |   2    2
+--R                           a q\|- q  + p
+--R                                                     Type: Expression Integer
+--E
+
+--S 47
+cc1:=aa.1-bb1
+--R
+--R   (5)
+--R                                +-------+
+--R                                | 2    2      2    2
+--R             (- p cos(a x) - q)\|q  - p   + (q  - p )sin(a x)
+--R       p log(------------------------------------------------)
+--R                              q cos(a x) + p
+--R     + 
+--R                                +-------+
+--R                                | 2    2        2    2
+--R             (- p cos(a x) - q)\|q  - p   + (- q  + p )sin(a x)
+--R       p log(--------------------------------------------------)
+--R                               q cos(a x) + p
+--R  /
+--R         +-------+
+--R         | 2    2
+--R     a q\|q  - p
+--R                                                     Type: Expression Integer
+--E
+
+--S 48
+cc2:=aa.1-bb2
+--R
+--R   (6)
+--R                                           +-------+
+--R         +---------+                       | 2    2      2    2
+--R         |   2    2     (- p cos(a x) - q)\|q  - p   + (q  - p )sin(a x)
+--R       p\|- q  + p  log(------------------------------------------------)
+--R                                         q cos(a x) + p
+--R     + 
+--R                                   +---------+
+--R          +-------+                |   2    2
+--R          | 2    2        sin(a x)\|- q  + p
+--R       2p\|q  - p  atan(-----------------------)
+--R                        (q + p)cos(a x) + q + p
+--R  /
+--R         +---------+ +-------+
+--R         |   2    2  | 2    2
+--R     a q\|- q  + p  \|q  - p
+--R                                                     Type: Expression Integer
+--E
+
+--S 49
+cc3:=aa.2-bb1
+--R
+--R   (7)
+--R                                           +-------+
+--R         +---------+                       | 2    2        2    2
+--R         |   2    2     (- p cos(a x) - q)\|q  - p   + (- q  + p )sin(a x)
+--R       p\|- q  + p  log(--------------------------------------------------)
+--R                                          q cos(a x) + p
+--R     + 
+--R                                     +---------+
+--R            +-------+                |   2    2
+--R            | 2    2        sin(a x)\|- q  + p
+--R       - 2p\|q  - p  atan(-----------------------)
+--R                          (q + p)cos(a x) + q + p
+--R  /
+--R         +---------+ +-------+
+--R         |   2    2  | 2    2
+--R     a q\|- q  + p  \|q  - p
+--R                                                     Type: Expression Integer
+--E
+
+--S 50     14:459 Schaums and Axiom agree
+cc4:=aa.2-bb2
+--R
+--R   (8)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.460~~~~~$\displaystyle
@@ -230,7 +765,7 @@ $$
 <<*>>=
 )clear all
 
---S 10 of 10
+--S 51     14:460 Axiom cannot compute this integral
 aa:=integrate(sec(a*x)^n,x)
 --R 
 --R



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Hello developer of axiom,

 

is there any possibility to download sources for windows?

 

Best regards,

 

Christopher Scholz


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<p class=3DMsoNormal><font size=3D2 face=3DArial><span =
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for
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Christopher,

Axiom does not run on windows.
Try the FriCAS project. <http://sourceforge.net/projects/fricas>

Tim



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To: "Christopher Scholz" <scholz@newgenerationx.de>
Subject: Re: [Axiom-developer] windows sources
References: <006601c8a4b6$7df328f0$6500a8c0@cptuhura>
From: Martin Rubey <martin.rubey@univie.ac.at>
Date: 25 Apr 2008 08:46:13 +0200
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Dear Christopher, Dear Tim,

Tim, thanks for forwarding.

Christopher,

"Christopher Scholz" <scholz@newgenerationx.de> writes:

> is there any possibility to download sources for windows?

the quick answer:

  svn co https://fricas.svn.sourceforge.net/svnroot/fricas/trunk fricas

Concerning the detailed answer, read on:

I guess you want to build from scratch?  In case, I attach step by step
instructions for downloading and building using CYGWIN below.

FriCAS should also work with MinGW, but currently (as far as I know), you won't
get graphics nor HyperDoc (the help facility), so if you are mainly interested
in "using" FriCAS, I guess Cygwin is the better bet.

There is yet another alternative, which is called "andLinux".  Bill Page knows
about it.

There is a cygwin binary produced by Alfredo Portes, I can't find the link
right now but I'm sure he'd be glad to help.

If you encounter any difficulties, please don't hesitate to ask.  I'm grateful
for every bit that improves the MS Windows port!  Finally, note that below we
use CLISP as Common Lisp implementation.  In principle, it should work with any
Common Lisp (supported: 
    * GCL, 2.6.7 or prerelease 2.6.8 
    * sbcl, 1.0.7 or later
    * clisp, 2.41 or later
    * openmcl, 1.1 prerelase 070512 or later
    * ECL, 0.9j or later)
with a little patching, of which sbcl should be fastest.

Hope this helps,

Martin


-------------------------------------------------------------------------------

INSTALL.CYGWIN:

These instructions show you how to build FriCAS on MS Windows from the sources
in the subversion repository.  You may want to consider building FriCAS from a
distribution tarball instead, which contains pregenerated algebra Lisp,
HyperDoc pages and graphic examples.  Moreover, using the tarball the build is
much faster - a few minutes instead of a few hours.  You can get a tarball via
http://fricas.sourceforge.net/download.html

First of all, do not be afraid!  The instructions below probably look more
intimidating than they really should be.  In case something goes wrong, do not
hesitate to ask at fricas-devel@googlegroups.com.

To compile FriCAS on MS Windows, we proceed as follows:

I) If you do not have cygwin installed, go to

    http://cygwin.com/

    Look for a link called setup.exe and save it to disk.

II) Start cygwin's setup program.  The first few questions can be answered with
    the default values, until you get to the "Select Packages" dialog.

    Clicking on a little + will expand the list of packages. You should select
    apart from the defaults the following:

    (DISCLAIMER: this list is likely to be overkill.  Also note that selecting
    will also select many packages they depend on, this should happen
    automatically.)

           In Devel: gcc-mingw
                     gcc-mingw-core
                     make
                     patchutils
                     subversion
           In Math:    clisp
           In Publishing: psutils
                          tetex
                          tetex-base
                          tetex-bin
                          tetex-extra
                          tetex-tiny
                          tetex-x11
           In Web: wget
           In X11: xterm
                   xorg-x11-devel
optional   In Editors: emacs
(see V)                emacs-X11

    Complete the cygwin installation process.

III) start cygwin - a black console window should appear


  find a place to build FriCAS.

  cd /cygdrive/c
  mkdir scratch
  cd scratch

    (it is essential that the path to scratch does not contain any spaces.
    Otherwise the build won't work...)

IV) follow the instructions in INSTALL (but note that we are going to build
    axiom using clisp), that is:

    1) Fetch sources:

  svn co https://fricas.svn.sourceforge.net/svnroot/fricas/trunk fricas
 

    2) Fetch nonstandard prerequisites:

  cd fricas
  mkdir zips
  cd zips
  wget https://axiom.svn.sourceforge.net/svnroot/axiom/trunk/axiom/zips/noweb-2.10a.tgz

    or, if this doesn't work:

  wget --no-check-certificate https://axiom.svn.sourceforge.net/svnroot/axiom/trunk/axiom/zips/noweb-2.10a.tgz

    3) create the build directory (again: without spaces!)

  cd ../..
  mkdir ax-build
  cd ax-build
 
    4) configure.  Possibly, you will have to restrict the PATH to Cygwin
        programs, because otherwise configure may pick, for example, Borland
        grep which causes failure later.  You can do this by typing

  export PATH=/usr/local/bin:/usr/bin:/bin:/usr/X11R6/bin

  ../configure --with-lisp=clisp

    5) build and install:

  make

    make will very likely fail with an error like

      mkdir /dev/null 2>/dev/null
      make[1]: [install-elisp] Error 1 (ignored)
      cp elisp/noweb-mode.el /dev/null
      cp: cannot create regular file `/dev/null': Invalid request code
      make[1]: *** [install-elisp] Error 1
      make[1]: Leaving directory `/cygdrive/c/scratch/ax-build/noweb/src'
      make: *** [stamp-noweb] Error 2

    we ignore this error (which occurs because the ELISP environment variable
    is set to /dev/null)

  touch stamp-noweb
  make

     6) make the graphics examples:

        IMPORTANT NOTE: this step failed when I tried.  After the first drawing
        appeared and disappeared, it did not continue.  The example graphics
        are in no way essential though and can be easily reproduced in the
        installed system.

     6a) start X:

  sh /usr/X11R6/bin/startxwin.sh

        a new (white) console should appear

     6b) run the examples

  cd /cygwin/c/scratch/ax-build/src/paste
  make gphts

        at this point (which will take a while), graphics should appear and
       disappear.

  cd ../..
  make

  
     7) install

  make install

V) you may want to install the emacs mode coming with FriCAS.  In this case you
   need to:

     1) start cygwin's setup program again and select the packages:

           In Editors: emacs
                       emacs-X11

     2) extract the emacs mode

  cd /cygwin/c/scratch/ax-build
  cp ../fricas/src/scripts/tex/axiom.sty .
  cp ../fricas/contrib/emacs/axiom.el.pamphlet .
  build/scripts/document axiom.el.pamphlet 

        you should obtain two files: axiom.el and axiom.el.dvi.  The latter
        contains the documentation of the mode and can be viewed with any dvi
        viewer.

     3) install the emacs mode and optionally a startup script:

  cp axiom.el /usr/share/emacs/site-lisp
  cp ../fricas/contrib/emacs/eaxiom /usr/bin


     4) if you installed the startup script, you can start axiom now with

  eaxiom

        or

  sh /usr/X11R6/bin/startxwin.sh
  eaxiom




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Subject: [Axiom-developer] 20080424.01.tpd.patch (CATS Shaums-Axiom
	equivalence testing (23))
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schaum23.input.pamphlet
  14:461 Schaums and Axiom agree
  14:462 Schaums and Axiom agree
  14:463 Schaums and Axiom agree
  14:464 Axiom cannot simplify this expression
  14:465 Schaums and Axiom agree
  14:466 Axiom cannot compute this integral
  14:467 Axiom cannot compute this integral
  14:468 Schaums and Axiom differ by a constant
  14:469 Schaums and Axiom agree
  14:470 Axiom cannot compute this integral
======================================================================
diff --git a/changelog b/changelog
index 80e94f3..314b281 100644
--- a/changelog
+++ b/changelog
@@ -1,3 +1,4 @@
+20080424 tpd src/input/schaum23.input show Schaums-Axiom equivalence
 20080423 tpd src/input/schaum22.input show Schaums-Axiom equivalence
 20080423 tpd src/input/schaum21.input show Schaums-Axiom equivalence
 20080423 tpd src/input/schaum20.input show Schaums-Axiom equivalence
diff --git a/src/input/schaum23.input.pamphlet b/src/input/schaum23.input.pamphlet
index 679e775..c24ef73 100644
--- a/src/input/schaum23.input.pamphlet
+++ b/src/input/schaum23.input.pamphlet
@@ -19,7 +19,7 @@ $$
 )set message auto off
 )clear all
 
---S 1 of 10
+--S 1
 aa:=integrate(csc(a*x),x)
 --R 
 --R
@@ -30,6 +30,148 @@ aa:=integrate(csc(a*x),x)
 --R                a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 2
+bb1:=1/a*log(csc(a*x)-cot(a*x))
+--R
+--R        log(csc(a x) - cot(a x))
+--R   (2)  ------------------------
+--R                    a
+--R                                                     Type: Expression Integer
+--E
+
+--S 3
+bb2:=1/a*log(tan((a*x)/2))
+--R
+--R                a x
+--R        log(tan(---))
+--R                 2
+--R   (3)  -------------
+--R              a
+--R                                                     Type: Expression Integer
+--E
+
+--S 4
+cc1:=aa-bb1
+--R
+--R              sin(a x)
+--R        log(------------) - log(csc(a x) - cot(a x))
+--R            cos(a x) + 1
+--R   (4)  --------------------------------------------
+--R                              a
+--R                                                     Type: Expression Integer
+--E
+
+--S 5
+cotrule:=rule(cot(a) == cos(a)/sin(a))
+--R
+--R                  cos(a)
+--R   (5)  cot(a) == ------
+--R                  sin(a)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 6
+dd1:=cotrule cc1
+--R
+--R              sin(a x)          csc(a x)sin(a x) - cos(a x)
+--R        log(------------) - log(---------------------------)
+--R            cos(a x) + 1                  sin(a x)
+--R   (6)  ----------------------------------------------------
+--R                                  a
+--R                                                     Type: Expression Integer
+--E
+
+--S 7
+cscrule:=rule(csc(a) == 1/sin(a))
+--R
+--R                     1
+--R   (7)  csc(a) == ------
+--R                  sin(a)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 8
+ee1:=cscrule dd1
+--R
+--R              sin(a x)          - cos(a x) + 1
+--R        log(------------) - log(--------------)
+--R            cos(a x) + 1           sin(a x)
+--R   (8)  ---------------------------------------
+--R                           a
+--R                                                     Type: Expression Integer
+--E
+
+--S 9
+ff1:=expandLog ee1
+--R
+--R        2log(sin(a x)) - log(cos(a x) + 1) - log(cos(a x) - 1) - log(- 1)
+--R   (9)  -----------------------------------------------------------------
+--R                                        a
+--R                                                     Type: Expression Integer
+--E
+
+--S 10
+gg1:=complexNormalize ff1
+--R
+--R           2log(- 1)
+--R   (10)  - ---------
+--R               a
+--R                                                     Type: Expression Integer
+--E
+
+--S 11
+cc2:=aa-bb2
+--R
+--R                   a x           sin(a x)
+--R         - log(tan(---)) + log(------------)
+--R                    2          cos(a x) + 1
+--R   (11)  -----------------------------------
+--R                          a
+--R                                                     Type: Expression Integer
+--E
+
+--S 12
+tanrule:=rule(tan(a) == sin(a)/cos(a))
+--R
+--R                   sin(a)
+--R   (12)  tan(a) == ------
+--R                   cos(a)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 13
+dd2:=tanrule cc2
+--R
+--R                                     a x
+--R                                 sin(---)
+--R               sin(a x)               2
+--R         log(------------) - log(--------)
+--R             cos(a x) + 1            a x
+--R                                 cos(---)
+--R                                      2
+--R   (13)  ---------------------------------
+--R                         a
+--R                                                     Type: Expression Integer
+--E
+
+--S 14
+ee2:=expandLog dd2
+--R
+--R                                 a x                                 a x
+--R         log(sin(a x)) - log(sin(---)) - log(cos(a x) + 1) + log(cos(---))
+--R                                  2                                   2
+--R   (14)  -----------------------------------------------------------------
+--R                                         a
+--R                                                     Type: Expression Integer
+--E
+
+--S 15     14:461 Schaums and Axiom agree
+ff2:=complexNormalize ee2
+--R
+--R   (15)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.462~~~~~$\displaystyle
@@ -40,7 +182,7 @@ $$
 <<*>>=
 )clear all
 
---S 2 of 10
+--S 16
 aa:=integrate(csc(a*x)^2,x)
 --R 
 --R
@@ -49,6 +191,40 @@ aa:=integrate(csc(a*x)^2,x)
 --R          a sin(a x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 17
+bb:=-cot(a*x)/a
+--R
+--R          cot(a x)
+--R   (2)  - --------
+--R              a
+--R                                                     Type: Expression Integer
+--E
+
+--S 18
+cc:=aa-bb
+--R
+--R        cot(a x)sin(a x) - cos(a x)
+--R   (3)  ---------------------------
+--R                 a sin(a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 19
+cotrule:=rule(cot(a) == cos(a)/sin(a))
+--R
+--R                  cos(a)
+--R   (4)  cot(a) == ------
+--R                  sin(a)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 20     14:462 Schaums and Axiom agree
+dd:=cotrule cc
+--R
+--R   (5)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.463~~~~~$\displaystyle
@@ -59,7 +235,7 @@ $$
 <<*>>=
 )clear all
 
---S 3 of 10
+--S 21
 aa:=integrate(csc(a*x)^3,x)
 --R 
 --R
@@ -71,6 +247,159 @@ aa:=integrate(csc(a*x)^3,x)
 --R                     2a cos(a x)  - 2a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 22
+bb:=-(csc(a*x)*cot(a*x))/(2*a)+1/(2*a)*log(tan((a*x)/2))
+--R
+--R                a x
+--R        log(tan(---)) - cot(a x)csc(a x)
+--R                 2
+--R   (2)  --------------------------------
+--R                       2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 23
+cc:=aa-bb
+--R
+--R   (3)
+--R                  2             a x              2           sin(a x)
+--R       (- cos(a x)  + 1)log(tan(---)) + (cos(a x)  - 1)log(------------)
+--R                                 2                         cos(a x) + 1
+--R     + 
+--R                2
+--R       (cos(a x)  - 1)cot(a x)csc(a x) + cos(a x)
+--R  /
+--R                2
+--R     2a cos(a x)  - 2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 24
+cotrule:=rule(cot(a) == cos(a)/sin(a))
+--R
+--R                  cos(a)
+--R   (4)  cot(a) == ------
+--R                  sin(a)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 25
+dd:=cotrule cc
+--R
+--R   (5)
+--R                  2                     a x
+--R       (- cos(a x)  + 1)sin(a x)log(tan(---))
+--R                                         2
+--R     + 
+--R                2                   sin(a x)
+--R       (cos(a x)  - 1)sin(a x)log(------------) + cos(a x)sin(a x)
+--R                                  cos(a x) + 1
+--R     + 
+--R                3
+--R       (cos(a x)  - cos(a x))csc(a x)
+--R  /
+--R                 2
+--R     (2a cos(a x)  - 2a)sin(a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 26
+tanrule:=rule(tan(a) == sin(a)/cos(a))
+--R
+--R                  sin(a)
+--R   (6)  tan(a) == ------
+--R                  cos(a)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 27
+ee:=tanrule dd
+--R
+--R   (7)
+--R                2                   sin(a x)
+--R       (cos(a x)  - 1)sin(a x)log(------------)
+--R                                  cos(a x) + 1
+--R     + 
+--R                                        a x
+--R                                    sin(---)
+--R                  2                      2
+--R       (- cos(a x)  + 1)sin(a x)log(--------) + cos(a x)sin(a x)
+--R                                        a x
+--R                                    cos(---)
+--R                                         2
+--R     + 
+--R                3
+--R       (cos(a x)  - cos(a x))csc(a x)
+--R  /
+--R                 2
+--R     (2a cos(a x)  - 2a)sin(a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 28
+cscrule:=rule(csc(a) == 1/sin(a))
+--R
+--R                     1
+--R   (8)  csc(a) == ------
+--R                  sin(a)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 29
+ff:=cscrule ee
+--R
+--R   (9)
+--R                2             2      sin(a x)
+--R       (cos(a x)  - 1)sin(a x) log(------------)
+--R                                   cos(a x) + 1
+--R     + 
+--R                                         a x
+--R                                     sin(---)
+--R                  2             2         2                      2           3
+--R       (- cos(a x)  + 1)sin(a x) log(--------) + cos(a x)sin(a x)  + cos(a x)
+--R                                         a x
+--R                                     cos(---)
+--R                                          2
+--R     + 
+--R       - cos(a x)
+--R  /
+--R                 2              2
+--R     (2a cos(a x)  - 2a)sin(a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 30
+gg:=expandLog ff
+--R
+--R   (10)
+--R                2             2
+--R       (cos(a x)  - 1)sin(a x) log(sin(a x))
+--R     + 
+--R                  2             2        a x
+--R       (- cos(a x)  + 1)sin(a x) log(sin(---))
+--R                                          2
+--R     + 
+--R                  2             2
+--R       (- cos(a x)  + 1)sin(a x) log(cos(a x) + 1)
+--R     + 
+--R                2             2        a x                     2           3
+--R       (cos(a x)  - 1)sin(a x) log(cos(---)) + cos(a x)sin(a x)  + cos(a x)
+--R                                        2
+--R     + 
+--R       - cos(a x)
+--R  /
+--R                 2              2
+--R     (2a cos(a x)  - 2a)sin(a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 31     14:463 Schaums and Axiom agree
+hh:=complexNormalize gg
+--R
+--R   (11)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.464~~~~~$\displaystyle
@@ -81,7 +410,7 @@ $$
 <<*>>=
 )clear all
 
---S 4 of 10
+--S 32
 aa:=integrate(csc(a*x)^n*cot(a*x),x)
 --R 
 --R
@@ -96,6 +425,31 @@ aa:=integrate(csc(a*x)^n*cot(a*x),x)
 --R                     a n
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 33
+bb:=-csc(a*x)^n/(n*a)
+--R
+--R                  n
+--R          csc(a x)
+--R   (2)  - ---------
+--R             a n
+--R                                                     Type: Expression Integer
+--E
+
+--S 34     14:464 Axiom cannot simplify this expression
+cc:=aa-bb
+--R
+--R                          1
+--R            n log(- -------------)
+--R                            2
+--R                    cos(a x)  - 1
+--R            ----------------------
+--R                       2                     n
+--R        - %e                       + csc(a x)
+--R   (3)  --------------------------------------
+--R                          a n
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.465~~~~~$\displaystyle
@@ -106,7 +460,7 @@ $$
 <<*>>=
 )clear all
 
---S 5 of 10
+--S 35
 aa:=integrate(1/csc(a*x),x)
 --R 
 --R
@@ -114,7 +468,23 @@ aa:=integrate(1/csc(a*x),x)
 --R   (1)  - --------
 --R              a
 --R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 36
+bb:=-cos(a*x)/a
+--R
+--R          cos(a x)
+--R   (2)  - --------
+--R              a
+--R                                                     Type: Expression Integer
 --E 
+
+--S 37     14:465 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.466~~~~~$\displaystyle
@@ -126,7 +496,7 @@ $$
 <<*>>=
 )clear all
 
---S 6 of 10
+--S 38     14:466 Axiom cannot compute this integral
 aa:=integrate(x*csc(a*x),x)
 --R 
 --R
@@ -147,7 +517,7 @@ $$
 <<*>>=
 )clear all
 
---S 7 of 10
+--S 39     14:467 Axiom cannot compute this integral
 aa:=integrate(csc(a*x)/x,x)
 --R 
 --R
@@ -167,7 +537,7 @@ $$
 <<*>>=
 )clear all
 
---S 8 of 10
+--S 40
 aa:=integrate(x*csc(a*x)^2,x)
 --R 
 --R
@@ -179,6 +549,64 @@ aa:=integrate(x*csc(a*x)^2,x)
 --R                                     a sin(a x)
 --R                                          Type: Union(Expression Integer,...)
 --E
+
+--S 41
+bb:=-(x*cot(a*x))/a+1/a^2*log(sin(a*x))
+--R
+--R        log(sin(a x)) - a x cot(a x)
+--R   (2)  ----------------------------
+--R                      2
+--R                     a
+--R                                                     Type: Expression Integer
+--E
+
+--S 42
+cc:=aa-bb
+--R
+--R   (3)
+--R                                               sin(a x)
+--R       - sin(a x)log(sin(a x)) + sin(a x)log(------------)
+--R                                             cos(a x) + 1
+--R     + 
+--R                           2
+--R       - sin(a x)log(------------) + a x cot(a x)sin(a x) - a x cos(a x)
+--R                     cos(a x) + 1
+--R  /
+--R      2
+--R     a sin(a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 43
+cotrule:=rule(cot(a) == cos(a)/sin(a))
+--R
+--R                  cos(a)
+--R   (4)  cot(a) == ------
+--R                  sin(a)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 44
+dd:=cotrule cc
+--R
+--R                                sin(a x)                2
+--R        - log(sin(a x)) + log(------------) - log(------------)
+--R                              cos(a x) + 1        cos(a x) + 1
+--R   (5)  -------------------------------------------------------
+--R                                    2
+--R                                   a
+--R                                                     Type: Expression Integer
+--E
+
+--S 45     14:468 Schaums and Axiom differ by a constant
+ee:=expandLog dd
+--R
+--R          log(2)
+--R   (6)  - ------
+--R             2
+--R            a
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.469~~~~~$\displaystyle
@@ -189,7 +617,7 @@ $$
 <<*>>=
 )clear all
 
---S 9 of 10
+--S 46
 aa:=integrate(1/(q+p*csc(a*x)),x)
 --R 
 --R
@@ -227,6 +655,156 @@ aa:=integrate(1/(q+p*csc(a*x)),x)
 --R                               a q\|- q  + p
 --R                                     Type: Union(List Expression Integer,...)
 --E 
+
+--S 47
+t1:=integrate(1/(p+q*sin(a*x)),x)
+--E
+
+--S 48
+bb1:=x/q-p/q*t1.1
+--R
+--R   (3)
+--R       -
+--R            p
+--R         *
+--R            log
+--R                                                           +-------+
+--R                                     2    2             2  | 2    2
+--R                   (p q sin(a x) + (q  - p )cos(a x) + q )\|q  - p
+--R                 + 
+--R                         2    3                3    2              3    2
+--R                   (- p q  + p )sin(a x) + (- q  + p q)cos(a x) - q  + p q
+--R              /
+--R                 q sin(a x) + p
+--R     + 
+--R           +-------+
+--R           | 2    2
+--R       a x\|q  - p
+--R  /
+--R         +-------+
+--R         | 2    2
+--R     a q\|q  - p
+--R                                                     Type: Expression Integer
+--E
+
+--S 49
+bb2:=x/q-p/q*t1.2
+--R
+--R                                              +---------+
+--R                                              |   2    2         +---------+
+--R                (p sin(a x) + q cos(a x) + q)\|- q  + p          |   2    2
+--R        2p atan(-----------------------------------------) + a x\|- q  + p
+--R                         2    2             2    2
+--R                       (q  - p )cos(a x) + q  - p
+--R   (4)  --------------------------------------------------------------------
+--R                                       +---------+
+--R                                       |   2    2
+--R                                   a q\|- q  + p
+--R                                                     Type: Expression Integer
+--E
+
+--S 50
+cc1:=aa.1-bb1
+--R
+--R   (5)
+--R         p
+--R      *
+--R         log
+--R                                                        +-------+
+--R                                  2    2             2  | 2    2
+--R                (p q sin(a x) + (q  - p )cos(a x) + q )\|q  - p
+--R              + 
+--R                    2    3              3    2              3    2
+--R                (p q  - p )sin(a x) + (q  - p q)cos(a x) + q  - p q
+--R           /
+--R              q sin(a x) + p
+--R     + 
+--R         p
+--R      *
+--R         log
+--R                                                        +-------+
+--R                                  2    2             2  | 2    2
+--R                (p q sin(a x) + (q  - p )cos(a x) + q )\|q  - p
+--R              + 
+--R                      2    3                3    2              3    2
+--R                (- p q  + p )sin(a x) + (- q  + p q)cos(a x) - q  + p q
+--R           /
+--R              q sin(a x) + p
+--R  /
+--R         +-------+
+--R         | 2    2
+--R     a q\|q  - p
+--R                                                     Type: Expression Integer
+--E
+
+--S 51
+cc2:=aa.2-bb1
+--R
+--R   (6)
+--R           +---------+
+--R           |   2    2
+--R         p\|- q  + p
+--R      *
+--R         log
+--R                                                        +-------+
+--R                                  2    2             2  | 2    2
+--R                (p q sin(a x) + (q  - p )cos(a x) + q )\|q  - p
+--R              + 
+--R                      2    3                3    2              3    2
+--R                (- p q  + p )sin(a x) + (- q  + p q)cos(a x) - q  + p q
+--R           /
+--R              q sin(a x) + p
+--R     + 
+--R                                                      +---------+
+--R          +-------+                                   |   2    2
+--R          | 2    2      (p sin(a x) + q cos(a x) + q)\|- q  + p
+--R       2p\|q  - p  atan(-----------------------------------------)
+--R                                 2    2             2    2
+--R                               (q  - p )cos(a x) + q  - p
+--R  /
+--R         +---------+ +-------+
+--R         |   2    2  | 2    2
+--R     a q\|- q  + p  \|q  - p
+--R                                                     Type: Expression Integer
+--E
+
+--S 52
+cc3:=aa.1-bb2
+--R
+--R   (7)
+--R           +---------+
+--R           |   2    2
+--R         p\|- q  + p
+--R      *
+--R         log
+--R                                                        +-------+
+--R                                  2    2             2  | 2    2
+--R                (p q sin(a x) + (q  - p )cos(a x) + q )\|q  - p
+--R              + 
+--R                    2    3              3    2              3    2
+--R                (p q  - p )sin(a x) + (q  - p q)cos(a x) + q  - p q
+--R           /
+--R              q sin(a x) + p
+--R     + 
+--R                                                        +---------+
+--R            +-------+                                   |   2    2
+--R            | 2    2      (p sin(a x) + q cos(a x) + q)\|- q  + p
+--R       - 2p\|q  - p  atan(-----------------------------------------)
+--R                                   2    2             2    2
+--R                                 (q  - p )cos(a x) + q  - p
+--R  /
+--R         +---------+ +-------+
+--R         |   2    2  | 2    2
+--R     a q\|- q  + p  \|q  - p
+--R                                                     Type: Expression Integer
+--E
+
+--S 53     14:469 Schaums and Axiom agree
+cc4:=aa.2-bb2
+--R
+--R   (8)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.470~~~~~$\displaystyle
@@ -238,7 +816,7 @@ $$
 <<*>>=
 )clear all
 
---S 10 of 10
+--S 54     14:470 Axiom cannot compute this integral
 aa:=integrate(csc(a*x)^n,x)
 --R 
 --R



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Subject: [Axiom-developer] the lisp community :-)
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http://www.catonmat.net/blog/musical-geek-friday-god-wrote-in-lisp-eternal-flame

just for your friday amusement.... :-)
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Subject: [Axiom-developer] Knuth on literate programming
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Don Knuth made these remarks in an interview with Andrew Binstock
<http://www.informit.com/articles/article.aspx?p=1193856>

Andrew: One of the few projects of yours that hasnt been embraced by
a widespread community is literate programming. What are your thoughts
about why literate programming didnt catch on? And is there anything
youd have done differently in retrospect regarding literate
programming?

Donald: Literate programming is a very personal thing. I think its
terrific, but that might well be because Im a very strange person. It
has tens of thousands of fans, but not millions.

In my experience, software created with literate programming has
turned out to be significantly better than software developed in more
traditional ways. Yet ordinary software is usually okay--Id give it
a grade of C (or maybe C++), but not F; hence, the traditional methods
stay with us. Since theyre understood by a vast community of
programmers, most people have no big incentive to change, just as Im
not motivated to learn Esperanto even though it might be preferable to
English and German and French and Russian (if everybody switched).

Jon Bentley probably hit the nail on the head when he once was asked
why literate programming hasnt taken the whole world by storm. He
observed that a small percentage of the worlds population is good at
programming, and a small percentage is good at writing; apparently I
am asking everybody to be in both subsets.

Yet to me, literate programming is certainly the most important thing
that came out of the TeX project. Not only has it enabled me to write
and maintain programs faster and more reliably than ever before, and
been one of my greatest sources of joy since the 1980s; it has
actually been indispensable at times. Some of my major programs, such
as the MMIX meta-simulator, could not have been written with any other
methodology that Ive ever heard of. The complexity was simply too
daunting for my limited brain to handle; without literate programming,
the whole enterprise would have flopped miserably.

If people do discover nice ways to use the newfangled multithreaded
machines, I would expect the discovery to come from people who
routinely use literate programming. Literate programming is what you
need to rise above the ordinary level of achievement. But I dont
believe in forcing ideas on anybody. If literate programming isnt
your style, please forget it and do what you like. If nobody likes it
but me, let it die.

On a positive note, Ive been pleased to discover that the conventions
of CWEB are already standard equipment within preinstalled software
such as Makefiles, when I get off-the-shelf Linux these days.




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To: root <daly@axiom-developer.org>
Subject: Re: [Axiom-developer] the lisp community :-)
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root wrote:
> http://www.catonmat.net/blog/musical-geek-friday-god-wrote-in-lisp-eternal-flame
> 
> just for your friday amusement.... :-)
> ------- End of forwarded message -------
> 
> 
> _______________________________________________
> Axiom-developer mailing list
> Axiom-developer@nongnu.org
> http://lists.nongnu.org/mailman/listinfo/axiom-developer
> 
Actually, there's an even better line on the page:

"The primary duty of an exception handler is to get the error out of the 
lap of the programmer and into the surprised face of the user. Provided 
you keep this cardinal rule in mind, you can't go far wrong."

Verity Stob



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Subject: [Axiom-developer] 20080425.01.tpd.patch (CATS Schaums-Axiom
	equivalence testing (24-25))
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There are some differences between Schaums and Axiom but these 
seem to occur in the complex plane. The likely problem is a 
difference between Schaum's and Axiom's choice of branch cuts.
Alternatively, the rules used for reduction have an implicit
branch cut which does not match.
This needs to be investigated further.

schaum24.input.pamphlet
  14:471 Axiom cannot simplify this expression
  14:472 Axiom cannot simplify this expression
  14:473 Axiom cannot simplify this expression
  14:474 Axiom cannot compute this integral
  14:475 Axiom cannot simplify this expression
  14:476 Axiom cannot simplify this expression
  14:477 Axiom cannot simplify this expression
  14:478 Axiom cannot simplify this expression
  14:479 Axiom cannot simplify this expression
  14:480 Axiom cannot compute this integral
  14:481 Axiom cannot simplify this expression
  14:482 Axiom cannot simplify this expression
  14:483 SCHAUMS AND AXIOM DIFFER? (BRANCH CUTS?)
  14:484 Axiom cannot compute this integral
  14:485 Axiom cannot simplify this expression
  14:486 Axiom cannot compute this integral
  14:487 SCHAUMS AND AXIOM DIFFER? (branch cuts?)
  14:488 Axiom and Schaums agree
  14:489 Axiom and Schaums agree
  14:490 Axiom and Schaums agree
  14:491 Axiom cannot compute this integral
  14:492 Schaums and Axiom agree
  14:493 Axiom cannot simplify these expressions
  14:494 Axiom cannot simplify these expressions
  14:495 Axiom cannot simplify these expressions
  14:496 Axiom cannot compute this integral
  14:497 Axiom cannot simplify these expressions
  14:498 Axiom cannot simplify these expressions
  14:499 Axiom cannot simplify these expressions
  14:500 Axiom cannot simplify this expression
  14:501 Axiom cannot compute this integral
  14:502 Axiom cannot simplify this expression
  14:503 Axiom cannot compute this integral
  14:504 Axiom cannot compute this integral
  14:505 SCHAUMS AND AXIOM DISAGREE? (branch cuts?)
  14:506 Axiom cannot compute this integral
  14:507 Axiom cannot compute this integral
  14:508 Axiom cannot compute this integral

schaum25.input.pamphlet
  14:509 Schaums and Axiom agree
  14:510 Schaums and Axiom agree
  14:511 Schaums and Axiom agree
  14:512 Axiom cannot compute this integral
  14:513 Schaums and Axiom agree by definition
  14:514 Axiom cannot compute this integral
  14:515 Schaums and Axiom agree
  14:516 Schaums and Axiom agree
  14:517 Axiom cannot simplify these expressions
  14:518 Schaums and Axiom agree
  14:519 Schaums and Axiom agree
  14:520 Schaums and Axiom agree
  14:521 Schaums and Axiom agree
  14:522 Schaums and Axiom agree by definition
  14:523 Axiom cannot compute this integral
  14:524 Axiom cannot compute this integral

========================================================================
diff --git a/changelog b/changelog
index 314b281..3956a7b 100644
--- a/changelog
+++ b/changelog
@@ -1,3 +1,5 @@
+20080425 tpd src/input/schaum25.input show Schaums-Axiom equivalence
+20080425 tpd src/input/schaum24.input show Schaums-Axiom equivalence
 20080424 tpd src/input/schaum23.input show Schaums-Axiom equivalence
 20080423 tpd src/input/schaum22.input show Schaums-Axiom equivalence
 20080423 tpd src/input/schaum21.input show Schaums-Axiom equivalence
diff --git a/src/input/schaum24.input.pamphlet b/src/input/schaum24.input.pamphlet
index 1a6b60a..9c034da 100644
--- a/src/input/schaum24.input.pamphlet
+++ b/src/input/schaum24.input.pamphlet
@@ -18,7 +18,7 @@ $$
 )set message auto off
 )clear all
 
---S 1 of 38
+--S 1
 aa:=integrate(asin(x/a),x)
 --R 
 --R
@@ -32,6 +32,31 @@ aa:=integrate(asin(x/a),x)
 --R                            2
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 2
+bb:=s+asin(x/a)+sqrt(a^2-x^2)
+--R
+--R         +---------+
+--R         |   2    2         x
+--R   (2)  \|- x  + a   + asin(-) + s
+--R                            a
+--R                                                     Type: Expression Integer
+--E
+
+--S 3      14:471 Axiom cannot simplify this expression
+cc:=aa-bb
+--R
+--R                    +---------+
+--R                    |   2    2
+--R                 2x\|- x  + a            x
+--R        - x atan(--------------) - 2asin(-) - 2s
+--R                      2    2             a
+--R                    2x  - a
+--R   (3)  ----------------------------------------
+--R                            2
+--R                                                     Type: Expression Integer
+--E
+
 @
 
 \section{\cite{1}:14.472~~~~~$\displaystyle
@@ -43,7 +68,7 @@ $$
 <<*>>=
 )clear all
 
---S 2 of 38
+--S 4
 aa:=integrate(x*asin(x/a),x)
 --R 
 --R
@@ -57,6 +82,32 @@ aa:=integrate(x*asin(x/a),x)
 --R                                8
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 5
+bb:=(x^2/2-a^2/4)*asin(x/a)+(x*sqrt(a^2-x^2))/4
+--R
+--R          +---------+
+--R          |   2    2       2    2      x
+--R        x\|- x  + a   + (2x  - a )asin(-)
+--R                                       a
+--R   (2)  ---------------------------------
+--R                        4
+--R                                                     Type: Expression Integer
+--E
+
+--S 6      14:472 Axiom cannot simplify this expression
+cc:=aa-bb
+--R
+--R                            +---------+
+--R                            |   2    2
+--R             2    2      2x\|- x  + a           2     2      x
+--R        (- 2x  + a )atan(--------------) + (- 4x  + 2a )asin(-)
+--R                              2    2                         a
+--R                            2x  - a
+--R   (3)  -------------------------------------------------------
+--R                                   8
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.473~~~~~$\displaystyle
@@ -67,7 +118,7 @@ $$
 <<*>>=
 )clear all
 
---S 3 of 38
+--S 7
 aa:=integrate(x^2*asin(x/a),x)
 --R 
 --R
@@ -81,6 +132,32 @@ aa:=integrate(x^2*asin(x/a),x)
 --R                                 18
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 8
+bb:=x^3/3*asin(x/a)+((x^2+2*a^2)*sqrt(a^2-x^2))/9
+--R
+--R                   +---------+
+--R          2     2  |   2    2      3     x
+--R        (x  + 2a )\|- x  + a   + 3x asin(-)
+--R                                         a
+--R   (2)  -----------------------------------
+--R                         9
+--R                                                     Type: Expression Integer
+--E
+
+--S 9      14:473 Axiom cannot simplify this expression
+cc:=aa-bb
+--R
+--R                    +---------+
+--R                    |   2    2
+--R           3     2x\|- x  + a        3     x
+--R        - x atan(--------------) - 2x asin(-)
+--R                      2    2               a
+--R                    2x  - a
+--R   (3)  -------------------------------------
+--R                          6
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.474~~~~~$\displaystyle
@@ -93,7 +170,7 @@ $$
 <<*>>=
 )clear all
 
---S 4 of 38
+--S 10     14:474 Axiom cannot compute this integral
 aa:=integrate(asin(x/a)/x,x)
 --R 
 --R
@@ -115,7 +192,7 @@ $$
 <<*>>=
 )clear all
 
---S 5 of 38
+--S 11
 aa:=integrate(asin(x/a)/x^2,x)
 --R 
 --R
@@ -130,6 +207,38 @@ aa:=integrate(asin(x/a)/x^2,x)
 --R                                       2a x
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 12
+bb:=-asin(x/a)/x-1/a*log((a+sqrt(a^2-x^2))/x)
+--R
+--R                 +---------+
+--R                 |   2    2
+--R                \|- x  + a   + a           x
+--R        - x log(----------------) - a asin(-)
+--R                        x                  a
+--R   (2)  -------------------------------------
+--R                         a x
+--R                                                     Type: Expression Integer
+--E
+
+--S 13     14:475 Axiom cannot simplify this expression
+cc:=aa-bb
+--R
+--R   (3)
+--R                +---------+               +---------+
+--R                |   2    2                |   2    2
+--R       - x log(\|- x  + a   + a) + x log(\|- x  + a   - a)
+--R     + 
+--R               +---------+                  +---------+
+--R               |   2    2                   |   2    2
+--R              \|- x  + a   + a           2x\|- x  + a              x
+--R       2x log(----------------) + a atan(--------------) + 2a asin(-)
+--R                      x                       2    2               a
+--R                                            2x  - a
+--R  /
+--R     2a x
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.476~~~~~$\displaystyle
@@ -140,7 +249,7 @@ $$
 <<*>>=
 )clear all
 
---S 6 of 38
+--S 14
 aa:=integrate(asin(x/a)^2,x)
 --R 
 --R
@@ -154,6 +263,36 @@ aa:=integrate(asin(x/a)^2,x)
 --R                                        4
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 15
+bb:=x*asin(x/a)^2-2*x+2*sqrt(a^2-x^2)*asin(x/a)
+--R
+--R                 +---------+
+--R              x  |   2    2           x 2
+--R   (2)  2asin(-)\|- x  + a   + x asin(-)  - 2x
+--R              a                       a
+--R                                                     Type: Expression Integer
+--E
+
+--S 16     14:476 Axiom cannot simplify this expression
+cc:=aa-bb
+--R
+--R   (3)
+--R                 +---------+ 2                        +---------+
+--R                 |   2    2        +---------+        |   2    2
+--R              2x\|- x  + a         |   2    2      2x\|- x  + a
+--R       x atan(--------------)  - 4\|- x  + a  atan(--------------)
+--R                   2    2                               2    2
+--R                 2x  - a                              2x  - a
+--R     + 
+--R                  +---------+
+--R               x  |   2    2            x 2
+--R       - 8asin(-)\|- x  + a   - 4x asin(-)
+--R               a                        a
+--R  /
+--R     4
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.477~~~~~$\displaystyle
@@ -164,7 +303,7 @@ $$
 <<*>>=
 )clear all
 
---S 7 of 38
+--S 17
 aa:=integrate(acos(x/a),x)
 --R 
 --R
@@ -178,6 +317,30 @@ aa:=integrate(acos(x/a),x)
 --R                           2
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 18
+bb:=x*acos(x/a)-sqrt(a^2-x^2)
+--R
+--R           +---------+
+--R           |   2    2           x
+--R   (2)  - \|- x  + a   + x acos(-)
+--R                                a
+--R                                                     Type: Expression Integer
+--E
+
+--S 19     14:477 Axiom cannot simplify this expression
+cc:=aa-bb
+--R
+--R                  +---------+
+--R                  |   2    2
+--R               2x\|- x  + a              x
+--R        x atan(--------------) - 2x acos(-)
+--R                    2    2               a
+--R                  2x  - a
+--R   (3)  -----------------------------------
+--R                         2
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.478~~~~~$\displaystyle
@@ -189,7 +352,7 @@ $$
 <<*>>=
 )clear all
 
---S 8 of 38
+--S 20
 aa:=integrate(x*acos(x/a),x)
 --R 
 --R
@@ -203,6 +366,32 @@ aa:=integrate(x*acos(x/a),x)
 --R                               8
 --R                                          Type: Union(Expression Integer,...)
 --E
+
+--S 21
+bb:=(x^2/2-a^2/4)*acos(x/a)-(x*sqrt(a^2-x^2))/4
+--R
+--R            +---------+
+--R            |   2    2       2    2      x
+--R        - x\|- x  + a   + (2x  - a )acos(-)
+--R                                         a
+--R   (2)  -----------------------------------
+--R                         4
+--R                                                     Type: Expression Integer
+--E
+
+--S 22     14:478 Axiom cannot simplify this expression
+cc:=aa-bb
+--R
+--R                          +---------+
+--R                          |   2    2
+--R           2    2      2x\|- x  + a           2     2      x
+--R        (2x  - a )atan(--------------) + (- 4x  + 2a )acos(-)
+--R                            2    2                         a
+--R                          2x  - a
+--R   (3)  -----------------------------------------------------
+--R                                  8
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.479~~~~~$\displaystyle
@@ -213,7 +402,7 @@ $$
 <<*>>=
 )clear all
 
---S 9 of 38
+--S 23
 aa:=integrate(x^2*acos(x/a),x)
 --R 
 --R
@@ -227,6 +416,32 @@ aa:=integrate(x^2*acos(x/a),x)
 --R                                 18
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 24
+bb:=x^3/3*acos(x/a)-((x^2+2*a^2)*sqrt(a^2-x^2))/9
+--R
+--R                     +---------+
+--R            2     2  |   2    2      3     x
+--R        (- x  - 2a )\|- x  + a   + 3x acos(-)
+--R                                           a
+--R   (2)  -------------------------------------
+--R                          9
+--R                                                     Type: Expression Integer
+--E
+
+--S 25     14:479 Axiom cannot simplify this expression
+cc:=aa-bb
+--R
+--R                  +---------+
+--R                  |   2    2
+--R         3     2x\|- x  + a        3     x
+--R        x atan(--------------) - 2x acos(-)
+--R                    2    2               a
+--R                  2x  - a
+--R   (3)  -----------------------------------
+--R                         6
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.480~~~~~$\displaystyle
@@ -237,7 +452,7 @@ $$
 <<*>>=
 )clear all
 
---S 10 of 38
+--S 26     14:480 Axiom cannot compute this integral
 aa:=integrate(acos(x/a)/x,x)
 --R 
 --R
@@ -258,7 +473,7 @@ $$
 <<*>>=
 )clear all
 
---S 11 of 38
+--S 27
 aa:=integrate(acos(x/a)/x^2,x)
 --R 
 --R
@@ -273,6 +488,38 @@ aa:=integrate(acos(x/a)/x^2,x)
 --R                                      2a x
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 28
+bb:=-acos(x/a)/x+1/a*log((a+sqrt(a^2-x^2))/x)
+--R
+--R               +---------+
+--R               |   2    2
+--R              \|- x  + a   + a           x
+--R        x log(----------------) - a acos(-)
+--R                      x                  a
+--R   (2)  -----------------------------------
+--R                        a x
+--R                                                     Type: Expression Integer
+--E
+
+--S 29     14:481 Axiom cannot simplify this expression
+cc:=aa-bb
+--R
+--R   (3)
+--R              +---------+               +---------+
+--R              |   2    2                |   2    2
+--R       x log(\|- x  + a   + a) - x log(\|- x  + a   - a)
+--R     + 
+--R                 +---------+                  +---------+
+--R                 |   2    2                   |   2    2
+--R                \|- x  + a   + a           2x\|- x  + a              x
+--R       - 2x log(----------------) - a atan(--------------) + 2a acos(-)
+--R                        x                       2    2               a
+--R                                              2x  - a
+--R  /
+--R     2a x
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.482~~~~~$\displaystyle
@@ -283,7 +530,7 @@ $$
 <<*>>=
 )clear all
 
---S 12 of 38
+--S 30
 aa:=integrate(acos(x/a)^2,x)
 --R 
 --R
@@ -296,7 +543,37 @@ aa:=integrate(acos(x/a)^2,x)
 --R   (1)  ----------------------------------------------------------------
 --R                                        4
 --R                                          Type: Union(Expression Integer,...)
---E 
+--E
+
+--S 31
+bb:=x*acos(x/a)^2-2*x-2*sqrt(a^2-x^2)*acos(x/a)
+--R
+--R                   +---------+
+--R                x  |   2    2           x 2
+--R   (2)  - 2acos(-)\|- x  + a   + x acos(-)  - 2x
+--R                a                       a
+--R                                                     Type: Expression Integer
+--E
+
+--S 32     14:482 Axiom cannot simplify this expression
+cc:=aa-bb
+--R
+--R   (3)
+--R                 +---------+ 2                        +---------+
+--R                 |   2    2        +---------+        |   2    2
+--R              2x\|- x  + a         |   2    2      2x\|- x  + a
+--R       x atan(--------------)  - 4\|- x  + a  atan(--------------)
+--R                   2    2                               2    2
+--R                 2x  - a                              2x  - a
+--R     + 
+--R                +---------+
+--R             x  |   2    2            x 2
+--R       8acos(-)\|- x  + a   - 4x acos(-)
+--R             a                        a
+--R  /
+--R     4
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.483~~~~~$\displaystyle
@@ -307,7 +584,7 @@ $$
 <<*>>=
 )clear all
 
---S 13 of 38
+--S 33
 aa:=integrate(atan(x/a),x)
 --R 
 --R
@@ -319,6 +596,62 @@ aa:=integrate(atan(x/a),x)
 --R                         2
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 34
+bb:=x*atan(x/a)-a/2*log(x^2+a^2)
+--R
+--R                 2    2            x
+--R        - a log(x  + a ) + 2x atan(-)
+--R                                   a
+--R   (2)  -----------------------------
+--R                      2
+--R                                                     Type: Expression Integer
+--E
+
+--S 35
+cc:=aa-bb
+--R
+--R                  x             2a x
+--R        - 2x atan(-) - x atan(-------)
+--R                  a            2    2
+--R                              x  - a
+--R   (3)  ------------------------------
+--R                       2
+--R                                                     Type: Expression Integer
+--E
+
+--S 36
+atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
+--R
+--R                            - x + %i
+--R                     %i log(--------)
+--R                             x + %i
+--R   (4)  atan(x) == - ----------------
+--R                             2
+--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
+--E
+
+--S 37
+dd:=atanrule cc
+--R
+--R                  2              2
+--R                 x  + 2%i a x - a               - x + %i a
+--R        %i x log(-----------------) + 2%i x log(----------)
+--R                  2              2               x + %i a
+--R                 x  - 2%i a x - a
+--R   (5)  ---------------------------------------------------
+--R                                 4
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 38     14:483 SCHAUMS AND AXIOM DIFFER? (BRANCH CUTS?)
+ee:=expandLog dd
+--R
+--R        %i x log(- 1)
+--R   (6)  -------------
+--R              2
+--R                                             Type: Expression Complex Integer
+--E
 @
 
 \section{\cite{1}:14.484~~~~~$\displaystyle
@@ -329,7 +662,7 @@ $$
 <<*>>=
 )clear all
 
---S 14 of 38
+--S 39     14:484 Axiom cannot compute this integral
 aa:=integrate(x*tan(x/a),x)
 --R 
 --R
@@ -349,7 +682,7 @@ $$
 <<*>>=
 )clear all
 
---S 15 of 38
+--S 40
 aa:=integrate(x^2*atan(x/a),x)
 --R 
 --R
@@ -361,6 +694,29 @@ aa:=integrate(x^2*atan(x/a),x)
 --R                           6
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 41
+bb:=x^3/2*atan(x/a)-(a*x^2)/6+a^3/6*log(x^2+a^2)
+--R
+--R         3     2    2      3     x       2
+--R        a log(x  + a ) + 3x atan(-) - a x
+--R                                 a
+--R   (2)  ----------------------------------
+--R                         6
+--R                                                     Type: Expression Integer
+--E
+
+--S 42     14:485 Axiom cannot simplify this expression
+cc:=aa-bb
+--R
+--R            3     x     3       2a x
+--R        - 3x atan(-) - x atan(-------)
+--R                  a            2    2
+--R                              x  - a
+--R   (3)  ------------------------------
+--R                       6
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.486~~~~~$\displaystyle
@@ -371,7 +727,7 @@ $$
 <<*>>=
 )clear all
 
---S 16 of 38
+--S 43     14:486 Axiom cannot compute this integral
 aa:=integrate(atan(x/a)/x,x)
 --R 
 --R
@@ -393,7 +749,7 @@ $$
 <<*>>=
 )clear all
 
---S 17 of 38
+--S 44
 aa:=integrate(atan(x/a)/x^2,x)
 --R 
 --R
@@ -405,6 +761,73 @@ aa:=integrate(atan(x/a)/x^2,x)
 --R                             2a x
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 45
+bb:=-1/x*atan(x/a)-1/(2*a)*log((x^2+a^2)/x^2)
+--R
+--R                 2    2
+--R                x  + a             x
+--R        - x log(-------) - 2a atan(-)
+--R                    2              a
+--R                   x
+--R   (2)  -----------------------------
+--R                     2a x
+--R                                                     Type: Expression Integer
+--E
+
+--S 46
+cc:=aa-bb
+--R
+--R   (3)
+--R                                         2    2
+--R            2    2                      x  + a             x             2a x
+--R   - x log(x  + a ) + 2x log(x) + x log(-------) + 2a atan(-) + a atan(-------)
+--R                                            2              a            2    2
+--R                                           x                           x  - a
+--R   ----------------------------------------------------------------------------
+--R                                       2a x
+--R                                                     Type: Expression Integer
+--E
+
+--S 47
+atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
+--R
+--R                            - x + %i
+--R                     %i log(--------)
+--R                             x + %i
+--R   (4)  atan(x) == - ----------------
+--R                             2
+--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
+--E
+
+--S 48
+dd:=atanrule cc
+--R
+--R   (5)
+--R                                                 2              2
+--R                 2    2                         x  + 2%i a x - a
+--R       - 2x log(x  + a ) + 4x log(x) - %i a log(-----------------)
+--R                                                 2              2
+--R                                                x  - 2%i a x - a
+--R     + 
+--R               2    2
+--R              x  + a               - x + %i a
+--R       2x log(-------) - 2%i a log(----------)
+--R                  2                 x + %i a
+--R                 x
+--R  /
+--R     4a x
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 49     14:487 SCHAUMS AND AXIOM DIFFER? (branch cuts?)
+ee:=expandLog dd
+--R
+--R          %i log(- 1)
+--R   (6)  - -----------
+--R               2x
+--R                                             Type: Expression Complex Integer
+--E
 @
 
 \section{\cite{1}:14.488~~~~~$\displaystyle
@@ -415,7 +838,7 @@ $$
 <<*>>=
 )clear all
 
---S 18 of 38
+--S 50
 aa:=integrate(acot(x/a),x)
 --R 
 --R
@@ -426,7 +849,85 @@ aa:=integrate(acot(x/a),x)
 --R   (1)  --------------------------------
 --R                        2
 --R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 51
+bb:=x*acot(x/a)+a/2*log(x^2+a^2)
+--R
+--R               2    2            x
+--R        a log(x  + a ) + 2x acot(-)
+--R                                 a
+--R   (2)  ---------------------------
+--R                     2
+--R                                                     Type: Expression Integer
 --E 
+
+--S 52
+cc:=aa-bb
+--R
+--R                 2a x             x
+--R        x atan(-------) - 2x acot(-)
+--R                2    2            a
+--R               x  - a
+--R   (3)  ----------------------------
+--R                      2
+--R                                                     Type: Expression Integer
+--E
+
+--S 53
+atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
+--R
+--R                            - x + %i
+--R                     %i log(--------)
+--R                             x + %i
+--R   (4)  atan(x) == - ----------------
+--R                             2
+--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
+--E
+
+--S 54
+dd:=atanrule cc
+--R
+--R                    2              2
+--R                   x  + 2%i a x - a             x
+--R        - %i x log(-----------------) - 4x acot(-)
+--R                    2              2            a
+--R                   x  - 2%i a x - a
+--R   (5)  ------------------------------------------
+--R                             4
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 55
+acotrule:=rule(acot(x) == -%i/2*log((%i*x-1)/(%i*x+1)))
+--R
+--R                            x + %i
+--R                     %i log(------)
+--R                            x - %i
+--R   (6)  acot(x) == - --------------
+--R                            2
+--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
+--E
+
+--S 56
+ee:=acotrule dd
+--R
+--R                    2              2
+--R                   x  + 2%i a x - a               x + %i a
+--R        - %i x log(-----------------) + 2%i x log(--------)
+--R                    2              2              x - %i a
+--R                   x  - 2%i a x - a
+--R   (7)  ---------------------------------------------------
+--R                                 4
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 57     14:488 Axiom and Schaums agree
+ff:=expandLog %
+--R
+--R   (8)  0
+--R                                             Type: Expression Complex Integer
+--E
 @
 
 \section{\cite{1}:14.489~~~~~$\displaystyle
@@ -437,7 +938,7 @@ $$
 <<*>>=
 )clear all
 
---S 19 of 38
+--S 58
 aa:=integrate(x*acot(x/a),x)
 --R 
 --R
@@ -449,6 +950,84 @@ aa:=integrate(x*acot(x/a),x)
 --R                      4
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 59
+bb:=1/2*(x^2+a^2)*acot(x/a)+(a*x)/2
+--R
+--R          2    2      x
+--R        (x  + a )acot(-) + a x
+--R                      a
+--R   (2)  ----------------------
+--R                   2
+--R                                                     Type: Expression Integer
+--E
+
+--S 60
+cc:=aa-bb
+--R
+--R          2    2        2a x          2     2      x
+--R        (x  + a )atan(-------) + (- 2x  - 2a )acot(-)
+--R                       2    2                      a
+--R                      x  - a
+--R   (3)  ---------------------------------------------
+--R                              4
+--R                                                     Type: Expression Integer
+--E
+
+--S 61
+acotrule:=rule(acot(x) == -%i/2*log((%i*x-1)/(%i*x+1)))
+--R
+--R                            x + %i
+--R                     %i log(------)
+--R                            x - %i
+--R   (4)  acot(x) == - --------------
+--R                            2
+--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
+--E
+
+--S 62
+dd:=acotrule cc
+--R
+--R             2       2     x + %i a      2    2        2a x
+--R        (%i x  + %i a )log(--------) + (x  + a )atan(-------)
+--R                           x - %i a                   2    2
+--R                                                     x  - a
+--R   (5)  -----------------------------------------------------
+--R                                  4
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 63
+atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
+--R
+--R                            - x + %i
+--R                     %i log(--------)
+--R                             x + %i
+--R   (6)  atan(x) == - ----------------
+--R                             2
+--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
+--E
+
+--S 64
+ee:=atanrule dd
+--R
+--R   (7)
+--R                         2              2
+--R          2       2     x  + 2%i a x - a           2        2     x + %i a
+--R   (- %i x  - %i a )log(-----------------) + (2%i x  + 2%i a )log(--------)
+--R                         2              2                         x - %i a
+--R                        x  - 2%i a x - a
+--R   ------------------------------------------------------------------------
+--R                                       8
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 65     14:489 Axiom and Schaums agree
+ff:=expandLog ee
+--R
+--R   (8)  0
+--R                                             Type: Expression Complex Integer
+--E
 @
 
 \section{\cite{1}:14.490~~~~~$\displaystyle
@@ -459,7 +1038,7 @@ $$
 <<*>>=
 )clear all
 
---S 20 of 38
+--S 66
 aa:=integrate(x^2*acot(x/a),x)
 --R 
 --R
@@ -470,7 +1049,85 @@ aa:=integrate(x^2*acot(x/a),x)
 --R   (1)  -----------------------------------------
 --R                            6
 --R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 67
+bb:=x^3/3*acot(x/a)+(a*x^2)/6-a^3/6*log(x^2+a^2)
+--R
+--R           3     2    2      3     x       2
+--R        - a log(x  + a ) + 2x acot(-) + a x
+--R                                   a
+--R   (2)  ------------------------------------
+--R                          6
+--R                                                     Type: Expression Integer
 --E 
+
+--S 68
+cc:=aa-bb
+--R
+--R         3       2a x       3     x
+--R        x atan(-------) - 2x acot(-)
+--R                2    2            a
+--R               x  - a
+--R   (3)  ----------------------------
+--R                      6
+--R                                                     Type: Expression Integer
+--E
+
+--S 69
+atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
+--R
+--R                            - x + %i
+--R                     %i log(--------)
+--R                             x + %i
+--R   (4)  atan(x) == - ----------------
+--R                             2
+--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
+--E
+
+--S 70
+dd:=atanrule cc
+--R
+--R                    2              2
+--R              3    x  + 2%i a x - a       3     x
+--R        - %i x log(-----------------) - 4x acot(-)
+--R                    2              2            a
+--R                   x  - 2%i a x - a
+--R   (5)  ------------------------------------------
+--R                            12
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 71
+acotrule:=rule(acot(x) == -%i/2*log((%i*x-1)/(%i*x+1)))
+--R
+--R                            x + %i
+--R                     %i log(------)
+--R                            x - %i
+--R   (6)  acot(x) == - --------------
+--R                            2
+--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
+--E
+
+--S 72
+ee:=acotrule dd
+--R
+--R                    2              2
+--R              3    x  + 2%i a x - a          3    x + %i a
+--R        - %i x log(-----------------) + 2%i x log(--------)
+--R                    2              2              x - %i a
+--R                   x  - 2%i a x - a
+--R   (7)  ---------------------------------------------------
+--R                                 12
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 73     14:490 Axiom and Schaums agree
+ff:=expandLog ee
+--R
+--R   (8)  0
+--R                                             Type: Expression Complex Integer
+--E
 @
 
 \section{\cite{1}:14.491~~~~~$\displaystyle
@@ -481,7 +1138,7 @@ $$
 <<*>>=
 )clear all
 
---S 21 of 38
+--S 74     14:491 Axiom cannot compute this integral
 aa:=integrate(acot(x/a)/x,x)
 --R 
 --R
@@ -502,7 +1159,7 @@ $$
 <<*>>=
 )clear all
 
---S 22 of 38
+--S 75
 aa:=integrate(acot(x/a)/x^2,x)
 --R 
 --R
@@ -514,6 +1171,101 @@ aa:=integrate(acot(x/a)/x^2,x)
 --R                            2a x
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 76
+bb:=-acot(x/a)/x+1/(2*a)*log((x^2+a^2)/x^2)
+--R
+--R               2    2
+--R              x  + a             x
+--R        x log(-------) - 2a acot(-)
+--R                  2              a
+--R                 x
+--R   (2)  ---------------------------
+--R                    2a x
+--R                                                     Type: Expression Integer
+--E
+
+--S 77
+cc:=aa-bb
+--R
+--R   (3)
+--R                                       2    2
+--R          2    2                      x  + a              2a x             x
+--R   x log(x  + a ) - 2x log(x) - x log(-------) - a atan(-------) + 2a acot(-)
+--R                                          2              2    2            a
+--R                                         x              x  - a
+--R   --------------------------------------------------------------------------
+--R                                      2a x
+--R                                                     Type: Expression Integer
+--E
+
+--S 78
+acotrule:=rule(acot(x) == -%i/2*log((%i*x-1)/(%i*x+1)))
+--R
+--R                            x + %i
+--R                     %i log(------)
+--R                            x - %i
+--R   (4)  acot(x) == - --------------
+--R                            2
+--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
+--E
+
+--S 79
+dd:=acotrule cc
+--R
+--R   (5)
+--R                                                                2    2
+--R              2    2                         x + %i a          x  + a
+--R       x log(x  + a ) - 2x log(x) - %i a log(--------) - x log(-------)
+--R                                             x - %i a              2
+--R                                                                  x
+--R     + 
+--R                  2a x
+--R       - a atan(-------)
+--R                 2    2
+--R                x  - a
+--R  /
+--R     2a x
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 80
+atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
+--R
+--R                            - x + %i
+--R                     %i log(--------)
+--R                             x + %i
+--R   (6)  atan(x) == - ----------------
+--R                             2
+--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
+--E
+
+--S 81
+ee:=atanrule dd
+--R
+--R   (7)
+--R                                               2              2
+--R               2    2                         x  + 2%i a x - a
+--R       2x log(x  + a ) - 4x log(x) + %i a log(-----------------)
+--R                                               2              2
+--R                                              x  - 2%i a x - a
+--R     + 
+--R                                       2    2
+--R                   x + %i a           x  + a
+--R       - 2%i a log(--------) - 2x log(-------)
+--R                   x - %i a               2
+--R                                         x
+--R  /
+--R     4a x
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 82     14:492 Schaums and Axiom agree
+ff:=expandLog ee
+--R
+--R   (8)  0
+--R                                             Type: Expression Complex Integer
+--E
 @
 
 \section{\cite{1}:14.493~~~~~$\displaystyle
@@ -534,7 +1286,7 @@ $$
 <<*>>=
 )clear all
 
---S 23 of 38
+--S 83
 aa:=integrate(asec(x/a),x)
 --R 
 --R
@@ -555,6 +1307,72 @@ aa:=integrate(asec(x/a),x)
 --R     2
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 84
+bb1:=x*asec(x/a)-a*log(x+sqrt(x^2-a^2))
+--R
+--R                 +-------+
+--R                 | 2    2                x
+--R   (2)  - a log(\|x  - a   + x) + x asec(-)
+--R                                         a
+--R                                                     Type: Expression Integer
+--E
+
+--S 85
+bb2:=x*asec(x/a)+a*log(x+sqrt(x^2-a^2))
+--R
+--R               +-------+
+--R               | 2    2                x
+--R   (3)  a log(\|x  - a   + x) + x asec(-)
+--R                                       a
+--R                                                     Type: Expression Integer
+--E
+
+--S 86
+cc1:=aa-bb1
+--R
+--R   (4)
+--R                                                 +---------+
+--R               +-------+                     +-+ |   2    2
+--R               | 2    2           +-+     2x\|2 \|- x  + a
+--R       2a log(\|x  - a   + x) - a\|2 atan(------------------)
+--R                                                 2     2
+--R                                               3x  - 2a
+--R     + 
+--R                 +---------+
+--R                 |   2    2
+--R              2a\|- x  + a                    x                 x
+--R       x atan(--------------) - 2a atan(------------) - 2x asec(-)
+--R                     2                   +---------+            a
+--R                    x                    |   2    2
+--R                                        \|- x  + a
+--R  /
+--R     2
+--R                                                     Type: Expression Integer
+--E
+
+--S 87     14:493 Axiom cannot simplify these expressions
+cc2:=aa-bb2
+--R
+--R   (5)
+--R                                                   +---------+
+--R                 +-------+                     +-+ |   2    2
+--R                 | 2    2           +-+     2x\|2 \|- x  + a
+--R       - 2a log(\|x  - a   + x) - a\|2 atan(------------------)
+--R                                                   2     2
+--R                                                 3x  - 2a
+--R     + 
+--R                 +---------+
+--R                 |   2    2
+--R              2a\|- x  + a                    x                 x
+--R       x atan(--------------) - 2a atan(------------) - 2x asec(-)
+--R                     2                   +---------+            a
+--R                    x                    |   2    2
+--R                                        \|- x  + a
+--R  /
+--R     2
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.494~~~~~$\displaystyle
@@ -575,7 +1393,7 @@ $$
 <<*>>=
 )clear all
 
---S 24 of 38
+--S 88
 aa:=integrate(x*asec(x/a),x)
 --R 
 --R
@@ -589,6 +1407,60 @@ aa:=integrate(x*asec(x/a),x)
 --R                               4
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 89
+bb1:=x^2/2*asec(x/a)-(a*sqrt(x^2-a^2))/2
+--R
+--R            +-------+
+--R            | 2    2     2     x
+--R        - a\|x  - a   + x asec(-)
+--R                               a
+--R   (2)  -------------------------
+--R                    2
+--R                                                     Type: Expression Integer
+--E
+
+--S 90
+bb2:=x^2/2*asec(x/a)+(a*sqrt(x^2-a^2))/2
+--R
+--R          +-------+
+--R          | 2    2     2     x
+--R        a\|x  - a   + x asec(-)
+--R                             a
+--R   (3)  -----------------------
+--R                   2
+--R                                                     Type: Expression Integer
+--E
+
+--S 91
+cc1:=aa-bb1
+--R
+--R   (4)
+--R                     +---------+
+--R                     |   2    2        +-------+      +---------+
+--R     2     2      2a\|- x  + a         | 2    2       |   2    2      2     x
+--R   (x  - 2a )atan(--------------) + 2a\|x  - a   + 2a\|- x  + a   - 2x asec(-)
+--R                         2                                                  a
+--R                        x
+--R   ---------------------------------------------------------------------------
+--R                                        4
+--R                                                     Type: Expression Integer
+--E
+
+--S 92     14:494 Axiom cannot simplify these expressions
+cc2:=aa-bb2
+--R
+--R   (5)
+--R                     +---------+
+--R                     |   2    2        +-------+      +---------+
+--R     2     2      2a\|- x  + a         | 2    2       |   2    2      2     x
+--R   (x  - 2a )atan(--------------) - 2a\|x  - a   + 2a\|- x  + a   - 2x asec(-)
+--R                         2                                                  a
+--R                        x
+--R   ---------------------------------------------------------------------------
+--R                                        4
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.495~~~~~$\displaystyle
@@ -616,7 +1488,7 @@ $$
 <<*>>=
 )clear all
 
---S 25 of 38
+--S 93
 aa:=integrate(x^2*asec(x/a),x)
 --R 
 --R
@@ -638,6 +1510,87 @@ aa:=integrate(x^2*asec(x/a),x)
 --R     6
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 94
+bb1:=x^3/3*asec(x/a)-(a*x*sqrt(x^2-a^2))/6-a^3/6*log(x+sqrt(x^2-a^2))
+--R
+--R                 +-------+            +-------+
+--R           3     | 2    2             | 2    2      3     x
+--R        - a log(\|x  - a   + x) - a x\|x  - a   + 2x asec(-)
+--R                                                          a
+--R   (2)  ----------------------------------------------------
+--R                                  6
+--R                                                     Type: Expression Integer
+--E
+
+--S 95
+bb2:=x^3/3*asec(x/a)+(a*x*sqrt(x^2-a^2))/6+a^3/6*log(x+sqrt(x^2-a^2))
+--R
+--R               +-------+            +-------+
+--R         3     | 2    2             | 2    2      3     x
+--R        a log(\|x  - a   + x) + a x\|x  - a   + 2x asec(-)
+--R                                                        a
+--R   (3)  --------------------------------------------------
+--R                                 6
+--R                                                     Type: Expression Integer
+--E
+
+--S 96
+cc1:=aa-bb1
+--R
+--R   (4)
+--R                                                  +---------+
+--R              +-------+                       +-+ |   2    2
+--R        3     | 2    2           3 +-+     2x\|2 \|- x  + a
+--R       a log(\|x  - a   + x) - 2a \|2 atan(------------------)
+--R                                                  2     2
+--R                                                3x  - 2a
+--R     + 
+--R                 +---------+
+--R                 |   2    2                                 +-------+
+--R        3     2a\|- x  + a        3           x             | 2    2
+--R       x atan(--------------) - 5a atan(------------) + a x\|x  - a
+--R                     2                   +---------+
+--R                    x                    |   2    2
+--R                                        \|- x  + a
+--R     + 
+--R           +---------+
+--R           |   2    2      3     x
+--R       a x\|- x  + a   - 2x asec(-)
+--R                                 a
+--R  /
+--R     6
+--R                                                     Type: Expression Integer
+--E
+
+--S 97     14:495 Axiom cannot simplify these expressions
+cc2:=aa-bb2
+--R
+--R   (5)
+--R                                                    +---------+
+--R                +-------+                       +-+ |   2    2
+--R          3     | 2    2           3 +-+     2x\|2 \|- x  + a
+--R       - a log(\|x  - a   + x) - 2a \|2 atan(------------------)
+--R                                                    2     2
+--R                                                  3x  - 2a
+--R     + 
+--R                 +---------+
+--R                 |   2    2                                 +-------+
+--R        3     2a\|- x  + a        3           x             | 2    2
+--R       x atan(--------------) - 5a atan(------------) - a x\|x  - a
+--R                     2                   +---------+
+--R                    x                    |   2    2
+--R                                        \|- x  + a
+--R     + 
+--R           +---------+
+--R           |   2    2      3     x
+--R       a x\|- x  + a   - 2x asec(-)
+--R                                 a
+--R  /
+--R     6
+--R                                                     Type: Expression Integer
+--E
+
 @
 
 \section{\cite{1}:14.496~~~~~$\displaystyle
@@ -650,7 +1603,7 @@ $$
 <<*>>=
 )clear all
 
---S 26 of 38
+--S 98     14:496 Axiom cannot compute this integral
 aa:=integrate(asec(x/a)/x,x)
 --R 
 --R
@@ -681,7 +1634,7 @@ $$
 <<*>>=
 )clear all
 
---S 27 of 38
+--S 99
 aa:=integrate(asec(x/a)/x^2,x)
 --R 
 --R
@@ -696,6 +1649,70 @@ aa:=integrate(asec(x/a)/x^2,x)
 --R                               2a x\|2
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 100
+bb1:=-asec(x/a)/x+sqrt(x^2-a^2)/(a*x)
+--R
+--R         +-------+
+--R         | 2    2           x
+--R        \|x  - a   - a asec(-)
+--R                            a
+--R   (2)  ----------------------
+--R                  a x
+--R                                                     Type: Expression Integer
+--E
+
+--S 101
+bb2:=-asec(x/a)/x-sqrt(x^2-a^2)/(a*x)
+--R
+--R           +-------+
+--R           | 2    2           x
+--R        - \|x  - a   - a asec(-)
+--R                              a
+--R   (3)  ------------------------
+--R                   a x
+--R                                                     Type: Expression Integer
+--E
+
+--S 102
+cc1:=aa-bb1
+--R
+--R   (4)
+--R                     +---------+                 +---------+
+--R                 +-+ |   2    2                  |   2    2           +-------+
+--R              2x\|2 \|- x  + a        +-+     2a\|- x  + a        +-+ | 2    2
+--R       x atan(------------------) - a\|2 atan(--------------) - 2\|2 \|x  - a
+--R                     2     2                         2
+--R                   3x  - 2a                         x
+--R     + 
+--R          +-+     x
+--R       2a\|2 asec(-)
+--R                  a
+--R  /
+--R          +-+
+--R     2a x\|2
+--R                                                     Type: Expression Integer
+--E
+
+--S 103    14:497 Axiom cannot simplify these expressions
+cc2:=aa-bb2
+--R
+--R   (5)
+--R                     +---------+                 +---------+
+--R                 +-+ |   2    2                  |   2    2           +-------+
+--R              2x\|2 \|- x  + a        +-+     2a\|- x  + a        +-+ | 2    2
+--R       x atan(------------------) - a\|2 atan(--------------) + 2\|2 \|x  - a
+--R                     2     2                         2
+--R                   3x  - 2a                         x
+--R     + 
+--R          +-+     x
+--R       2a\|2 asec(-)
+--R                  a
+--R  /
+--R          +-+
+--R     2a x\|2
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.498~~~~~$\displaystyle
@@ -716,7 +1733,7 @@ $$
 <<*>>=
 )clear all
 
---S 28 of 38
+--S 104
 aa:=integrate(acsc(x/a),x)
 --R 
 --R
@@ -737,6 +1754,73 @@ aa:=integrate(acsc(x/a),x)
 --R     2
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 105
+bb1:=x*acsc(x/a)+a*log(x+sqrt(x^2-a^2))
+--R
+--R               +-------+
+--R               | 2    2                x
+--R   (2)  a log(\|x  - a   + x) + x acsc(-)
+--R                                       a
+--R                                                     Type: Expression Integer
+--E
+
+--S 106
+bb2:=x*acsc(x/a)-a*log(x+sqrt(x^2-a^2))
+--R
+--R                 +-------+
+--R                 | 2    2                x
+--R   (3)  - a log(\|x  - a   + x) + x acsc(-)
+--R                                         a
+--R                                                     Type: Expression Integer
+--E
+
+--S 107
+cc1:=aa-bb1
+--R
+--R   (4)
+--R                                                   +---------+
+--R                 +-------+                     +-+ |   2    2
+--R                 | 2    2           +-+     2x\|2 \|- x  + a
+--R       - 2a log(\|x  - a   + x) + a\|2 atan(------------------)
+--R                                                   2     2
+--R                                                 3x  - 2a
+--R     + 
+--R                   +---------+
+--R                   |   2    2
+--R                2a\|- x  + a                    x                 x
+--R       - x atan(--------------) + 2a atan(------------) - 2x acsc(-)
+--R                       2                   +---------+            a
+--R                      x                    |   2    2
+--R                                          \|- x  + a
+--R  /
+--R     2
+--R                                                     Type: Expression Integer
+--E
+
+--S 108    14:498 Axiom cannot simplify these expressions
+cc2:=aa-bb2
+--R
+--R   (5)
+--R                                                 +---------+
+--R               +-------+                     +-+ |   2    2
+--R               | 2    2           +-+     2x\|2 \|- x  + a
+--R       2a log(\|x  - a   + x) + a\|2 atan(------------------)
+--R                                                 2     2
+--R                                               3x  - 2a
+--R     + 
+--R                   +---------+
+--R                   |   2    2
+--R                2a\|- x  + a                    x                 x
+--R       - x atan(--------------) + 2a atan(------------) - 2x acsc(-)
+--R                       2                   +---------+            a
+--R                      x                    |   2    2
+--R                                          \|- x  + a
+--R  /
+--R     2
+--R                                                     Type: Expression Integer
+--E
+
 @
 
 \section{\cite{1}:14.499~~~~~$\displaystyle
@@ -757,7 +1841,7 @@ $$
 <<*>>=
 )clear all
 
---S 29 of 38
+--S 109
 aa:=integrate(x*acsc(x/a),x)
 --R 
 --R
@@ -771,6 +1855,60 @@ aa:=integrate(x*acsc(x/a),x)
 --R                                4
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 110
+bb1:=x^2/2*acsc(x/a)+(a*sqrt(x^2-a^2))/2
+--R
+--R          +-------+
+--R          | 2    2     2     x
+--R        a\|x  - a   + x acsc(-)
+--R                             a
+--R   (2)  -----------------------
+--R                   2
+--R                                                     Type: Expression Integer
+--E
+
+--S 111
+bb2:=x^2/2*acsc(x/a)-(a*sqrt(x^2-a^2))/2
+--R
+--R            +-------+
+--R            | 2    2     2     x
+--R        - a\|x  - a   + x acsc(-)
+--R                               a
+--R   (3)  -------------------------
+--R                    2
+--R                                                     Type: Expression Integer
+--E
+
+--S 112
+cc1:=aa-bb1
+--R
+--R   (4)
+--R                       +---------+
+--R                       |   2    2        +-------+      +---------+
+--R       2     2      2a\|- x  + a         | 2    2       |   2    2      2     x
+--R   (- x  + 2a )atan(--------------) - 2a\|x  - a   - 2a\|- x  + a   - 2x acsc(-)
+--R                           2                                                  a
+--R                          x
+--R   -----------------------------------------------------------------------------
+--R                                         4
+--R                                                     Type: Expression Integer
+--E
+
+--S 113    14:499 Axiom cannot simplify these expressions
+cc2:=aa-bb2
+--R
+--R   (5)
+--R                       +---------+
+--R                       |   2    2        +-------+      +---------+
+--R       2     2      2a\|- x  + a         | 2    2       |   2    2      2     x
+--R   (- x  + 2a )atan(--------------) + 2a\|x  - a   - 2a\|- x  + a   - 2x acsc(-)
+--R                           2                                                  a
+--R                          x
+--R   -----------------------------------------------------------------------------
+--R                                         4
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.500~~~~~$\displaystyle
@@ -798,7 +1936,7 @@ $$
 <<*>>=
 )clear all
 
---S 30 of 38
+--S 114
 aa:=integrate(x^2*acsc(x/a),x)
 --R 
 --R
@@ -820,6 +1958,86 @@ aa:=integrate(x^2*acsc(x/a),x)
 --R     6
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 115
+bb1:=x^3/3*acsc(x/a)+(a*x*sqrt(x^2-a^2))/6+a^3/6*log(x+sqrt(x^2-a^2))
+--R
+--R               +-------+            +-------+
+--R         3     | 2    2             | 2    2      3     x
+--R        a log(\|x  - a   + x) + a x\|x  - a   + 2x acsc(-)
+--R                                                        a
+--R   (2)  --------------------------------------------------
+--R                                 6
+--R                                                     Type: Expression Integer
+--E
+
+--S 116
+bb2:=x^3/3*acsc(x/a)-(a*x*sqrt(x^2-a^2))/6-a^3/6*log(x+sqrt(x^2-a^2))
+--R
+--R                 +-------+            +-------+
+--R           3     | 2    2             | 2    2      3     x
+--R        - a log(\|x  - a   + x) - a x\|x  - a   + 2x acsc(-)
+--R                                                          a
+--R   (3)  ----------------------------------------------------
+--R                                  6
+--R                                                     Type: Expression Integer
+--E
+
+--S 117
+cc1:=aa-bb1
+--R
+--R   (4)
+--R                                                    +---------+
+--R                +-------+                       +-+ |   2    2
+--R          3     | 2    2           3 +-+     2x\|2 \|- x  + a
+--R       - a log(\|x  - a   + x) + 2a \|2 atan(------------------)
+--R                                                    2     2
+--R                                                  3x  - 2a
+--R     + 
+--R                   +---------+
+--R                   |   2    2                                 +-------+
+--R          3     2a\|- x  + a        3           x             | 2    2
+--R       - x atan(--------------) + 5a atan(------------) - a x\|x  - a
+--R                       2                   +---------+
+--R                      x                    |   2    2
+--R                                          \|- x  + a
+--R     + 
+--R             +---------+
+--R             |   2    2      3     x
+--R       - a x\|- x  + a   - 2x acsc(-)
+--R                                   a
+--R  /
+--R     6
+--R                                                     Type: Expression Integer
+--E
+
+--S 118    14:500 Axiom cannot simplify this expression
+cc2:=aa-bb2
+--R
+--R   (5)
+--R                                                  +---------+
+--R              +-------+                       +-+ |   2    2
+--R        3     | 2    2           3 +-+     2x\|2 \|- x  + a
+--R       a log(\|x  - a   + x) + 2a \|2 atan(------------------)
+--R                                                  2     2
+--R                                                3x  - 2a
+--R     + 
+--R                   +---------+
+--R                   |   2    2                                 +-------+
+--R          3     2a\|- x  + a        3           x             | 2    2
+--R       - x atan(--------------) + 5a atan(------------) + a x\|x  - a
+--R                       2                   +---------+
+--R                      x                    |   2    2
+--R                                          \|- x  + a
+--R     + 
+--R             +---------+
+--R             |   2    2      3     x
+--R       - a x\|- x  + a   - 2x acsc(-)
+--R                                   a
+--R  /
+--R     6
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.501~~~~~$\displaystyle
@@ -832,7 +2050,7 @@ $$
 <<*>>=
 )clear all
 
---S 31 of 38
+--S 119    14:501 Axiom cannot compute this integral
 aa:=integrate(acsc(x/a)/x,x)
 --R 
 --R
@@ -863,7 +2081,7 @@ $$
 <<*>>=
 )clear all
 
---S 32 of 38
+--S 120
 aa:=integrate(acsc(x/a)/x^2,x)
 --R 
 --R
@@ -878,6 +2096,72 @@ aa:=integrate(acsc(x/a)/x^2,x)
 --R                                2a x\|2
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 121
+bb1:=-acsc(x/a)/x-sqrt(x^2-a^2)/(a*x)
+--R
+--R           +-------+
+--R           | 2    2           x
+--R        - \|x  - a   - a acsc(-)
+--R                              a
+--R   (2)  ------------------------
+--R                   a x
+--R                                                     Type: Expression Integer
+--E
+
+--S 122
+bb2:=-acsc(x/a)/x+sqrt(x^2-a^2)/(a*x)
+--R
+--R         +-------+
+--R         | 2    2           x
+--R        \|x  - a   - a acsc(-)
+--R                            a
+--R   (3)  ----------------------
+--R                  a x
+--R                                                     Type: Expression Integer
+--E
+
+--S 123
+cc1:=aa-bb1
+--R
+--R   (4)
+--R                       +---------+                 +---------+
+--R                   +-+ |   2    2                  |   2    2
+--R                2x\|2 \|- x  + a        +-+     2a\|- x  + a
+--R       - x atan(------------------) + a\|2 atan(--------------)
+--R                       2     2                         2
+--R                     3x  - 2a                         x
+--R     + 
+--R             +-------+
+--R         +-+ | 2    2       +-+     x
+--R       2\|2 \|x  - a   + 2a\|2 acsc(-)
+--R                                    a
+--R  /
+--R          +-+
+--R     2a x\|2
+--R                                                     Type: Expression Integer
+--E
+
+--S 124    14:502 Axiom cannot simplify this expression
+cc2:=aa-bb2
+--R
+--R   (5)
+--R                       +---------+                 +---------+
+--R                   +-+ |   2    2                  |   2    2
+--R                2x\|2 \|- x  + a        +-+     2a\|- x  + a
+--R       - x atan(------------------) + a\|2 atan(--------------)
+--R                       2     2                         2
+--R                     3x  - 2a                         x
+--R     + 
+--R               +-------+
+--R           +-+ | 2    2       +-+     x
+--R       - 2\|2 \|x  - a   + 2a\|2 acsc(-)
+--R                                      a
+--R  /
+--R          +-+
+--R     2a x\|2
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.503~~~~~$\displaystyle
@@ -888,7 +2172,7 @@ $$
 <<*>>=
 )clear all
 
---S 33 of 38
+--S 125    14:503 Axiom cannot compute this integral
 aa:=integrate(x^m*asin(x/a),x)
 --R 
 --R
@@ -908,7 +2192,7 @@ $$
 <<*>>=
 )clear all
 
---S 34 of 38
+--S 126    14:504 Axiom cannot compute this integral
 aa:=integrate(x^m*acos(x/a),x)
 --R 
 --R
@@ -926,10 +2210,15 @@ $$\int{x^m\tan^{-1}\frac{x}{a}}=
 \frac{x^{m_1}}{m+1}\tan^{-1}\frac{x}{a}
 -\frac{a}{m+1}\int{\frac{x^{m+1}}{x^2+a^2}}
 $$
+This appears to be an interesting integral. Axiom found a closed
+form solution to the problem. However, the t1 integral below does
+not have a closed form solution. Note that we did not return a
+result for the prior two integrals, nor for the next integral. They
+have the same form but are expressed in terms of asin, acos, and acot.
 <<*>>=
 )clear all
 
---S 35 of 38
+--S 127
 aa:=integrate(x*m*atan(x/a),x)
 --R 
 --R
@@ -941,6 +2230,97 @@ aa:=integrate(x*m*atan(x/a),x)
 --R                          4
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 128
+t1:=integrate(x^(m+1)/(x^2+a^2),x)
+--E
+@
+Since we cannot get a closed form version of the prior integral
+we proceed to try to prove that Axiom got a correct answer. We
+do this by computing the derivate of 'aa' above and finding the
+difference from the original formula.
+
+So first we generate the derivative:
+<<*>>=
+
+--S 129
+bb:=D(aa,x)
+--R
+--R                     2a x
+--R          m x atan(-------)
+--R                    2    2
+--R                   x  - a
+--R   (3)  - -----------------
+--R                  2
+--R                                                     Type: Expression Integer
+--E
+@
+Then we input the original expression
+<<*>>=
+--S 130
+aa1:=x*m*atan(x/a)
+--R
+--R                 x
+--R   (4)  m x atan(-)
+--R                 a
+--R                                                     Type: Expression Integer
+--E
+@
+Now we take their difference
+<<*>>=
+--S 131
+dd:=aa1-bb
+--R
+--R                  x               2a x
+--R        2m x atan(-) + m x atan(-------)
+--R                  a              2    2
+--R                                x  - a
+--R   (5)  --------------------------------
+--R                        2
+--R                                                     Type: Expression Integer
+--E
+@
+Now we input the atan transformation
+<<*>>=
+--S 132
+atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
+--R
+--R                            - x + %i
+--R                     %i log(--------)
+--R                             x + %i
+--R   (6)  atan(x) == - ----------------
+--R                             2
+--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
+--E
+@
+And apply the transformation to the difference
+<<*>>=
+--S 133
+ee:=atanrule dd
+--R
+--R                      2              2
+--R                     x  + 2%i a x - a                 - x + %i a
+--R        - %i m x log(-----------------) - 2%i m x log(----------)
+--R                      2              2                 x + %i a
+--R                     x  - 2%i a x - a
+--R   (7)  ---------------------------------------------------------
+--R                                    4
+--R                                             Type: Expression Complex Integer
+--E
+@
+And now we simplify
+<<*>>=
+--S 134    14:505 SCHAUMS AND AXIOM DISAGREE? (branch cuts?)
+ff:=expandLog ee
+--R
+--R          %i m x log(- 1)
+--R   (8)  - ---------------
+--R                 2
+--R                                             Type: Expression Complex Integer
+--E
+And we get the surprising result that they are not equal.
+In fact, they differ by a complex value depending on x.
+Likely there is a branch-cut issue lurking somewhere.
 @
 
 \section{\cite{1}:14.506~~~~~$\displaystyle
@@ -952,7 +2332,7 @@ $$
 <<*>>=
 )clear all
 
---S 36 of 38
+--S 135    14:506 Axiom cannot compute this integral
 aa:=integrate(x^m*acot(x/a),x)
 --R 
 --R
@@ -982,7 +2362,7 @@ $$
 <<*>>=
 )clear all
 
---S 37 of 38
+--S 136    14:507 Axiom cannot compute this integral
 aa:=integrate(x^m*asec(x/a),x)
 --R 
 --R
@@ -1012,7 +2392,7 @@ $$
 <<*>>=
 )clear all
 
---S 38 of 38
+--S 137    14:508 Axiom cannot compute this integral
 aa:=integrate(x^m*acsc(x/a),x)
 --R 
 --R
diff --git a/src/input/schaum25.input.pamphlet b/src/input/schaum25.input.pamphlet
index 250e7c3..0a55f34 100644
--- a/src/input/schaum25.input.pamphlet
+++ b/src/input/schaum25.input.pamphlet
@@ -18,16 +18,32 @@ $$
 )set message auto off
 )clear all
 
---S 1 of 16
-aa:=integrate(e^(a*x),x)
---R 
+--S 1
+aa:=integrate(%e^(a*x),x)
 --R
---R          a x log(e)
+--R          a x
 --R        %e
---R   (1)  ------------
---R          a log(e)
+--R   (1)  -----
+--R          a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 2
+bb:=%e^(a*x)/a
+--R
+--R          a x
+--R        %e
+--R   (2)  -----
+--R          a
+--R                                                     Type: Expression Integer
+--E
+
+--S 3      14:509 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.510~~~~~$\displaystyle
@@ -38,17 +54,34 @@ $$
 <<*>>=
 )clear all
 
---S 2 of 16
-aa:=integrate(x*e^(a*x),x)
---R 
+--S 4
+aa:=integrate(x*%e^(a*x),x)
 --R
---R                          a x log(e)
---R        (a x log(e) - 1)%e
---R   (1)  ----------------------------
---R                   2      2
---R                  a log(e)
+--R                   a x
+--R        (a x - 1)%e
+--R   (1)  --------------
+--R               2
+--R              a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 5
+bb:=%e^(a*x)/a*(x-1/a)
+--R
+--R                   a x
+--R        (a x - 1)%e
+--R   (2)  --------------
+--R               2
+--R              a
+--R                                                     Type: Expression Integer
+--E
+
+--S 6      14:510 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.511~~~~~$\displaystyle
@@ -59,17 +92,34 @@ $$
 <<*>>=
 )clear all
 
---S 3 of 16
-aa:=integrate(x^2*e^(a*x),x)
---R 
+--S 7
+aa:=integrate(x^2*%e^(a*x),x)
 --R
---R          2 2      2                     a x log(e)
---R        (a x log(e)  - 2a x log(e) + 2)%e
---R   (1)  -------------------------------------------
---R                          3      3
---R                         a log(e)
+--R          2 2              a x
+--R        (a x  - 2a x + 2)%e
+--R   (1)  ----------------------
+--R                   3
+--R                  a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 8
+bb:=%e^(a*x)/a*(x^2-(2*x)/a+2/a^2)
+--R
+--R          2 2              a x
+--R        (a x  - 2a x + 2)%e
+--R   (2)  ----------------------
+--R                   3
+--R                  a
+--R                                                     Type: Expression Integer
+--E
+
+--S 9      14:511 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.512~~~~~$\displaystyle
@@ -89,16 +139,16 @@ $$
 <<*>>=
 )clear all
 
---S 4 of 16
-aa:=integrate(x^n*e^(a*x),x)
---R 
+--S 10     14:512 Axiom cannot compute this integral
+aa:=integrate(x^n*%e^(a*x),x)
 --R
 --R           x
---I         ++    n %I a
---I   (1)   |   %I e    d%I
+--I         ++    %I a  n
+--I   (1)   |   %e    %I d%I
 --R        ++
 --R                                          Type: Union(Expression Integer,...)
---E 
+--E
+
 @
 
 \section{\cite{1}:14.513~~~~~$\displaystyle
@@ -110,11 +160,10 @@ $$
 <<*>>=
 )clear all
 
---S 5 of 16
-aa:=integrate(e^(a*x)/x,x)
---R 
+--S 11     14:513 Schaums and Axiom agree by definition
+aa:=integrate(%e^(a*x)/x,x)
 --R
---R   (1)  Ei(a x log(e))
+--R   (1)  Ei(a x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
 @
@@ -127,15 +176,14 @@ $$
 <<*>>=
 )clear all
 
---S 6 of 16
-aa:=integrate(e^(a*x)/x^n,x)
---R 
+--S 12     14:514 Axiom cannot compute this integral
+aa:=integrate(%e^(a*x)/x^n,x)
 --R
---I           x  %I a
---R         ++  e
---I   (1)   |   ----- d%I
---R        ++      n
---I              %I
+--I           x   %I a
+--R         ++  %e
+--I   (1)   |   ------ d%I
+--R        ++       n
+--I               %I
 --R                                          Type: Union(Expression Integer,...)
 --E 
 @
@@ -148,16 +196,32 @@ $$
 <<*>>=
 )clear all
 
---S 7 of 16
-aa:=integrate(1/(p+q*e^(a*x)),x)
---R 
+--S 13
+aa:=integrate(1/(p+q*%e^(a*x)),x)
 --R
---R                  a x log(e)
---R        - log(q %e           + p) + a x log(e)
---R   (1)  --------------------------------------
---R                      a p log(e)
+--R                  a x
+--R        - log(q %e    + p) + a x
+--R   (1)  ------------------------
+--R                   a p
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 14
+bb:=x/p-1/(a*p)*log(p+q*%e^(a*x))
+--R
+--R                  a x
+--R        - log(q %e    + p) + a x
+--R   (2)  ------------------------
+--R                   a p
+--R                                                     Type: Expression Integer
+--E
+
+--S 15     14:515 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.516~~~~~$\displaystyle
@@ -168,16 +232,34 @@ $$
 <<*>>=
 )clear all
 
---S 8 of 16
-aa:=integrate(1/(p+q*e^(a*x)),x)
---R 
+--S 16
+aa:=integrate(1/(p+q*%e^(a*x))^2,x)
 --R
---R                  a x log(e)
---R        - log(q %e           + p) + a x log(e)
---R   (1)  --------------------------------------
---R                      a p log(e)
+--R               a x             a x                a x
+--R        (- q %e    - p)log(q %e    + p) + a q x %e    + a p x + p
+--R   (1)  ---------------------------------------------------------
+--R                               2    a x      3
+--R                            a p q %e    + a p
 --R                                          Type: Union(Expression Integer,...)
 --E
+
+--S 17
+bb:=x/p^2+1/(a*p*(p+q*%e^(a*x)))-1/(a*p^2)*log(p+q*%e^(a*x))
+--R
+--R               a x             a x                a x
+--R        (- q %e    - p)log(q %e    + p) + a q x %e    + a p x + p
+--R   (2)  ---------------------------------------------------------
+--R                               2    a x      3
+--R                            a p q %e    + a p
+--R                                                     Type: Expression Integer
+--E
+
+--S 18     14:516 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.517~~~~~$\displaystyle
@@ -197,16 +279,114 @@ $$
 <<*>>=
 )clear all
 
---S 9 of 16
-aa:=integrate(1/(p*e^(a*x)+q*e^(a*x)),x)
---R 
+--S 19
+aa:=integrate(1/(p*%e^(a*x)+q*%e^-(a*x)),x)
 --R
---R                        1
---R   (1)  - -----------------------------
---R                             a x log(e)
---R          (a q + a p)log(e)%e
---R                                          Type: Union(Expression Integer,...)
+--R                   a x 2      +-----+          a x
+--R             (p (%e   )  - q)\|- p q  + 2p q %e            a x +---+
+--R         log(-------------------------------------)      %e   \|p q
+--R                              a x 2                 atan(-----------)
+--R                         p (%e   )  + q                       q
+--R   (1)  [------------------------------------------,-----------------]
+--R                            +-----+                        +---+
+--R                         2a\|- p q                       a\|p q
+--R                                     Type: Union(List Expression Integer,...)
 --E 
+
+--S 20
+bb1:=1/(a*sqrt(p*q))*atan(sqrt(p/q)*%e^(a*x))
+--R
+--R                   +-+
+--R               a x |p
+--R        atan(%e    |- )
+--R                  \|q
+--R   (2)  ---------------
+--R              +---+
+--R            a\|p q
+--R                                                     Type: Expression Integer
+--E
+
+--S 21
+bb2:=1/(2*a*sqrt(-p*q))*log((%e^(a*x)-sqrt(-q/p))/(%e^(a*x)+sqrt(-q/p)))
+--R
+--R               +---+
+--R               |  q      a x
+--R            -  |- -  + %e
+--R              \|  p
+--R        log(----------------)
+--R              +---+
+--R              |  q      a x
+--R              |- -  + %e
+--R             \|  p
+--R   (3)  ---------------------
+--R                 +-----+
+--R              2a\|- p q
+--R                                                     Type: Expression Integer
+--E
+
+--S 22
+cc1:=aa.1-bb1
+--R
+--R   (4)
+--R                   a x 2      +-----+          a x                        +-+
+--R    +---+    (p (%e   )  - q)\|- p q  + 2p q %e         +-----+       a x |p
+--R   \|p q log(-------------------------------------) - 2\|- p q atan(%e    |- )
+--R                              a x 2                                      \|q
+--R                         p (%e   )  + q
+--R   ---------------------------------------------------------------------------
+--R                                    +-----+ +---+
+--R                                 2a\|- p q \|p q
+--R                                                     Type: Expression Integer
+--E
+
+--S 23
+cc2:=aa.2-bb1
+--R
+--R               a x +---+               +-+
+--R             %e   \|p q            a x |p
+--R        atan(-----------) - atan(%e    |- )
+--R                  q                   \|q
+--R   (5)  -----------------------------------
+--R                        +---+
+--R                      a\|p q
+--R                                                     Type: Expression Integer
+--E
+
+--S 24
+cc3:=aa.1-bb2
+--R
+--R                                                            +---+
+--R                                                            |  q      a x
+--R                  a x 2      +-----+          a x        -  |- -  + %e
+--R            (p (%e   )  - q)\|- p q  + 2p q %e             \|  p
+--R        log(-------------------------------------) - log(----------------)
+--R                             a x 2                         +---+
+--R                        p (%e   )  + q                     |  q      a x
+--R                                                           |- -  + %e
+--R                                                          \|  p
+--R   (6)  ------------------------------------------------------------------
+--R                                       +-----+
+--R                                    2a\|- p q
+--R                                                     Type: Expression Integer
+--E
+
+--S 25     14:517 Axiom cannot simplify these expressions
+cc4:=aa.2-bb2
+--R
+--R                       +---+
+--R                       |  q      a x
+--R                    -  |- -  + %e                       a x +---+
+--R           +---+      \|  p               +-----+     %e   \|p q
+--R        - \|p q log(----------------) + 2\|- p q atan(-----------)
+--R                      +---+                                q
+--R                      |  q      a x
+--R                      |- -  + %e
+--R                     \|  p
+--R   (7)  ----------------------------------------------------------
+--R                                +-----+ +---+
+--R                             2a\|- p q \|p q
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.518~~~~~$\displaystyle
@@ -217,17 +397,34 @@ $$
 <<*>>=
 )clear all
 
---S 10 of 16
-aa:=integrate(e^(a*x)*sin(b*x),x)
---R 
+--S 26
+aa:=integrate(%e^(a*x)*sin(b*x),x)
 --R
---R                                         a x log(e)
---R        (a log(e)sin(b x) - b cos(b x))%e
---R   (1)  -------------------------------------------
---R                        2      2    2
---R                       a log(e)  + b
+--R            a x                       a x
+--R        a %e   sin(b x) - b cos(b x)%e
+--R   (1)  ---------------------------------
+--R                      2    2
+--R                     b  + a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 27
+bb:=((%e^(a*x))*(a*sin(b*x)-b*cos(b*x)))/(a^2+b^2)
+--R
+--R            a x                       a x
+--R        a %e   sin(b x) - b cos(b x)%e
+--R   (2)  ---------------------------------
+--R                      2    2
+--R                     b  + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 28     14:518 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.519~~~~~$\displaystyle
@@ -238,17 +435,34 @@ $$
 <<*>>=
 )clear all
 
---S 11 of 16
-aa:=integrate(e^(a*x)*cos(b*x),x)
---R 
+--S 29
+aa:=integrate(%e^(a*x)*cos(b*x),x)
 --R
---R                                         a x log(e)
---R        (b sin(b x) + a cos(b x)log(e))%e
---R   (1)  -------------------------------------------
---R                        2      2    2
---R                       a log(e)  + b
+--R            a x                       a x
+--R        b %e   sin(b x) + a cos(b x)%e
+--R   (1)  ---------------------------------
+--R                      2    2
+--R                     b  + a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 30
+bb:=((%e^(a*x))*(a*cos(b*x)+b*sin(b*x)))/(a^2+b^2)
+--R
+--R            a x                       a x
+--R        b %e   sin(b x) + a cos(b x)%e
+--R   (2)  ---------------------------------
+--R                      2    2
+--R                     b  + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 31     14:519 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.520~~~~~$\displaystyle
@@ -260,24 +474,36 @@ $$
 <<*>>=
 )clear all
 
---S 12 of 16
-aa:=integrate(x*e^(a*x)*sin(b*x),x)
---R 
+--S 32
+aa:=integrate(x*%e^(a*x)*sin(b*x),x)
 --R
 --R   (1)
---R           3        3    2      2      2            2
---R         (a x log(e)  - a log(e)  + a b x log(e) + b )sin(b x)
---R       + 
---R            2                  2                          3
---R         - a b x cos(b x)log(e)  + 2a b cos(b x)log(e) - b x cos(b x)
---R    *
---R         a x log(e)
---R       %e
---R  /
---R      4      4     2 2      2    4
---R     a log(e)  + 2a b log(e)  + b
+--R        2    3      2    2   a x                3    2                     a x
+--R   ((a b  + a )x + b  - a )%e   sin(b x) + ((- b  - a b)x + 2a b)cos(b x)%e
+--R   ---------------------------------------------------------------------------
+--R                                  4     2 2    4
+--R                                 b  + 2a b  + a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 33
+bb:=(x*%e^(a*x)*(a*sin(b*x)-b*cos(b*x)))/(a^2+b^2)-(%e^(a*x)*((a^2-b^2)*sin(b*x)-2*a*b*cos(b*x)))/(a^2+b^2)^2
+--R
+--R   (2)
+--R        2    3      2    2   a x                3    2                     a x
+--R   ((a b  + a )x + b  - a )%e   sin(b x) + ((- b  - a b)x + 2a b)cos(b x)%e
+--R   ---------------------------------------------------------------------------
+--R                                  4     2 2    4
+--R                                 b  + 2a b  + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 34     14:520 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.521~~~~~$\displaystyle
@@ -289,24 +515,36 @@ $$
 <<*>>=
 )clear all
 
---S 13 of 16
-aa:=integrate(x*e^(a*x)*cos(b*x),x)
---R 
+--S 35
+aa:=integrate(x*%e^(a*x)*cos(b*x),x)
 --R
 --R   (1)
---R           2          2                  3              3                3
---R         (a b x log(e)  - 2a b log(e) + b x)sin(b x) + a x cos(b x)log(e)
---R       + 
---R            2              2      2                    2
---R         - a cos(b x)log(e)  + a b x cos(b x)log(e) + b cos(b x)
---R    *
---R         a x log(e)
---R       %e
---R  /
---R      4      4     2 2      2    4
---R     a log(e)  + 2a b log(e)  + b
+--R      3    2             a x                2    3      2    2           a x
+--R   ((b  + a b)x - 2a b)%e   sin(b x) + ((a b  + a )x + b  - a )cos(b x)%e
+--R   -------------------------------------------------------------------------
+--R                                 4     2 2    4
+--R                                b  + 2a b  + a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 36
+bb:=(x*%e^(a*x)*(a*cos(b*x)+b*sin(b*x)))/(a^2+b^2)-(%e^(a*x)*((a^2-b^2)*cos(b*x)+2*a*b*sin(b*x)))/(a^2+b^2)^2
+--R
+--R   (2)
+--R      3    2             a x                2    3      2    2           a x
+--R   ((b  + a b)x - 2a b)%e   sin(b x) + ((a b  + a )x + b  - a )cos(b x)%e
+--R   -------------------------------------------------------------------------
+--R                                 4     2 2    4
+--R                                b  + 2a b  + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 37     14:521 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.522~~~~~$\displaystyle
@@ -317,14 +555,13 @@ $$
 <<*>>=
 )clear all
 
---S 14 of 16
-aa:=integrate(e^(a*x)*log(x),x)
---R 
+--S 38     14:522 Schaums and Axiom agree by definition
+aa:=integrate(%e^(a*x)*log(x),x)
 --R
---R           x
---I         ++          %I a
---I   (1)   |   log(%I)e    d%I
---R        ++
+--R          a x
+--R        %e   log(x) - Ei(a x)
+--R   (1)  ---------------------
+--R                  a
 --R                                          Type: Union(Expression Integer,...)
 --E 
 @
@@ -338,13 +575,12 @@ $$
 <<*>>=
 )clear all
 
---S 15 of 16
-aa:=integrate(e^(a*x)*sin(b*x)^n,x)
---R 
+--S 39     14:523 Axiom cannot compute this integral
+aa:=integrate(%e^(a*x)*sin(b*x)^n,x)
 --R
 --R           x
---I         ++   %I a         n
---I   (1)   |   e    sin(%I b) d%I
+--I         ++    %I a         n
+--I   (1)   |   %e    sin(%I b) d%I
 --R        ++
 --R                                          Type: Union(Expression Integer,...)
 --E 
@@ -359,13 +595,12 @@ $$
 <<*>>=
 )clear all
 
---S 16 of 16
-aa:=integrate(e^(a*x)*cos(b*x)^n,x)
---R 
+--S 40     14:524 Axiom cannot compute this integral
+aa:=integrate(%e^(a*x)*cos(b*x)^n,x)
 --R
 --R           x
---I         ++   %I a         n
---I   (1)   |   e    cos(%I b) d%I
+--I         ++    %I a         n
+--I   (1)   |   %e    cos(%I b) d%I
 --R        ++
 --R                                          Type: Union(Expression Integer,...)
 --E 



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Subject: [Axiom-developer] 20080426.01.tpd.patch (CATS Schaums-Axiom
	equivalence testing (26-28))
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On at least 2 of these problems Schaums and Axiom seem to disagree 
on the results, namely:
  14:569 SCHAUMS AND AXIOM DISAGREE?
  14:571 SCHAUMS AND AXIOM DISAGREE?
as the compute result is not constant but does not seem to have a 
simplification that eliminates x.
This needs to be studied further.

schaum26.input.pamphlet
  14:525 Schaums and Axiom agree
  14:526 Schaums and Axiom agree
  14:527 Schaums and Axiom agree
  14:528 Schaums and Axiom agree
  14:529 Schaums and Axiom agree
  14:530 Schaums and Axiom agree
  14:531 Schaums and Axiom agree
  14:532 Schaums and Axiom agree
  14:533 Schaums and Axiom agree by definition
  14:534 Axiom cannot compute this integral
  14:535 Axiom cannot compute this integral
  14:536 Axiom cannot compute this integral
  14:537 Schaums and Axiom agree
  14:538 Schaums and Axiom agree
  14:539 Axiom cannot compute this integral

schaum27.input.pamphlet
  14:540 Schaums and Axiom agree
  14:541 Schaums and Axiom agree
  14:542 Schaums and Axiom agree
  14:543 Axiom cannot compute this integral
  14:544 Axiom cannot compute this integral
  14:545 Axiom cannot simplify this expression
  14:546 Axiom cannot compute this integral
  14:547 Schaums and Axiom agree
  14:548 Axiom cannot simplify this expression
  14:549 Schaums and Axiom differ by a constant
  14:550 Axiom cannot simplify this expression
  14:551 Schaums and Axiom agree
  14:552 Schaums and Axiom agree
  14:553 Axiom cannot simplify this expression
  14:554 Axiom cannot simplify this expression
  14:555 Axiom cannot simplify this expression
  14:556 Axiom cannot simplify this expression
  14:557 Axiom cannot compute this integral
  14:558 Axiom cannot compute this integral
  14:559 Axiom cannot compute this integral
  14:560 Axiom cannot compute this integral
  14:561 Axiom cannot compute this integral

schaum28.input.pamphlet
  14:562 Schaums and Axiom agree
  14:563 Schaums and Axiom agree
  14:564 Schaums and Axiom agree
  14:565 Axiom cannot compute this integral
  14:566 Axiom cannot compute this integral
  14:567 Schaums and Axiom agree
  14:568 Axiom cannot compute this integral
  14:569 SCHAUMS AND AXIOM DISAGREE?
  14:570 Schaums and Axiom agree
  14:571 SCHAUMS AND AXIOM DISAGREE?
  14:572 Schaums and Axiom agree
  14:573 Schaums and Axiom agree
  14:574 Schaums and Axiom agree
  14:575 Schaums and Axiom differ by a constant
  14:576 Schaums and Axiom differ by a constant
  14:577 Schaums and Axiom differ by a constant
  14:578 Schaums and Axiom differ by a constant
  14:579 Axiom cannot compute this integral
  14:580 Axiom cannot compute this integral
  14:581 Axiom cannot simplify this expression
  14:582 Axiom cannot simplify this expression
  14:583 Axiom cannot simplify this expression
  14:584 Axiom cannot compute this integral
  14:585 Axiom cannot compute this integral
  14:586 Axiom cannot compute this integral
  14:587 Axiom cannot compute this integral
  14:588 Axiom cannot compute this integral
  14:589 Axiom cannot compute this integral

========================================================================
diff --git a/changelog b/changelog
index 3956a7b..c94aa65 100644
--- a/changelog
+++ b/changelog
@@ -1,3 +1,6 @@
+20080426 tpd src/input/schaum28.input show Schaums-Axiom equivalence
+20080426 tpd src/input/schaum27.input show Schaums-Axiom equivalence
+20080426 tpd src/input/schaum26.input show Schaums-Axiom equivalence
 20080425 tpd src/input/schaum25.input show Schaums-Axiom equivalence
 20080425 tpd src/input/schaum24.input show Schaums-Axiom equivalence
 20080424 tpd src/input/schaum23.input show Schaums-Axiom equivalence
diff --git a/src/input/schaum26.input.pamphlet b/src/input/schaum26.input.pamphlet
index 7bf7244..9bdeec5 100644
--- a/src/input/schaum26.input.pamphlet
+++ b/src/input/schaum26.input.pamphlet
@@ -18,13 +18,27 @@ $$
 )set message auto off
 )clear all
 
---S 1 of 16
+--S 1
 aa:=integrate(log(x),x)
 --R 
 --R
 --R   (1)  x log(x) - x
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 2
+bb:=x*log(x)-x
+--R
+--R   (2)  x log(x) - x
+--R                                                     Type: Expression Integer
+--E
+
+--S 3      14:525 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.526~~~~~$\displaystyle
@@ -35,7 +49,7 @@ $$
 <<*>>=
 )clear all
 
---S 2 of 16
+--S 4
 aa:=integrate(x*log(x),x)
 --R 
 --R
@@ -44,7 +58,24 @@ aa:=integrate(x*log(x),x)
 --R   (1)  --------------
 --R               4
 --R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 5
+bb:=x^2/2*(log(x)-1/2)
+--R
+--R          2          2
+--R        2x log(x) - x
+--R   (2)  --------------
+--R               4
+--R                                                     Type: Expression Integer
 --E 
+
+--S 6      14:526 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.527~~~~~$\displaystyle
@@ -55,7 +86,7 @@ $$
 <<*>>=
 )clear all
 
---S 3 of 16
+--S 7
 aa:=integrate(x^m*log(x),x)
 --R 
 --R
@@ -65,7 +96,55 @@ aa:=integrate(x^m*log(x),x)
 --R                   2
 --R                  m  + 2m + 1
 --R                                          Type: Union(Expression Integer,...)
---E 
+--E
+
+--S 8
+bb:=x^(m+1)/(m+1)*(log(x)-1/(m+1))
+--R
+--R                            m + 1
+--R        ((m + 1)log(x) - 1)x
+--R   (2)  -------------------------
+--R                2
+--R               m  + 2m + 1
+--R                                                     Type: Expression Integer
+--E
+
+--S 9
+cc:=aa-bb
+--R
+--R                               m log(x)                         m + 1
+--R        ((m + 1)x log(x) - x)%e         + ((- m - 1)log(x) + 1)x
+--R   (3)  -------------------------------------------------------------
+--R                                  2
+--R                                 m  + 2m + 1
+--R                                                     Type: Expression Integer
+--E
+
+--S 10
+explog:=rule(%e^(n*log(x)) == x^n)
+--R
+--R          n log(x)     n
+--R   (4)  %e         == x
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 11
+dd:=explog cc
+--R
+--R                              m + 1                         m
+--R        ((- m - 1)log(x) + 1)x      + ((m + 1)x log(x) - x)x
+--R   (5)  -----------------------------------------------------
+--R                              2
+--R                             m  + 2m + 1
+--R                                                     Type: Expression Integer
+--E
+
+--S 12     14:527 Schaums and Axiom agree
+ee:=complexNormalize dd
+--R
+--R   (6)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.528~~~~~$\displaystyle
@@ -76,7 +155,7 @@ $$
 <<*>>=
 )clear all
 
---S 4 of 16
+--S 13
 aa:=integrate(log(x)/x,x)
 --R 
 --R
@@ -85,7 +164,24 @@ aa:=integrate(log(x)/x,x)
 --R   (1)  -------
 --R           2
 --R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 14
+bb:=1/2*log(x)^2
+--R
+--R              2
+--R        log(x)
+--R   (2)  -------
+--R           2
+--R                                                     Type: Expression Integer
 --E 
+
+--S 15     14:528 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.529~~~~~$\displaystyle
@@ -96,7 +192,7 @@ $$
 <<*>>=
 )clear all
 
---S 5 of 16
+--S 16
 aa:=integrate(log(x)/x^2,x)
 --R 
 --R
@@ -105,6 +201,22 @@ aa:=integrate(log(x)/x^2,x)
 --R              x
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 17
+bb:=-log(x)/x-1/x
+--R
+--R        - log(x) - 1
+--R   (2)  ------------
+--R              x
+--R                                                     Type: Expression Integer
+--E
+
+--S 18     14:529 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.530~~~~~$\displaystyle
@@ -115,14 +227,29 @@ $$
 <<*>>=
 )clear all
 
---S 6 of 16
+--S 19
 aa:=integrate(log(x)^2,x)
 --R 
 --R
 --R                2
 --R   (1)  x log(x)  - 2x log(x) + 2x
 --R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 20
+bb:=x*log(x)^2-2*x*log(x)+2*x
+--R
+--R                2
+--R   (2)  x log(x)  - 2x log(x) + 2x
+--R                                                     Type: Expression Integer
 --E 
+
+--S 21     14:530 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.531~~~~~$\displaystyle
@@ -133,7 +260,7 @@ $$
 <<*>>=
 )clear all
 
---S 7 of 16
+--S 22
 aa:=integrate(log(x)^n/x,x)
 --R 
 --R
@@ -142,7 +269,52 @@ aa:=integrate(log(x)^n/x,x)
 --R   (1)  ---------------------
 --R                n + 1
 --R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 23
+bb:=log(x)^(n+1)/(n+1)
+--R
+--R              n + 1
+--R        log(x)
+--R   (2)  -----------
+--R           n + 1
+--R                                                     Type: Expression Integer
 --E 
+
+--S 24
+cc:=aa-bb
+--R
+--R                n log(log(x))         n + 1
+--R        log(x)%e              - log(x)
+--R   (3)  -----------------------------------
+--R                       n + 1
+--R                                                     Type: Expression Integer
+--E
+
+--S 25
+explog:=rule(%e^(n*log(x)) == x^n)
+--R
+--R          n log(x)     n
+--R   (4)  %e         == x
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 26
+dd:=explog cc
+--R
+--R                n + 1               n
+--R        - log(x)      + log(x)log(x)
+--R   (5)  -----------------------------
+--R                    n + 1
+--R                                                     Type: Expression Integer
+--E
+
+--S 27     14:531 Schaums and Axiom agree
+ee:=complexNormalize dd
+--R
+--R   (6)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.532~~~~~$\displaystyle
@@ -153,13 +325,28 @@ $$
 <<*>>=
 )clear all
 
---S 8 of 16
+--S 28
 aa:=integrate(1/(x*log(x)),x)
 --R 
 --R
 --R   (1)  log(log(x))
 --R                                          Type: Union(Expression Integer,...)
 --E
+
+--S 29
+bb:=log(log(x))
+--R
+--R   (2)  log(log(x))
+--R                                                     Type: Expression Integer
+--E
+
+--S 30     14:532 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
+
 @
 
 \section{\cite{1}:14.533~~~~~$\displaystyle
@@ -171,7 +358,7 @@ $$
 <<*>>=
 )clear all
 
---S 9 of 16
+--S 31     14:533 Schaums and Axiom agree by definition
 aa:=integrate(1/log(x),x)
 --R 
 --R
@@ -189,7 +376,7 @@ $$
 <<*>>=
 )clear all
 
---S 10 of 16
+--S 32     14:534 Axiom cannot compute this integral
 aa:=integrate(x^m/log(x),x)
 --R 
 --R
@@ -209,7 +396,7 @@ $$
 <<*>>=
 )clear all
 
---S 11 of 16
+--S 33     14:535 Axiom cannot compute this integral
 aa:=integrate(log(x)^n,x)
 --R 
 --R
@@ -229,7 +416,7 @@ $$
 <<*>>=
 )clear all
 
---S 12 of 16
+--S 34     14:536 Axiom cannot compute this integral
 aa:=integrate(x^m*log(x)^n,x)
 --R 
 --R
@@ -249,7 +436,7 @@ $$
 <<*>>=
 )clear all
 
---S 13 of 16
+--S 35
 aa:=integrate(log(x^2+a^2),x)
 --R 
 --R
@@ -258,6 +445,22 @@ aa:=integrate(log(x^2+a^2),x)
 --R                                 a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 36
+bb:=x*log(x^2+a^2)-2*x+2*a*atan(x/a)
+--R
+--R               2    2            x
+--R   (2)  x log(x  + a ) + 2a atan(-) - 2x
+--R                                 a
+--R                                                     Type: Expression Integer
+--E
+
+--S 37     14:537 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.538~~~~~$\displaystyle
@@ -268,7 +471,7 @@ $$
 <<*>>=
 )clear all
 
---S 14 of 16
+--S 38
 aa:=integrate(log(x^2-a^2),x)
 --R 
 --R
@@ -276,6 +479,31 @@ aa:=integrate(log(x^2-a^2),x)
 --R   (1)  x log(x  - a ) + a log(x + a) - a log(x - a) - 2x
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 39
+bb:=x*log(x^2-a^2)-2*x+a*log((x+a)/(x-a))
+--R
+--R               2    2          x + a
+--R   (2)  x log(x  - a ) + a log(-----) - 2x
+--R                               x - a
+--R                                                     Type: Expression Integer
+--E
+
+--S 40
+cc:=aa-bb
+--R
+--R                                            x + a
+--R   (3)  a log(x + a) - a log(x - a) - a log(-----)
+--R                                            x - a
+--R                                                     Type: Expression Integer
+--E
+
+--S 41     14:538 Schaums and Axiom agree
+dd:=expandLog cc
+--R
+--R   (4)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.539~~~~~$\displaystyle
@@ -287,7 +515,7 @@ $$
 <<*>>=
 )clear all
 
---S 15a of 16
+--S 42
 aa:=integrate(x^m*log(x^2+a^2),x)
 --R 
 --R
@@ -296,11 +524,11 @@ aa:=integrate(x^m*log(x^2+a^2),x)
 --I   (1)   |   log(a  + %I )%I d%I
 --R        ++
 --R                                          Type: Union(Expression Integer,...)
---E 
+--E
 
 )clear all
 
---S 15b of 16
+--S 43     14:539 Axiom cannot compute this integral
 aa:=integrate(x^m*log(x^2-a^2),x)
 --R 
 --R
diff --git a/src/input/schaum27.input.pamphlet b/src/input/schaum27.input.pamphlet
index bb9f4d2..cc233e4 100644
--- a/src/input/schaum27.input.pamphlet
+++ b/src/input/schaum27.input.pamphlet
@@ -18,7 +18,7 @@ $$
 )set message auto off
 )clear all
 
---S 1 of 22
+--S 1
 aa:=integrate(sinh(a*x),x)
 --R
 --R        cosh(a x)
@@ -26,6 +26,22 @@ aa:=integrate(sinh(a*x),x)
 --R            a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 2
+bb:=cosh(a*x)/a
+--R
+--R        cosh(a x)
+--R   (2)  ---------
+--R            a
+--R                                                     Type: Expression Integer
+--E
+
+--S 3      14:540 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.541~~~~~$\displaystyle
@@ -36,7 +52,7 @@ $$
 <<*>>=
 )clear all
 
---S 2 of 22
+--S 4
 aa:=integrate(x*sinh(a*x),x)
 --R 
 --R
@@ -46,6 +62,23 @@ aa:=integrate(x*sinh(a*x),x)
 --R                     a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 5
+bb:=(x*cosh(a*x))/a-sinh(a*x)/a^2
+--R
+--R        - sinh(a x) + a x cosh(a x)
+--R   (2)  ---------------------------
+--R                      2
+--R                     a
+--R                                                     Type: Expression Integer
+--E
+
+--S 6      14:541 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.542~~~~~$\displaystyle
@@ -56,7 +89,7 @@ $$
 <<*>>=
 )clear all
 
---S 3 of 22
+--S 7
 aa:=integrate(x^2*sinh(a*x),x)
 --R 
 --R
@@ -67,6 +100,24 @@ aa:=integrate(x^2*sinh(a*x),x)
 --R                          a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 8
+bb:=(x^2/a+2/a^3)*cosh(a*x)-(2*x)/a^2*sinh(a*x)
+--R
+--R                             2 2
+--R        - 2a x sinh(a x) + (a x  + 2)cosh(a x)
+--R   (2)  --------------------------------------
+--R                           3
+--R                          a
+--R                                                     Type: Expression Integer
+--E
+
+--S 9      14:542 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.543~~~~~$\displaystyle
@@ -77,7 +128,7 @@ $$
 <<*>>=
 )clear all
 
---S 4 of 22
+--S 10     14:543 Axiom cannot compute this integral
 aa:=integrate(sinh(a*x)/x,x)
 --R 
 --R
@@ -97,7 +148,7 @@ $$
 <<*>>=
 )clear all
 
---S 5 of 22
+--S 11     14:544 Axiom cannot compute this integral
 aa:=integrate(sinh(a*x)/x^2,x)
 --R 
 --R
@@ -118,7 +169,7 @@ $$
 <<*>>=
 )clear all
 
---S 6 of 22
+--S 12
 aa:=integrate(1/sinh(a*x),x)
 --R 
 --R
@@ -127,6 +178,31 @@ aa:=integrate(1/sinh(a*x),x)
 --R                                        a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 13
+bb:=1/a*log(tanh(a*x)/2)
+--R
+--R            tanh(a x)
+--R        log(---------)
+--R                2
+--R   (2)  --------------
+--R               a
+--R                                                     Type: Expression Integer
+--E
+
+--S 14     14:545 Axiom cannot simplify this expression
+cc:=aa-bb
+--R
+--R   (3)
+--R             tanh(a x)
+--R       - log(---------) - log(sinh(a x) + cosh(a x) + 1)
+--R                 2
+--R     + 
+--R       log(sinh(a x) + cosh(a x) - 1)
+--R  /
+--R     a
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.546~~~~~$\displaystyle
@@ -138,7 +214,7 @@ $$
 <<*>>=
 )clear all
 
---S 7 of 22
+--S 15     14:546 Axiom cannot compute this integral
 aa:=integrate(x/sinh(a*x),x)
 --R 
 --R
@@ -158,7 +234,7 @@ $$
 <<*>>=
 )clear all
 
---S 8 of 22
+--S 16
 aa:=integrate(sinh(a*x)^2,x)
 --R 
 --R
@@ -167,6 +243,22 @@ aa:=integrate(sinh(a*x)^2,x)
 --R                   2a
 --R                                          Type: Union(Expression Integer,...)
 --E
+
+--S 17
+bb:=(sinh(a*x)*cosh(a*x))/(2*a)-x/2
+--R
+--R        cosh(a x)sinh(a x) - a x
+--R   (2)  ------------------------
+--R                   2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 18     14:547 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.548~~~~~$\displaystyle
@@ -177,7 +269,7 @@ $$
 <<*>>=
 )clear all
 
---S 9 of 22
+--S 19
 aa:=integrate(x*sinh(a*x)^2,x)
 --R 
 --R
@@ -188,6 +280,87 @@ aa:=integrate(x*sinh(a*x)^2,x)
 --R                                    8a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 20
+bb:=(x*sinh(2*a*x))/(4*a)-cosh(2*a*x)/(8*a^2)-x^2/4
+--R
+--R                                         2 2
+--R        2a x sinh(2a x) - cosh(2a x) - 2a x
+--R   (2)  ------------------------------------
+--R                           2
+--R                         8a
+--R                                                     Type: Expression Integer
+--E
+
+--S 21
+cc:=aa-bb
+--R
+--R   (3)
+--R                                    2
+--R       - 2a x sinh(2a x) - sinh(a x)  + 4a x cosh(a x)sinh(a x) + cosh(2a x)
+--R     + 
+--R                  2
+--R       - cosh(a x)
+--R  /
+--R       2
+--R     8a
+--R                                                     Type: Expression Integer
+--E
+
+--S 22
+sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2)
+--R
+--R               2    cosh(2x) - 1
+--R   (4)  sinh(x)  == ------------
+--R                          2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 23
+dd:=sinhsqrrule cc
+--R
+--R   (5)
+--R                                                                        2
+--R   - 4a x sinh(2a x) + 8a x cosh(a x)sinh(a x) + cosh(2a x) - 2cosh(a x)  + 1
+--R   --------------------------------------------------------------------------
+--R                                         2
+--R                                      16a
+--R                                                     Type: Expression Integer
+--E
+
+--S 24
+coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2)
+--R
+--R               2    cosh(2x) + 1
+--R   (6)  cosh(x)  == ------------
+--R                          2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 25
+ee:=coshsqrrule dd
+--R
+--R        - x sinh(2a x) + 2x cosh(a x)sinh(a x)
+--R   (7)  --------------------------------------
+--R                          4a
+--R                                                     Type: Expression Integer
+--E
+
+--S 26
+sinhcoshrule:=rule(sinh(x)*cosh(y) == 1/2*(sinh(x+y)+sinh(x-y)))
+--R
+--I                             %K sinh(y + x) - %K sinh(y - x)
+--I   (8)  %K cosh(y)sinh(x) == -------------------------------
+--R                                            2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 27     14:548 Axiom cannot simplify this expression
+ff:=sinhcoshrule ee
+--R
+--R   (9)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.549~~~~~$\displaystyle
@@ -198,7 +371,7 @@ $$
 <<*>>=
 )clear all
 
---S 10 of 22
+--S 28
 aa:=integrate(1/sinh(a*x)^2,x)
 --R 
 --R
@@ -208,6 +381,158 @@ aa:=integrate(1/sinh(a*x)^2,x)
 --R          a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  - a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 29
+bb:=-coth(a*x)/a
+--R
+--R          coth(a x)
+--R   (2)  - ---------
+--R              a
+--R                                                     Type: Expression Integer
+--E
+
+--S 30
+cc:=aa-bb
+--R
+--R   (3)
+--R                         2
+--R       coth(a x)sinh(a x)  + 2cosh(a x)coth(a x)sinh(a x)
+--R     + 
+--R                 2
+--R       (cosh(a x)  - 1)coth(a x) - 2
+--R  /
+--R                2                                      2
+--R     a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  - a
+--R                                                     Type: Expression Integer
+--E
+
+--S 31
+sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2)
+--R
+--R               2    cosh(2x) - 1
+--R   (4)  sinh(x)  == ------------
+--R                          2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 32
+dd:=sinhsqrrule cc
+--R
+--R   (5)
+--R                                                          2
+--R   4cosh(a x)coth(a x)sinh(a x) + (cosh(2a x) + 2cosh(a x)  - 3)coth(a x) - 4
+--R   --------------------------------------------------------------------------
+--R                                                               2
+--R            4a cosh(a x)sinh(a x) + a cosh(2a x) + 2a cosh(a x)  - 3a
+--R                                                     Type: Expression Integer
+--E
+
+--S 33
+coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2)
+--R
+--R               2    cosh(2x) + 1
+--R   (6)  cosh(x)  == ------------
+--R                          2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 34
+ee:=coshsqrrule dd
+--R
+--R        2cosh(a x)coth(a x)sinh(a x) + (cosh(2a x) - 1)coth(a x) - 2
+--R   (7)  ------------------------------------------------------------
+--R                  2a cosh(a x)sinh(a x) + a cosh(2a x) - a
+--R                                                     Type: Expression Integer
+--E
+
+--S 35
+sinhcoshrule:=rule(sinh(x)*cosh(y) == 1/2*(sinh(x+y)+sinh(x-y)))
+--I                             %B sinh(y + x) - %B sinh(y - x)
+--I   (8)  %B cosh(y)sinh(x) == -------------------------------
+--R                                            2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 36
+ff:=sinhcoshrule ee
+--R
+--R        coth(a x)sinh(2a x) + (cosh(2a x) - 1)coth(a x) - 2
+--R   (9)  ---------------------------------------------------
+--R                  a sinh(2a x) + a cosh(2a x) - a
+--R                                                     Type: Expression Integer
+--E
+
+--S 37
+cothrule:=rule(coth(x) == cosh(x)/sinh(x))
+--R
+--R                    cosh(x)
+--R   (10)  coth(x) == -------
+--R                    sinh(x)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 38
+gg:=cothrule ff
+--R
+--R         cosh(a x)sinh(2a x) - 2sinh(a x) + cosh(a x)cosh(2a x) - cosh(a x)
+--R   (11)  ------------------------------------------------------------------
+--R                 a sinh(a x)sinh(2a x) + (a cosh(2a x) - a)sinh(a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 39
+hh:=sinhcoshrule gg
+--R
+--R         sinh(3a x) - 3sinh(a x) + 2cosh(a x)cosh(2a x) - 2cosh(a x)
+--R   (12)  -----------------------------------------------------------
+--R             a sinh(3a x) + 2a sinh(a x)sinh(2a x) - 3a sinh(a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 40
+sinhsinhrule:=rule(sinh(x)*sinh(y)==1/2*(cosh(x+y)-cosh(x-y)))
+--R
+--I                              %M cosh(y + x) - %M cosh(y - x)
+--I   (13)  %M sinh(x)sinh(y) == -------------------------------
+--R                                             2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 41
+ii:=sinhsinhrule gg
+--R
+--R         2cosh(a x)sinh(2a x) - 4sinh(a x) + 2cosh(a x)cosh(2a x) - 2cosh(a x)
+--R   (14)  ---------------------------------------------------------------------
+--R               (2a cosh(2a x) - 2a)sinh(a x) + a cosh(3a x) - a cosh(a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 42
+coshcoshrule:=rule(cosh(x)*cosh(y)==1/2*(cosh(x+y)+cosh(x-y)))
+--R
+--I                              %N cosh(y + x) + %N cosh(y - x)
+--I   (15)  %N cosh(x)cosh(y) == -------------------------------
+--R                                             2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 43
+jj:=coshcoshrule ii
+--R
+--R         2cosh(a x)sinh(2a x) - 4sinh(a x) + cosh(3a x) - cosh(a x)
+--R   (16)  ----------------------------------------------------------
+--R         (2a cosh(2a x) - 2a)sinh(a x) + a cosh(3a x) - a cosh(a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 44     14:549 Schaums and Axiom differ by a constant
+kk:=sinhcoshrule jj
+--R
+--R         1
+--R   (17)  -
+--R         a
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.550~~~~~$\displaystyle
@@ -218,7 +543,7 @@ $$
 <<*>>=
 )clear all
 
---S 11 of 22
+--S 45
 aa:=integrate(sinh(a*x)*sinh(p*x),x)
 --R 
 --R
@@ -228,6 +553,36 @@ aa:=integrate(sinh(a*x)*sinh(p*x),x)
 --R        (p  - a )sinh(a x)  + (- p  + a )cosh(a x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 46
+bb:=(sinh(a+p)*x)/(2*(a+p))-(sinh(a-p)*x)/(2*(a-p))
+--R
+--R        (p - a)x sinh(p + a) + (- p - a)x sinh(p - a)
+--R   (2)  ---------------------------------------------
+--R                            2     2
+--R                          2p  - 2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 47     14:550 Axiom cannot simplify this expression
+cc:=aa-bb
+--R
+--R   (3)
+--R       2a cosh(a x)sinh(p x)
+--R     + 
+--R                                                               2
+--R       ((- p + a)x sinh(p + a) + (p + a)x sinh(p - a))sinh(a x)
+--R     + 
+--R                                                   2
+--R       - 2p cosh(p x)sinh(a x) + (p - a)x cosh(a x) sinh(p + a)
+--R     + 
+--R                           2
+--R       (- p - a)x cosh(a x) sinh(p - a)
+--R  /
+--R        2     2          2        2     2          2
+--R     (2p  - 2a )sinh(a x)  + (- 2p  + 2a )cosh(a x)
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.551~~~~~$\displaystyle
@@ -238,7 +593,7 @@ $$
 <<*>>=
 )clear all
 
---S 12 of 22
+--S 48
 aa:=integrate(sinh(a*x)*sin(p*x),x)
 --R 
 --R
@@ -255,6 +610,71 @@ aa:=integrate(sinh(a*x)*sin(p*x),x)
 --R     (2p  + 2a )sinh(a x) + (2p  + 2a )cosh(a x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 49
+bb:=(a*cosh(a*x)*sin(p*x)-p*sinh(a*x)*cos(p*x))/(a^2+p^2)
+--R
+--R        - p cos(p x)sinh(a x) + a cosh(a x)sin(p x)
+--R   (2)  -------------------------------------------
+--R                           2    2
+--R                          p  + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 50
+cc:=aa-bb
+--R
+--R   (3)
+--R                                         2                 2
+--R       (a sin(p x) + p cos(p x))sinh(a x)  + (- a cosh(a x)  + a)sin(p x)
+--R     + 
+--R                            2
+--R       - p cos(p x)cosh(a x)  + p cos(p x)
+--R  /
+--R        2     2                2     2
+--R     (2p  + 2a )sinh(a x) + (2p  + 2a )cosh(a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 51
+sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2)
+--R
+--R               2    cosh(2x) - 1
+--R   (4)  sinh(x)  == ------------
+--R                          2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 52
+dd:=sinhsqrrule cc
+--R
+--R   (5)
+--R                                   2
+--R       (a cosh(2a x) - 2a cosh(a x)  + a)sin(p x) + p cos(p x)cosh(2a x)
+--R     + 
+--R                             2
+--R       - 2p cos(p x)cosh(a x)  + p cos(p x)
+--R  /
+--R        2     2                2     2
+--R     (4p  + 4a )sinh(a x) + (4p  + 4a )cosh(a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 53
+coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2)
+--R
+--R               2    cosh(2x) + 1
+--R   (6)  cosh(x)  == ------------
+--R                          2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 54     14:551 Schaums and Axiom agree
+ee:=coshsqrrule dd
+--R
+--R   (7)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.552~~~~~$\displaystyle
@@ -265,7 +685,7 @@ $$
 <<*>>=
 )clear all
 
---S 13 of 22
+--S 55
 aa:=integrate(sinh(a*x)*cos(p*x),x)
 --R 
 --R
@@ -282,6 +702,71 @@ aa:=integrate(sinh(a*x)*cos(p*x),x)
 --R     (2p  + 2a )sinh(a x) + (2p  + 2a )cosh(a x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 56
+bb:=(a*cosh(a*x)*cos(p*x)+p*sinh(a*x)*sin(p*x))/(a^2+p^2)
+--R
+--R        p sin(p x)sinh(a x) + a cos(p x)cosh(a x)
+--R   (2)  -----------------------------------------
+--R                          2    2
+--R                         p  + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 57
+cc:=aa-bb
+--R
+--R   (3)
+--R                                           2               2
+--R       (- p sin(p x) + a cos(p x))sinh(a x)  + (p cosh(a x)  - p)sin(p x)
+--R     + 
+--R                            2
+--R       - a cos(p x)cosh(a x)  + a cos(p x)
+--R  /
+--R        2     2                2     2
+--R     (2p  + 2a )sinh(a x) + (2p  + 2a )cosh(a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 58
+sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2)
+--R
+--R               2    cosh(2x) - 1
+--R   (4)  sinh(x)  == ------------
+--R                          2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 59
+dd:=sinhsqrrule cc
+--R
+--R   (5)
+--R                                     2
+--R       (- p cosh(2a x) + 2p cosh(a x)  - p)sin(p x) + a cos(p x)cosh(2a x)
+--R     + 
+--R                             2
+--R       - 2a cos(p x)cosh(a x)  + a cos(p x)
+--R  /
+--R        2     2                2     2
+--R     (4p  + 4a )sinh(a x) + (4p  + 4a )cosh(a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 60
+coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2)
+--R
+--R               2    cosh(2x) + 1
+--R   (6)  cosh(x)  == ------------
+--R                          2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 61     14:552 Schaums and Axiom agree
+ee:=coshsqrrule dd
+--R
+--R   (7)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.553~~~~~$\displaystyle
@@ -293,7 +778,7 @@ $$
 <<*>>=
 )clear all
 
---S 14 of 22
+--S 62
 aa:=integrate(1/(p+q*sinh(a*x)),x)
 --R 
 --R
@@ -322,6 +807,60 @@ aa:=integrate(1/(p+q*sinh(a*x)),x)
 --R     a\|q  + p
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 63
+bb:=1/(a*sqrt(p^2+q^2))*log((q*%e^(a*x)+p-sqrt(p^2+q^2))/(q*%e^(a*x)+p+sqrt(p^2+q^2)))
+--R
+--R               +-------+
+--R               | 2    2        a x
+--R            - \|q  + p   + q %e    + p
+--R        log(--------------------------)
+--R              +-------+
+--R              | 2    2        a x
+--R             \|q  + p   + q %e    + p
+--R   (2)  -------------------------------
+--R                    +-------+
+--R                    | 2    2
+--R                  a\|q  + p
+--R                                                     Type: Expression Integer
+--E
+
+--S 64     14:553 Axiom cannot simplify this expression
+cc:=aa-bb
+--R
+--R   (3)
+--R       log
+--R                   2         2      2                              2         2
+--R                  q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
+--R                + 
+--R                                    2     2
+--R                  2p q cosh(a x) + q  + 2p
+--R             *
+--R                 +-------+
+--R                 | 2    2
+--R                \|q  + p
+--R            + 
+--R                   3     2                   3     2                  2     3
+--R              (- 2q  - 2p q)sinh(a x) + (- 2q  - 2p q)cosh(a x) - 2p q  - 2p
+--R         /
+--R                         2                                             2
+--R              q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
+--R            + 
+--R              2p cosh(a x) - q
+--R     + 
+--R                +-------+
+--R                | 2    2        a x
+--R             - \|q  + p   + q %e    + p
+--R       - log(--------------------------)
+--R               +-------+
+--R               | 2    2        a x
+--R              \|q  + p   + q %e    + p
+--R  /
+--R       +-------+
+--R       | 2    2
+--R     a\|q  + p
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.554~~~~~$\displaystyle
@@ -333,7 +872,7 @@ $$
 <<*>>=
 )clear all
 
---S 15 of 22
+--S 65
 aa:=integrate(1/(p*q*sinh(a*x))^2,x)
 --R 
 --R
@@ -344,6 +883,137 @@ aa:=integrate(1/(p*q*sinh(a*x))^2,x)
 --R     a p q sinh(a x)  + 2a p q cosh(a x)sinh(a x) + a p q cosh(a x)  - a p q
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 66
+t1:=integrate(1/(p+q*sinh(a*x)),x)
+--R
+--R   (2)
+--R     log
+--R                 2         2      2                              2         2
+--R                q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
+--R              + 
+--R                                  2     2
+--R                2p q cosh(a x) + q  + 2p
+--R           *
+--R               +-------+
+--R               | 2    2
+--R              \|q  + p
+--R          + 
+--R                 3     2                   3     2                  2     3
+--R            (- 2q  - 2p q)sinh(a x) + (- 2q  - 2p q)cosh(a x) - 2p q  - 2p
+--R       /
+--R                       2                                             2
+--R            q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
+--R          + 
+--R            2p cosh(a x) - q
+--R  /
+--R       +-------+
+--R       | 2    2
+--R     a\|q  + p
+--R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 67
+bb:=(-q*cosh(a*x))/(a*(p^2+q^2)*(p+q*sinh(a*x)))+p/(p^2+q^2)*t1
+--R
+--R   (3)
+--R                           2
+--R         (p q sinh(a x) + p )
+--R      *
+--R         log
+--R                     2         2      2                              2         2
+--R                    q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
+--R                  + 
+--R                                      2     2
+--R                    2p q cosh(a x) + q  + 2p
+--R               *
+--R                   +-------+
+--R                   | 2    2
+--R                  \|q  + p
+--R              + 
+--R                     3     2                   3     2                  2     3
+--R                (- 2q  - 2p q)sinh(a x) + (- 2q  - 2p q)cosh(a x) - 2p q  - 2p
+--R           /
+--R                           2                                             2
+--R                q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
+--R              + 
+--R                2p cosh(a x) - q
+--R     + 
+--R                     +-------+
+--R                     | 2    2
+--R       - q cosh(a x)\|q  + p
+--R  /
+--R                                               +-------+
+--R          3      2                   2      3  | 2    2
+--R     ((a q  + a p q)sinh(a x) + a p q  + a p )\|q  + p
+--R                                                     Type: Expression Integer
+--E
+
+--S 68     14:554 Axiom cannot simplify this expression
+cc:=aa-bb
+--R
+--R   (4)
+--R              3 3         3        3 3             4 2          2
+--R           - p q sinh(a x)  + (- 2p q cosh(a x) - p q )sinh(a x)
+--R         + 
+--R               3 3         2     4 2             3 3              4 2         2
+--R           (- p q cosh(a x)  - 2p q cosh(a x) + p q )sinh(a x) - p q cosh(a x)
+--R         + 
+--R            4 2
+--R           p q
+--R      *
+--R         log
+--R                     2         2      2                              2         2
+--R                    q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
+--R                  + 
+--R                                      2     2
+--R                    2p q cosh(a x) + q  + 2p
+--R               *
+--R                   +-------+
+--R                   | 2    2
+--R                  \|q  + p
+--R              + 
+--R                     3     2                   3     2                  2     3
+--R                (- 2q  - 2p q)sinh(a x) + (- 2q  - 2p q)cosh(a x) - 2p q  - 2p
+--R           /
+--R                           2                                             2
+--R                q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
+--R              + 
+--R                2p cosh(a x) - q
+--R     + 
+--R            2 3                  2      2 3         2     3     2
+--R           p q cosh(a x)sinh(a x)  + (2p q cosh(a x)  - 2q  - 2p q)sinh(a x)
+--R         + 
+--R            2 3         3    2 3                2     3
+--R           p q cosh(a x)  - p q cosh(a x) - 2p q  - 2p
+--R      *
+--R          +-------+
+--R          | 2    2
+--R         \|q  + p
+--R  /
+--R             2 5      4 3          3
+--R         (a p q  + a p q )sinh(a x)
+--R       + 
+--R               2 5       4 3                3 4      5 2          2
+--R         ((2a p q  + 2a p q )cosh(a x) + a p q  + a p q )sinh(a x)
+--R       + 
+--R                 2 5      4 3          2        3 4       5 2                2 5
+--R             (a p q  + a p q )cosh(a x)  + (2a p q  + 2a p q )cosh(a x) - a p q
+--R           + 
+--R                  4 3
+--R             - a p q
+--R        *
+--R           sinh(a x)
+--R       + 
+--R             3 4      5 2          2      3 4      5 2
+--R         (a p q  + a p q )cosh(a x)  - a p q  - a p q
+--R    *
+--R        +-------+
+--R        | 2    2
+--R       \|q  + p
+--R                                                     Type: Expression Integer
+--E
+
 @
 
 \section{\cite{1}:14.555~~~~~$\displaystyle
@@ -363,7 +1033,7 @@ $$
 <<*>>=
 )clear all
 
---S 16 of 22
+--S 69
 aa:=integrate(1/(p^2+q^2*sinh(a*x)^2),x)
 --R 
 --R
@@ -426,6 +1096,180 @@ aa:=integrate(1/(p^2+q^2*sinh(a*x)^2),x)
 --R     ]
 --R                                     Type: Union(List Expression Integer,...)
 --E 
+
+--S 70
+bb1:=1/(a*p*sqrt(q^2-p^2))*atan((sqrt(q^2-p^2)*tanh(a*x))/p)
+--R
+--R                       +-------+
+--R                       | 2    2
+--R             tanh(a x)\|q  - p
+--R        atan(-------------------)
+--R                      p
+--R   (2)  -------------------------
+--R                  +-------+
+--R                  | 2    2
+--R              a p\|q  - p
+--R                                                     Type: Expression Integer
+--E
+
+--S 71
+bb2:=1/(2*a*p*sqrt(p^2-q^2))*log((p+sqrt(p^2-q^2)*tanh(a*x))/(p-sqrt(p^2-q^2)*tanh(a*x)))
+--R
+--R                        +---------+
+--R                        |   2    2
+--R            - tanh(a x)\|- q  + p   - p
+--R        log(---------------------------)
+--R                       +---------+
+--R                       |   2    2
+--R             tanh(a x)\|- q  + p   - p
+--R   (3)  --------------------------------
+--R                     +---------+
+--R                     |   2    2
+--R                2a p\|- q  + p
+--R                                                     Type: Expression Integer
+--E
+
+--S 72
+cc1:=aa.1-bb1
+--R
+--R   (4)
+--R          +-------+
+--R          | 2    2
+--R         \|q  - p
+--R      *
+--R         log
+--R                     4         4     4                  3
+--R                    q sinh(a x)  + 4q cosh(a x)sinh(a x)
+--R                  + 
+--R                       4         2     4     2 2          2
+--R                    (6q cosh(a x)  - 2q  + 4p q )sinh(a x)
+--R                  + 
+--R                       4         3        4     2 2
+--R                    (4q cosh(a x)  + (- 4q  + 8p q )cosh(a x))sinh(a x)
+--R                  + 
+--R                     4         4        4     2 2          2    4     2 2     4
+--R                    q cosh(a x)  + (- 2q  + 4p q )cosh(a x)  + q  - 8p q  + 8p
+--R               *
+--R                   +---------+
+--R                   |   2    2
+--R                  \|- q  + p
+--R              + 
+--R                     4     3 2          2        4     3 2
+--R                (4p q  - 4p q )sinh(a x)  + (8p q  - 8p q )cosh(a x)sinh(a x)
+--R              + 
+--R                     4     3 2          2       4      3 2     5
+--R                (4p q  - 4p q )cosh(a x)  - 4p q  + 12p q  - 8p
+--R           /
+--R                 2         4     2                  3
+--R                q sinh(a x)  + 4q cosh(a x)sinh(a x)
+--R              + 
+--R                   2         2     2     2          2
+--R                (6q cosh(a x)  - 2q  + 4p )sinh(a x)
+--R              + 
+--R                   2         3        2     2                        2         4
+--R                (4q cosh(a x)  + (- 4q  + 8p )cosh(a x))sinh(a x) + q cosh(a x)
+--R              + 
+--R                     2     2          2    2
+--R                (- 2q  + 4p )cosh(a x)  + q
+--R     + 
+--R                                     +-------+
+--R           +---------+               | 2    2
+--R           |   2    2      tanh(a x)\|q  - p
+--R       - 2\|- q  + p  atan(-------------------)
+--R                                    p
+--R  /
+--R          +---------+ +-------+
+--R          |   2    2  | 2    2
+--R     2a p\|- q  + p  \|q  - p
+--R                                                     Type: Expression Integer
+--E
+
+--S 73
+cc2:=aa.2-bb1
+--R
+--R   (5)
+--R                        +-------+
+--R                        | 2    2
+--R              tanh(a x)\|q  - p
+--R       - atan(-------------------)
+--R                       p
+--R     + 
+--R       atan
+--R                2         2     2                      2         2    2     2
+--R              (q sinh(a x)  + 2q cosh(a x)sinh(a x) + q cosh(a x)  - q  + 2p )
+--R           *
+--R               +-------+
+--R               | 2    2
+--R              \|q  - p
+--R         /
+--R                2     3
+--R            2p q  - 2p
+--R  /
+--R         +-------+
+--R         | 2    2
+--R     a p\|q  - p
+--R                                                     Type: Expression Integer
+--E
+
+--S 74
+cc3:=aa.2-bb1
+--R
+--R   (6)
+--R                        +-------+
+--R                        | 2    2
+--R              tanh(a x)\|q  - p
+--R       - atan(-------------------)
+--R                       p
+--R     + 
+--R       atan
+--R                2         2     2                      2         2    2     2
+--R              (q sinh(a x)  + 2q cosh(a x)sinh(a x) + q cosh(a x)  - q  + 2p )
+--R           *
+--R               +-------+
+--R               | 2    2
+--R              \|q  - p
+--R         /
+--R                2     3
+--R            2p q  - 2p
+--R  /
+--R         +-------+
+--R         | 2    2
+--R     a p\|q  - p
+--R                                                     Type: Expression Integer
+--E
+
+--S 75     14:555 Axiom cannot simplify this expression
+cc4:=aa.2-bb2
+--R
+--R   (7)
+--R                                   +---------+
+--R          +-------+                |   2    2
+--R          | 2    2     - tanh(a x)\|- q  + p   - p
+--R       - \|q  - p  log(---------------------------)
+--R                                  +---------+
+--R                                  |   2    2
+--R                        tanh(a x)\|- q  + p   - p
+--R     + 
+--R           +---------+
+--R           |   2    2
+--R         2\|- q  + p
+--R      *
+--R         atan
+--R                  2         2     2                      2         2    2     2
+--R                (q sinh(a x)  + 2q cosh(a x)sinh(a x) + q cosh(a x)  - q  + 2p )
+--R             *
+--R                 +-------+
+--R                 | 2    2
+--R                \|q  - p
+--R           /
+--R                  2     3
+--R              2p q  - 2p
+--R  /
+--R          +---------+ +-------+
+--R          |   2    2  | 2    2
+--R     2a p\|- q  + p  \|q  - p
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.556~~~~~$\displaystyle
@@ -437,7 +1281,7 @@ $$
 <<*>>=
 )clear all
 
---S 17 of 22
+--S 76
 aa:=integrate(1/(p^2+q^2*sinh(a*x)^2),x)
 --R 
 --R
@@ -500,6 +1344,113 @@ aa:=integrate(1/(p^2+q^2*sinh(a*x)^2),x)
 --R     ]
 --R                                     Type: Union(List Expression Integer,...)
 --E 
+
+--S 77
+bb:=1/(2*a*p*sqrt(p^2+q^2))*log((p+sqrt(p^2+q^2)*tanh(a*x))/(p-sqrt(p^2+q^2)*tanh(a*x)))
+--R
+--R                        +-------+
+--R                        | 2    2
+--R            - tanh(a x)\|q  + p   - p
+--R        log(-------------------------)
+--R                       +-------+
+--R                       | 2    2
+--R             tanh(a x)\|q  + p   - p
+--R   (2)  ------------------------------
+--R                     +-------+
+--R                     | 2    2
+--R                2a p\|q  + p
+--R                                                     Type: Expression Integer
+--E
+
+--S 78
+cc1:=aa.1-bb
+--R
+--R   (3)
+--R          +-------+
+--R          | 2    2
+--R         \|q  + p
+--R      *
+--R         log
+--R                     4         4     4                  3
+--R                    q sinh(a x)  + 4q cosh(a x)sinh(a x)
+--R                  + 
+--R                       4         2     4     2 2          2
+--R                    (6q cosh(a x)  - 2q  + 4p q )sinh(a x)
+--R                  + 
+--R                       4         3        4     2 2
+--R                    (4q cosh(a x)  + (- 4q  + 8p q )cosh(a x))sinh(a x)
+--R                  + 
+--R                     4         4        4     2 2          2    4     2 2     4
+--R                    q cosh(a x)  + (- 2q  + 4p q )cosh(a x)  + q  - 8p q  + 8p
+--R               *
+--R                   +---------+
+--R                   |   2    2
+--R                  \|- q  + p
+--R              + 
+--R                     4     3 2          2        4     3 2
+--R                (4p q  - 4p q )sinh(a x)  + (8p q  - 8p q )cosh(a x)sinh(a x)
+--R              + 
+--R                     4     3 2          2       4      3 2     5
+--R                (4p q  - 4p q )cosh(a x)  - 4p q  + 12p q  - 8p
+--R           /
+--R                 2         4     2                  3
+--R                q sinh(a x)  + 4q cosh(a x)sinh(a x)
+--R              + 
+--R                   2         2     2     2          2
+--R                (6q cosh(a x)  - 2q  + 4p )sinh(a x)
+--R              + 
+--R                   2         3        2     2                        2         4
+--R                (4q cosh(a x)  + (- 4q  + 8p )cosh(a x))sinh(a x) + q cosh(a x)
+--R              + 
+--R                     2     2          2    2
+--R                (- 2q  + 4p )cosh(a x)  + q
+--R     + 
+--R                                     +-------+
+--R          +---------+                | 2    2
+--R          |   2    2     - tanh(a x)\|q  + p   - p
+--R       - \|- q  + p  log(-------------------------)
+--R                                    +-------+
+--R                                    | 2    2
+--R                          tanh(a x)\|q  + p   - p
+--R  /
+--R          +---------+ +-------+
+--R          |   2    2  | 2    2
+--R     2a p\|- q  + p  \|q  + p
+--R                                                     Type: Expression Integer
+--E
+
+--S 79     14:556 Axiom cannot simplify this expression
+cc2:=aa.2-bb
+--R
+--R   (4)
+--R                                   +-------+
+--R          +-------+                | 2    2
+--R          | 2    2     - tanh(a x)\|q  + p   - p
+--R       - \|q  - p  log(-------------------------)
+--R                                  +-------+
+--R                                  | 2    2
+--R                        tanh(a x)\|q  + p   - p
+--R     + 
+--R           +-------+
+--R           | 2    2
+--R         2\|q  + p
+--R      *
+--R         atan
+--R                  2         2     2                      2         2    2     2
+--R                (q sinh(a x)  + 2q cosh(a x)sinh(a x) + q cosh(a x)  - q  + 2p )
+--R             *
+--R                 +-------+
+--R                 | 2    2
+--R                \|q  - p
+--R           /
+--R                  2     3
+--R              2p q  - 2p
+--R  /
+--R          +-------+ +-------+
+--R          | 2    2  | 2    2
+--R     2a p\|q  - p  \|q  + p
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.557~~~~~$\displaystyle
@@ -510,7 +1461,7 @@ $$
 <<*>>=
 )clear all
 
---S 18 of 22
+--S 80     14:557 Axiom cannot compute this integral
 aa:=integrate(x^m*sinh(a*x),x)
 --R 
 --R
@@ -530,7 +1481,7 @@ $$
 <<*>>=
 )clear all
 
---S 19 of 22
+--S 81     14:558 Axiom cannot compute this integral
 aa:=integrate(sinh(a*x)^n,x)
 --R 
 --R
@@ -550,16 +1501,17 @@ $$
 <<*>>=
 )clear all
 
---S 20 of 22
-aa:=integrate(sinh(a*x)/a^n,x)
+--S 82     14:559 Axiom cannot compute this integral
+aa:=integrate(sinh(a*x)/x^n,x)
 --R
---R                 2                                  2
---R        sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  + 1
---R   (1)  -------------------------------------------------
---R                                               n
---R                 (2a sinh(a x) + 2a cosh(a x))a
+--R           x
+--I         ++  sinh(%T a)
+--I   (3)   |   ---------- d%T
+--R        ++         n
+--I                 %T
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
 @
 
 \section{\cite{1}:14.560~~~~~$\displaystyle
@@ -571,7 +1523,7 @@ $$
 <<*>>=
 )clear all
 
---S 21 of 22
+--S 83     14:560 Axiom cannot compute this integral
 aa:=integrate(1/sinh(a*x)^n,x)
 --R 
 --R
@@ -594,7 +1546,7 @@ $$
 <<*>>=
 )clear all
 
---S 22 of 22
+--S 84     14:561 Axiom cannot compute this integral
 aa:=integrate(x/sinh(a*x)^n,x)
 --R 
 --R
diff --git a/src/input/schaum28.input.pamphlet b/src/input/schaum28.input.pamphlet
index b3fc3c6..5c68b06 100644
--- a/src/input/schaum28.input.pamphlet
+++ b/src/input/schaum28.input.pamphlet
@@ -18,7 +18,7 @@ $$
 )set message auto off
 )clear all
 
---S 1 of 28
+--S 1
 aa:=integrate(cosh(a*x),x)
 --R 
 --R
@@ -27,6 +27,22 @@ aa:=integrate(cosh(a*x),x)
 --R            a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 2
+bb:=sinh(a*x)/a
+--R
+--R        sinh(a x)
+--R   (2)  ---------
+--R            a
+--R                                                     Type: Expression Integer
+--E
+
+--S 3      14:562 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.563~~~~~$\displaystyle
@@ -37,7 +53,7 @@ $$
 <<*>>=
 )clear all
 
---S 2 of 28
+--S 4
 aa:=integrate(x*cosh(a*x),x)
 --R 
 --R
@@ -47,6 +63,23 @@ aa:=integrate(x*cosh(a*x),x)
 --R                    a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 5
+bb:=(x*sinh(a*x))/a-cosh(a*x)/a^2
+--R
+--R        a x sinh(a x) - cosh(a x)
+--R   (2)  -------------------------
+--R                     2
+--R                    a
+--R                                                     Type: Expression Integer
+--E
+
+--S 6      14:563 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.564~~~~~$\displaystyle
@@ -57,7 +90,7 @@ $$
 <<*>>=
 )clear all
 
---S 3 of 28
+--S 7
 aa:=integrate(x^2*cosh(a*x),x)
 --R 
 --R
@@ -68,6 +101,24 @@ aa:=integrate(x^2*cosh(a*x),x)
 --R                         a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 8
+bb:=-(2*x*cosh(a*x))/a^2+(x^2/a+2/a^3)*sinh(a*x)
+--R
+--R          2 2
+--R        (a x  + 2)sinh(a x) - 2a x cosh(a x)
+--R   (2)  ------------------------------------
+--R                          3
+--R                         a
+--R                                                     Type: Expression Integer
+--E
+
+--S 9      14:564 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.565~~~~~$\displaystyle
@@ -80,7 +131,7 @@ $$
 <<*>>=
 )clear all
 
---S 4 of 28
+--S 10     14:565 Axiom cannot compute this integral
 aa:=integrate(cosh(a*x)/x,x)
 --R 
 --R
@@ -100,7 +151,7 @@ $$
 <<*>>=
 )clear all
 
---S 5 of 28
+--S 11     14:566 Axiom cannot compute this integral
 aa:=integrate(cosh(a*x)/x^2,x)
 --R 
 --R
@@ -121,7 +172,7 @@ $$
 <<*>>=
 )clear all
 
---S 6 of 28
+--S 12
 aa:=integrate(1/cosh(a*x),x)
 --R 
 --R
@@ -130,6 +181,33 @@ aa:=integrate(1/cosh(a*x),x)
 --R                      a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 13
+bb:=2/a*atan(%e^(a*x))
+--R
+--R                a x
+--R        2atan(%e   )
+--R   (2)  ------------
+--R              a
+--R                                                     Type: Expression Integer
+--E
+
+--S 14
+cc:=aa-bb
+--R
+--R                                               a x
+--R        2atan(sinh(a x) + cosh(a x)) - 2atan(%e   )
+--R   (3)  -------------------------------------------
+--R                             a
+--R                                                     Type: Expression Integer
+--E
+
+--S 15     14:567 Schaums and Axiom agree
+dd:=complexNormalize cc
+--R
+--R   (4)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.568~~~~~$\displaystyle
@@ -141,7 +219,7 @@ $$
 <<*>>=
 )clear all
 
---S 7 of 28
+--S 16     14:568 Axiom cannot compute this integral
 aa:=integrate(x/cosh(a*x),x)
 --R 
 --R
@@ -161,7 +239,7 @@ $$
 <<*>>=
 )clear all
 
---S 8 of 28
+--S 17
 aa:=integrate(cosh(a*x)^2,x)
 --R 
 --R
@@ -170,6 +248,42 @@ aa:=integrate(cosh(a*x)^2,x)
 --R                   2a
 --R                                          Type: Union(Expression Integer,...)
 --E
+
+--S 18
+bb:=x/2+(sinh(a*x)*cosh(a*x))/2
+--R
+--R        cosh(a x)sinh(a x) + x
+--R   (2)  ----------------------
+--R                   2
+--R                                                     Type: Expression Integer
+--E
+
+--S 19
+cc:=aa-bb
+--R
+--R        (- a + 1)cosh(a x)sinh(a x)
+--R   (3)  ---------------------------
+--R                     2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 20
+sinhcoshrule:=rule(sinh(x)*cosh(y) == 1/2*(sinh(x+y)+sinh(x-y)))
+--R
+--I                             %B sinh(y + x) - %B sinh(y - x)
+--I   (4)  %B cosh(y)sinh(x) == -------------------------------
+--R                                            2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 21     14:569 SCHAUMS AND AXIOM DISAGREE?
+dd:=sinhcoshrule cc
+--R
+--R        (- a + 1)sinh(2a x)
+--R   (5)  -------------------
+--R                 4a
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.570~~~~~$\displaystyle
@@ -180,7 +294,7 @@ $$
 <<*>>=
 )clear all
 
---S 9 of 28
+--S 22
 aa:=integrate(x*cosh(a*x)^2,x)
 --R 
 --R
@@ -191,6 +305,87 @@ aa:=integrate(x*cosh(a*x)^2,x)
 --R                                    8a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 23
+bb:=x^2/4+(x*sinh(2*a*x))/(4*a)-cosh(2*a*x)/(8*a^2)
+--R
+--R                                         2 2
+--R        2a x sinh(2a x) - cosh(2a x) + 2a x
+--R   (2)  ------------------------------------
+--R                           2
+--R                         8a
+--R                                                     Type: Expression Integer
+--E
+
+--S 24
+cc:=aa-bb
+--R
+--R   (3)
+--R                                    2
+--R       - 2a x sinh(2a x) - sinh(a x)  + 4a x cosh(a x)sinh(a x) + cosh(2a x)
+--R     + 
+--R                  2
+--R       - cosh(a x)
+--R  /
+--R       2
+--R     8a
+--R                                                     Type: Expression Integer
+--E
+
+--S 25
+sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2)
+--R
+--R               2    cosh(2x) - 1
+--R   (4)  sinh(x)  == ------------
+--R                          2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 26
+dd:=sinhsqrrule cc
+--R
+--R   (5)
+--R                                                                        2
+--R   - 4a x sinh(2a x) + 8a x cosh(a x)sinh(a x) + cosh(2a x) - 2cosh(a x)  + 1
+--R   --------------------------------------------------------------------------
+--R                                         2
+--R                                      16a
+--R                                                     Type: Expression Integer
+--E
+
+--S 27
+coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2)
+--R
+--R               2    cosh(2x) + 1
+--R   (6)  cosh(x)  == ------------
+--R                          2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 28
+ee:=coshsqrrule dd
+--R
+--R        - x sinh(2a x) + 2x cosh(a x)sinh(a x)
+--R   (7)  --------------------------------------
+--R                          4a
+--R                                                     Type: Expression Integer
+--E
+
+--S 29
+sinhcoshrule:=rule(sinh(x)*cosh(y) == 1/2*(sinh(x+y)+sinh(x-y)))
+--R
+--I                             %S sinh(y + x) - %S sinh(y - x)
+--I   (8)  %S cosh(y)sinh(x) == -------------------------------
+--R                                            2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 30     14:570 Schaums and Axiom agree
+ff:=sinhcoshrule ee
+--R
+--R   (9)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.571~~~~~$\displaystyle
@@ -201,7 +396,7 @@ $$
 <<*>>=
 )clear all
 
---S 10 of 28
+--S 31
 aa:=integrate(1/cosh(a*x)^2,x)
 --R 
 --R
@@ -211,6 +406,176 @@ aa:=integrate(1/cosh(a*x)^2,x)
 --R          a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  + a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 32
+bb:=tanh(a*x)/a
+--R
+--R        tanh(a x)
+--R   (2)  ---------
+--R            a
+--R                                                     Type: Expression Integer
+--E
+
+--S 33
+cc:=aa-bb
+--R
+--R                    2                                  2
+--R        (- sinh(a x)  - 2cosh(a x)sinh(a x) - cosh(a x)  - 1)tanh(a x) - 2
+--R   (3)  ------------------------------------------------------------------
+--R                         2                                      2
+--R              a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 34
+tanhrule:=rule(tanh(x) == sinh(x)/cosh(x))
+--R
+--R                   sinh(x)
+--R   (4)  tanh(x) == -------
+--R                   cosh(x)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 35
+dd:=tanhrule cc
+--R
+--R   (5)
+--R                  3                      2               2
+--R       - sinh(a x)  - 2cosh(a x)sinh(a x)  + (- cosh(a x)  - 1)sinh(a x)
+--R     + 
+--R       - 2cosh(a x)
+--R  /
+--R                         2               2                       3
+--R     a cosh(a x)sinh(a x)  + 2a cosh(a x) sinh(a x) + a cosh(a x)  + a cosh(a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 36
+sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2)
+--R
+--R               2    cosh(2x) - 1
+--R   (6)  sinh(x)  == ------------
+--R                          2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 37
+ee:=sinhsqrrule dd
+--R
+--R   (7)
+--R                   3                2
+--R       - 2sinh(a x)  + (- 2cosh(a x)  - 2)sinh(a x) - 2cosh(a x)cosh(2a x)
+--R     + 
+--R       - 2cosh(a x)
+--R  /
+--R                   2                                                3
+--R       4a cosh(a x) sinh(a x) + a cosh(a x)cosh(2a x) + 2a cosh(a x)
+--R     + 
+--R       a cosh(a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 38
+coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2)
+--R
+--R               2    cosh(2x) + 1
+--R   (8)  cosh(x)  == ------------
+--R                          2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 39
+ff:=coshsqrrule ee
+--R
+--R   (9)
+--R                   3
+--R       - 2sinh(a x)  + (- cosh(2a x) - 3)sinh(a x) - 2cosh(a x)cosh(2a x)
+--R     + 
+--R       - 2cosh(a x)
+--R  /
+--R                                                                           3
+--R       (2a cosh(2a x) + 2a)sinh(a x) + a cosh(a x)cosh(2a x) + 2a cosh(a x)
+--R     + 
+--R       a cosh(a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 40
+sinhcuberule:=rule(sinh(x)^3 == 1/4*sinh(3*x)-3/4*sinh(x))
+--R
+--R                3    sinh(3x) - 3sinh(x)
+--R   (10)  sinh(x)  == -------------------
+--R                              4
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 41
+gg:=sinhcuberule ff
+--R
+--R   (11)
+--R       - sinh(3a x) + (- 2cosh(2a x) - 3)sinh(a x) - 4cosh(a x)cosh(2a x)
+--R     + 
+--R       - 4cosh(a x)
+--R  /
+--R                                                                            3
+--R       (4a cosh(2a x) + 4a)sinh(a x) + 2a cosh(a x)cosh(2a x) + 4a cosh(a x)
+--R     + 
+--R       2a cosh(a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 42
+coshcuberule:=rule(cosh(x)^3 == 1/4*cosh(3*x)-3/4*cosh(x))
+--R
+--R                3    cosh(3x) - 3cosh(x)
+--R   (12)  cosh(x)  == -------------------
+--R                              4
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 43
+hh:=coshcuberule gg
+--R
+--R   (13)
+--R       - sinh(3a x) + (- 2cosh(2a x) - 3)sinh(a x) - 4cosh(a x)cosh(2a x)
+--R     + 
+--R       - 4cosh(a x)
+--R  /
+--R       (4a cosh(2a x) + 4a)sinh(a x) + a cosh(3a x) + 2a cosh(a x)cosh(2a x)
+--R     + 
+--R       - a cosh(a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 44
+coshcoshrule:=rule(cosh(x)*cosh(y)==1/2*(cosh(x+y)+cosh(x-y)))
+--R
+--I                              %U cosh(y + x) + %U cosh(y - x)
+--I   (14)  %U cosh(x)cosh(y) == -------------------------------
+--R                                             2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 45
+ii:=coshcoshrule hh
+--R
+--R   (15)
+--R   - sinh(3a x) + (- 2cosh(2a x) - 3)sinh(a x) - 2cosh(3a x) - 6cosh(a x)
+--R   ----------------------------------------------------------------------
+--R                (4a cosh(2a x) + 4a)sinh(a x) + 2a cosh(3a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 46     14:571 SCHAUMS AND AXIOM DISAGREE?
+jj:=complexNormalize ii
+--R
+--R               a x 2
+--R         - 2(%e   )  - 2
+--R   (16)  ---------------
+--R               a x 2
+--R         2a (%e   )  - a
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.572~~~~~$\displaystyle
@@ -221,7 +586,7 @@ $$
 <<*>>=
 )clear all
 
---S 11 of 28
+--S 47
 aa:=integrate(cosh(a*x)*cosh(p*x),x)
 --R 
 --R
@@ -231,6 +596,106 @@ aa:=integrate(cosh(a*x)*cosh(p*x),x)
 --R         (p  - a )sinh(a x)  + (- p  + a )cosh(a x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 48
+bb:=(sinh(a-p)*x)/(2*(a-p))+(sinh(a+p)*x)/(2*(a+p))
+--R
+--R        (p - a)x sinh(p + a) + (p + a)x sinh(p - a)
+--R   (2)  -------------------------------------------
+--R                           2     2
+--R                         2p  - 2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 49
+cc:=aa-bb
+--R
+--R   (3)
+--R       - 2p cosh(a x)sinh(p x)
+--R     + 
+--R                                                                 2
+--R       ((- p + a)x sinh(p + a) + (- p - a)x sinh(p - a))sinh(a x)
+--R     + 
+--R                                                 2
+--R       2a cosh(p x)sinh(a x) + (p - a)x cosh(a x) sinh(p + a)
+--R     + 
+--R                         2
+--R       (p + a)x cosh(a x) sinh(p - a)
+--R  /
+--R        2     2          2        2     2          2
+--R     (2p  - 2a )sinh(a x)  + (- 2p  + 2a )cosh(a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 50
+sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2)
+--R
+--R               2    cosh(2x) - 1
+--R   (4)  sinh(x)  == ------------
+--R                          2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 51
+dd:=sinhsqrrule cc
+--R
+--R   (5)
+--R       - 4p cosh(a x)sinh(p x) + 4a cosh(p x)sinh(a x)
+--R     + 
+--R                                                    2
+--R       ((- p + a)x cosh(2a x) + (2p - 2a)x cosh(a x)  + (p - a)x)sinh(p + a)
+--R     + 
+--R                                                    2
+--R       ((- p - a)x cosh(2a x) + (2p + 2a)x cosh(a x)  + (p + a)x)sinh(p - a)
+--R  /
+--R        2     2                   2     2          2     2     2
+--R     (2p  - 2a )cosh(2a x) + (- 4p  + 4a )cosh(a x)  - 2p  + 2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 52
+coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2)
+--R
+--R               2    cosh(2x) + 1
+--R   (6)  cosh(x)  == ------------
+--R                          2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 53
+ee:=coshsqrrule dd
+--R
+--R   (7)
+--R       2p cosh(a x)sinh(p x) - 2a cosh(p x)sinh(a x) + (- p + a)x sinh(p + a)
+--R     + 
+--R       (- p - a)x sinh(p - a)
+--R  /
+--R       2     2
+--R     2p  - 2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 54
+sinhcoshrule:=rule(sinh(x)*cosh(y) == 1/2*(sinh(x+y)+sinh(x-y)))
+--R
+--I                             %V sinh(y + x) - %V sinh(y - x)
+--I   (8)  %V cosh(y)sinh(x) == -------------------------------
+--R                                            2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 55     14:572 Schaums and Axiom agree
+ff:=sinhcoshrule ee
+--R
+--R   (9)
+--R       (p - a)sinh((p + a)x) + (p + a)sinh((p - a)x) + (- p + a)x sinh(p + a)
+--R     + 
+--R       (- p - a)x sinh(p - a)
+--R  /
+--R       2     2
+--R     2p  - 2a
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.573~~~~~$\displaystyle
@@ -241,7 +706,7 @@ $$
 <<*>>=
 )clear all
 
---S 12 of 28
+--S 56
 aa:=integrate(cosh(a*x)*sin(p*x),x)
 --R 
 --R
@@ -258,6 +723,70 @@ aa:=integrate(cosh(a*x)*sin(p*x),x)
 --R     (2p  + 2a )sinh(a x) + (2p  + 2a )cosh(a x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 57
+bb:=(a*sinh(a*x)*sin(p*x)-p*cosh(a*x)*cos(p*x))/(a^2+p^2)
+--R
+--R        a sin(p x)sinh(a x) - p cos(p x)cosh(a x)
+--R   (2)  -----------------------------------------
+--R                          2    2
+--R                         p  + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 58
+cc:=aa-bb
+--R
+--R   (3)
+--R                                           2               2
+--R       (- a sin(p x) - p cos(p x))sinh(a x)  + (a cosh(a x)  - a)sin(p x)
+--R     + 
+--R                          2
+--R       p cos(p x)cosh(a x)  - p cos(p x)
+--R  /
+--R        2     2                2     2
+--R     (2p  + 2a )sinh(a x) + (2p  + 2a )cosh(a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 59
+coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2)
+--R
+--R               2    cosh(2x) + 1
+--R   (4)  cosh(x)  == ------------
+--R                          2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 60
+dd:=coshsqrrule cc
+--R
+--R   (5)
+--R                                             2
+--R       (- 2a sin(p x) - 2p cos(p x))sinh(a x)  + (a cosh(2a x) - a)sin(p x)
+--R     + 
+--R       p cos(p x)cosh(2a x) - p cos(p x)
+--R  /
+--R        2     2                2     2
+--R     (4p  + 4a )sinh(a x) + (4p  + 4a )cosh(a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 61
+sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2)
+--R
+--R               2    cosh(2x) - 1
+--R   (6)  sinh(x)  == ------------
+--R                          2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 62     14:573 Schaums and Axiom agree
+ee:=sinhsqrrule dd
+--R
+--R   (7)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.574~~~~~$\displaystyle
@@ -268,7 +797,7 @@ $$
 <<*>>=
 )clear all
 
---S 13 of 28
+--S 63
 aa:=integrate(cosh(a*x)*cos(p*x),x)
 --R 
 --R
@@ -285,6 +814,70 @@ aa:=integrate(cosh(a*x)*cos(p*x),x)
 --R     (2p  + 2a )sinh(a x) + (2p  + 2a )cosh(a x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 64
+bb:=(a*sinh(a*x)*cos(p*x)+p*cosh(a*x)*sin(p*x))/(a^2+p^2)
+--R
+--R        a cos(p x)sinh(a x) + p cosh(a x)sin(p x)
+--R   (2)  -----------------------------------------
+--R                          2    2
+--R                         p  + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 65
+cc:=aa-bb
+--R
+--R   (3)
+--R                                         2                 2
+--R       (p sin(p x) - a cos(p x))sinh(a x)  + (- p cosh(a x)  + p)sin(p x)
+--R     + 
+--R                          2
+--R       a cos(p x)cosh(a x)  - a cos(p x)
+--R  /
+--R        2     2                2     2
+--R     (2p  + 2a )sinh(a x) + (2p  + 2a )cosh(a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 66
+coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2)
+--R
+--R               2    cosh(2x) + 1
+--R   (4)  cosh(x)  == ------------
+--R                          2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 67
+dd:=coshsqrrule cc
+--R
+--R   (5)
+--R                                           2
+--R       (2p sin(p x) - 2a cos(p x))sinh(a x)  + (- p cosh(2a x) + p)sin(p x)
+--R     + 
+--R       a cos(p x)cosh(2a x) - a cos(p x)
+--R  /
+--R        2     2                2     2
+--R     (4p  + 4a )sinh(a x) + (4p  + 4a )cosh(a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 68
+sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2)
+--R
+--R               2    cosh(2x) - 1
+--R   (6)  sinh(x)  == ------------
+--R                          2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 69     14:574 Schaums and Axiom agree
+ee:=sinhsqrrule dd
+--R
+--R   (7)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.575~~~~~$\displaystyle
@@ -295,7 +888,7 @@ $$
 <<*>>=
 )clear all
 
---S 14 of 28
+--S 70
 aa:=integrate(1/(cosh(a*x)+1),x)
 --R 
 --R
@@ -304,6 +897,112 @@ aa:=integrate(1/(cosh(a*x)+1),x)
 --R          a sinh(a x) + a cosh(a x) + a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 71
+bb:=1/a*tanh((a*x)/2)
+--R
+--R             a x
+--R        tanh(---)
+--R              2
+--R   (2)  ---------
+--R            a
+--R                                                     Type: Expression Integer
+--E
+
+--S 72
+cc:=aa-bb
+--R
+--R                                          a x
+--R        (- sinh(a x) - cosh(a x) - 1)tanh(---) - 2
+--R                                           2
+--R   (3)  ------------------------------------------
+--R               a sinh(a x) + a cosh(a x) + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 73
+tanhrule:=rule(tanh(x) == sinh(x)/cosh(x))
+--R
+--R                   sinh(x)
+--R   (4)  tanh(x) == -------
+--R                   cosh(x)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 74
+dd:=tanhrule cc
+--R
+--R               a x                                   a x          a x
+--R        - sinh(---)sinh(a x) + (- cosh(a x) - 1)sinh(---) - 2cosh(---)
+--R                2                                     2            2
+--R   (5)  --------------------------------------------------------------
+--R                  a x                    a x                    a x
+--R           a cosh(---)sinh(a x) + a cosh(---)cosh(a x) + a cosh(---)
+--R                   2                      2                      2
+--R                                                     Type: Expression Integer
+--E
+
+--S 75
+sinhcoshrule:=rule(sinh(x)*cosh(y) == 1/2*(sinh(x+y)+sinh(x-y)))
+--R
+--I                             %B sinh(y + x) - %B sinh(y - x)
+--I   (6)  %B cosh(y)sinh(x) == -------------------------------
+--R                                            2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 76
+ee:=sinhcoshrule dd
+--R
+--R                  3a x          a x                  a x          a x
+--R           - sinh(----) - 2sinh(---)sinh(a x) - sinh(---) - 4cosh(---)
+--R                    2            2                    2            2
+--R   (7)  -----------------------------------------------------------------
+--R               3a x           a x            a x                     a x
+--R        a sinh(----) + a sinh(---) + 2a cosh(---)cosh(a x) + 2a cosh(---)
+--R                 2             2              2                       2
+--R                                                     Type: Expression Integer
+--E
+
+--S 77
+sinhsinhrule:=rule(sinh(x)*sinh(y)==1/2*(cosh(x+y)-cosh(x-y)))
+--R
+--I                             %B cosh(y + x) - %B cosh(y - x)
+--I   (8)  %B sinh(x)sinh(y) == -------------------------------
+--R                                            2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 78
+ff:=sinhsinhrule ee
+--R
+--R                       3a x         a x         3a x          a x
+--R                - sinh(----) - sinh(---) - cosh(----) - 3cosh(---)
+--R                         2           2            2            2
+--R   (9)  -----------------------------------------------------------------
+--R               3a x           a x            a x                     a x
+--R        a sinh(----) + a sinh(---) + 2a cosh(---)cosh(a x) + 2a cosh(---)
+--R                 2             2              2                       2
+--R                                                     Type: Expression Integer
+--E
+
+--S 79
+coshcoshrule:=rule(cosh(x)*cosh(y)==1/2*(cosh(x+y)+cosh(x-y)))
+--R
+--I                               %BC cosh(y + x) + %BC cosh(y - x)
+--I   (10)  %BC cosh(x)cosh(y) == ---------------------------------
+--R                                               2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 80     14:575 Schaums and Axiom differ by a constant
+gg:=coshcoshrule ff
+--R
+--R           1
+--R   (11)  - -
+--R           a
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.576~~~~~$\displaystyle
@@ -314,7 +1013,7 @@ $$
 <<*>>=
 )clear all
 
---S 15 of 28
+--S 81
 aa:=integrate(1/(cosh(a*x)-1),x)
 --R 
 --R
@@ -323,6 +1022,112 @@ aa:=integrate(1/(cosh(a*x)-1),x)
 --R          a sinh(a x) + a cosh(a x) - a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 82
+bb:=-1/a*coth((a*x)/2)
+--R
+--R               a x
+--R          coth(---)
+--R                2
+--R   (2)  - ---------
+--R              a
+--R                                                     Type: Expression Integer
+--E
+
+--S 83
+cc:=aa-bb
+--R
+--R             a x                                 a x
+--R        coth(---)sinh(a x) + (cosh(a x) - 1)coth(---) - 2
+--R              2                                   2
+--R   (3)  -------------------------------------------------
+--R                  a sinh(a x) + a cosh(a x) - a
+--R                                                     Type: Expression Integer
+--E
+
+--S 84
+cothrule:=rule(coth(x) == cosh(x)/sinh(x))
+--R
+--R                   cosh(x)
+--R   (4)  coth(x) == -------
+--R                   sinh(x)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 85
+dd:=cothrule cc
+--R
+--R             a x                   a x         a x                  a x
+--R        cosh(---)sinh(a x) - 2sinh(---) + cosh(---)cosh(a x) - cosh(---)
+--R              2                     2           2                    2
+--R   (5)  ----------------------------------------------------------------
+--R                       a x                                   a x
+--R                a sinh(---)sinh(a x) + (a cosh(a x) - a)sinh(---)
+--R                        2                                     2
+--R                                                     Type: Expression Integer
+--E
+
+--S 86
+sinhcoshrule:=rule(sinh(x)*cosh(y) == 1/2*(sinh(x+y)+sinh(x-y)))
+--R
+--I                              %BD sinh(y + x) - %BD sinh(y - x)
+--I   (6)  %BD cosh(y)sinh(x) == ---------------------------------
+--R                                              2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 87
+ee:=sinhcoshrule dd
+--R
+--R             3a x          a x          a x                   a x
+--R        sinh(----) - 3sinh(---) + 2cosh(---)cosh(a x) - 2cosh(---)
+--R               2            2            2                     2
+--R   (7)  ----------------------------------------------------------
+--R                   3a x            a x                     a x
+--R            a sinh(----) + 2a sinh(---)sinh(a x) - 3a sinh(---)
+--R                     2              2                       2
+--R                                                     Type: Expression Integer
+--E
+
+--S 88
+sinhsinhrule:=rule(sinh(x)*sinh(y)==1/2*(cosh(x+y)-cosh(x-y)))
+--R
+--I                              %BE cosh(y + x) - %BE cosh(y - x)
+--I   (8)  %BE sinh(x)sinh(y) == ---------------------------------
+--R                                              2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 89
+ff:=sinhsinhrule ee
+--R
+--R             3a x          a x          a x                   a x
+--R        sinh(----) - 3sinh(---) + 2cosh(---)cosh(a x) - 2cosh(---)
+--R               2            2            2                     2
+--R   (9)  ----------------------------------------------------------
+--R                3a x            a x           3a x           a x
+--R         a sinh(----) - 3a sinh(---) + a cosh(----) - a cosh(---)
+--R                  2              2              2             2
+--R                                                     Type: Expression Integer
+--E
+
+--S 90
+coshcoshrule:=rule(cosh(x)*cosh(y)==1/2*(cosh(x+y)+cosh(x-y)))
+--R
+--I                               %BF cosh(y + x) + %BF cosh(y - x)
+--I   (10)  %BF cosh(x)cosh(y) == ---------------------------------
+--R                                               2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 91     14:576 Schaums and Axiom differ by a constant
+gg:=coshcoshrule ff
+--R
+--R         1
+--R   (11)  -
+--R         a
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.577~~~~~$\displaystyle
@@ -333,7 +1138,7 @@ $$
 <<*>>=
 )clear all
 
---S 16 of 28
+--S 92
 aa:=integrate(x/(cosh(a*x)+1),x)
 --R 
 --R
@@ -346,6 +1151,181 @@ aa:=integrate(x/(cosh(a*x)+1),x)
 --R     a sinh(a x) + a cosh(a x) + a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 93
+bb:=x/a*tanh((a*x)/2)-2/a^2*log(cosh((a*x)/2))
+--R
+--R                    a x              a x
+--R        - 2log(cosh(---)) + a x tanh(---)
+--R                     2                2
+--R   (2)  ---------------------------------
+--R                         2
+--R                        a
+--R                                                     Type: Expression Integer
+--E
+
+--S 94
+cc:=aa-bb
+--R
+--R   (3)
+--R       (- 2sinh(a x) - 2cosh(a x) - 2)log(sinh(a x) + cosh(a x) + 1)
+--R     + 
+--R                                             a x
+--R       (2sinh(a x) + 2cosh(a x) + 2)log(cosh(---))
+--R                                              2
+--R     + 
+--R                                                   a x
+--R       (- a x sinh(a x) - a x cosh(a x) - a x)tanh(---) + 2a x sinh(a x)
+--R                                                    2
+--R     + 
+--R       2a x cosh(a x)
+--R  /
+--R      2             2             2
+--R     a sinh(a x) + a cosh(a x) + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 95
+tanhrule:=rule(tanh(x) == sinh(x)/cosh(x))
+--R
+--R                   sinh(x)
+--R   (4)  tanh(x) == -------
+--R                   cosh(x)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 96
+dd:=tanhrule cc
+--R
+--R   (5)
+--R                  a x                   a x                   a x
+--R         (- 2cosh(---)sinh(a x) - 2cosh(---)cosh(a x) - 2cosh(---))
+--R                   2                     2                     2
+--R      *
+--R         log(sinh(a x) + cosh(a x) + 1)
+--R     + 
+--R              a x                   a x                   a x           a x
+--R       (2cosh(---)sinh(a x) + 2cosh(---)cosh(a x) + 2cosh(---))log(cosh(---))
+--R               2                     2                     2             2
+--R     + 
+--R                   a x              a x
+--R       (- a x sinh(---) + 2a x cosh(---))sinh(a x)
+--R                    2                2
+--R     + 
+--R                                   a x              a x
+--R       (- a x cosh(a x) - a x)sinh(---) + 2a x cosh(---)cosh(a x)
+--R                                    2                2
+--R  /
+--R      2     a x              2     a x              2     a x
+--R     a cosh(---)sinh(a x) + a cosh(---)cosh(a x) + a cosh(---)
+--R             2                      2                      2
+--R                                                     Type: Expression Integer
+--E
+
+--S 97
+coshcoshrule:=rule(cosh(x)*cosh(y)==1/2*(cosh(x+y)+cosh(x-y)))
+--R
+--I                              %BG cosh(y + x) + %BG cosh(y - x)
+--I   (6)  %BG cosh(x)cosh(y) == ---------------------------------
+--R                                              2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 98
+ee:=coshcoshrule dd
+--R
+--R   (7)
+--R                  a x                   3a x          a x
+--R         (- 4cosh(---)sinh(a x) - 2cosh(----) - 6cosh(---))
+--R                   2                      2            2
+--R      *
+--R         log(sinh(a x) + cosh(a x) + 1)
+--R     + 
+--R              a x                   3a x          a x           a x
+--R       (4cosh(---)sinh(a x) + 2cosh(----) + 6cosh(---))log(cosh(---))
+--R               2                      2            2             2
+--R     + 
+--R                    a x              a x
+--R       (- 2a x sinh(---) + 4a x cosh(---))sinh(a x)
+--R                     2                2
+--R     + 
+--R                                     a x              3a x              a x
+--R       (- 2a x cosh(a x) - 2a x)sinh(---) + 2a x cosh(----) + 2a x cosh(---)
+--R                                      2                 2                2
+--R  /
+--R       2     a x              2     3a x      2     a x
+--R     2a cosh(---)sinh(a x) + a cosh(----) + 3a cosh(---)
+--R              2                       2              2
+--R                                                     Type: Expression Integer
+--E
+
+--S 99
+sinhcoshrule:=rule(sinh(x)*cosh(y) == 1/2*(sinh(x+y)+sinh(x-y)))
+--R
+--I                              %BH sinh(y + x) - %BH sinh(y - x)
+--I   (8)  %BH cosh(y)sinh(x) == ---------------------------------
+--R                                              2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 100
+ff:=sinhcoshrule ee
+--R
+--R   (9)
+--R                  3a x          a x          3a x          a x
+--R         (- 2sinh(----) - 2sinh(---) - 2cosh(----) - 6cosh(---))
+--R                    2            2             2            2
+--R      *
+--R         log(sinh(a x) + cosh(a x) + 1)
+--R     + 
+--R              3a x          a x          3a x          a x           a x
+--R       (2sinh(----) + 2sinh(---) + 2cosh(----) + 6cosh(---))log(cosh(---))
+--R                2            2             2            2             2
+--R     + 
+--R                3a x              a x                      a x
+--R       a x sinh(----) - 2a x sinh(---)sinh(a x) + a x sinh(---)
+--R                  2                2                        2
+--R     + 
+--R                 3a x              a x
+--R       2a x cosh(----) + 2a x cosh(---)
+--R                   2                2
+--R  /
+--R      2     3a x     2     a x     2     3a x      2     a x
+--R     a sinh(----) + a sinh(---) + a cosh(----) + 3a cosh(---)
+--R              2             2              2              2
+--R                                                     Type: Expression Integer
+--E
+
+--S 101
+sinhsinhrule:=rule(sinh(x)*sinh(y)==1/2*(cosh(x+y)-cosh(x-y)))
+--R
+--I                               %BI cosh(y + x) - %BI cosh(y - x)
+--I   (10)  %BI sinh(x)sinh(y) == ---------------------------------
+--R                                               2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 102
+gg:=sinhsinhrule ff
+--R
+--R                                                       a x
+--R         - 2log(sinh(a x) + cosh(a x) + 1) + 2log(cosh(---)) + a x
+--R                                                        2
+--R   (11)  ---------------------------------------------------------
+--R                                      2
+--R                                     a
+--R                                                     Type: Expression Integer
+--E
+
+--S 103    14:577 Schaums and Axiom differ by a constant
+complexNormalize gg
+--R
+--R           2log(2)
+--R   (12)  - -------
+--R               2
+--R              a
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.578~~~~~$\displaystyle
@@ -356,7 +1336,7 @@ $$
 <<*>>=
 )clear all
 
---S 17 of 28
+--S 104
 aa:=integrate(x/(cosh(a*x)-1),x)
 --R 
 --R
@@ -369,6 +1349,181 @@ aa:=integrate(x/(cosh(a*x)-1),x)
 --R     a sinh(a x) + a cosh(a x) - a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 105
+bb:=-x/a*coth((a*x)/2)+2/a^2*log(sinh((a*x)/2))
+--R
+--R                  a x              a x
+--R        2log(sinh(---)) - a x coth(---)
+--R                   2                2
+--R   (2)  -------------------------------
+--R                        2
+--R                       a
+--R                                                     Type: Expression Integer
+--E
+
+--S 106
+cc:=aa-bb
+--R
+--R   (3)
+--R       (2sinh(a x) + 2cosh(a x) - 2)log(sinh(a x) + cosh(a x) - 1)
+--R     + 
+--R                                               a x
+--R       (- 2sinh(a x) - 2cosh(a x) + 2)log(sinh(---))
+--R                                                2
+--R     + 
+--R                 a x                                               a x
+--R       (a x coth(---) - 2a x)sinh(a x) + (a x cosh(a x) - a x)coth(---)
+--R                  2                                                 2
+--R     + 
+--R       - 2a x cosh(a x)
+--R  /
+--R      2             2             2
+--R     a sinh(a x) + a cosh(a x) - a
+--R                                                     Type: Expression Integer
+--E
+
+--S 107
+cothrule:=rule(coth(x) == cosh(x)/sinh(x))
+--R
+--R                   cosh(x)
+--R   (4)  coth(x) == -------
+--R                   sinh(x)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 108
+dd:=cothrule cc
+--R
+--R   (5)
+--R                a x                                  a x
+--R         (2sinh(---)sinh(a x) + (2cosh(a x) - 2)sinh(---))
+--R                 2                                    2
+--R      *
+--R         log(sinh(a x) + cosh(a x) - 1)
+--R     + 
+--R                a x                                    a x           a x
+--R       (- 2sinh(---)sinh(a x) + (- 2cosh(a x) + 2)sinh(---))log(sinh(---))
+--R                 2                                      2             2
+--R     + 
+--R                    a x             a x                                 a x
+--R       (- 2a x sinh(---) + a x cosh(---))sinh(a x) - 2a x cosh(a x)sinh(---)
+--R                     2               2                                   2
+--R     + 
+--R                a x                      a x
+--R       a x cosh(---)cosh(a x) - a x cosh(---)
+--R                 2                        2
+--R  /
+--R      2     a x               2             2      a x
+--R     a sinh(---)sinh(a x) + (a cosh(a x) - a )sinh(---)
+--R             2                                      2
+--R                                                     Type: Expression Integer
+--E
+
+--S 109
+sinhcoshrule:=rule(sinh(x)*cosh(y) == 1/2*(sinh(x+y)+sinh(x-y)))
+--R
+--I                              %BJ sinh(y + x) - %BJ sinh(y - x)
+--I   (6)  %BJ cosh(y)sinh(x) == ---------------------------------
+--R                                              2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 110
+ee:=sinhcoshrule dd
+--R
+--R   (7)
+--R                3a x          a x                   a x
+--R         (2sinh(----) + 4sinh(---)sinh(a x) - 6sinh(---))
+--R                  2            2                     2
+--R      *
+--R         log(sinh(a x) + cosh(a x) - 1)
+--R     + 
+--R                3a x          a x                   a x           a x
+--R       (- 2sinh(----) - 4sinh(---)sinh(a x) + 6sinh(---))log(sinh(---))
+--R                  2            2                     2             2
+--R     + 
+--R                  3a x              a x                       a x
+--R       - a x sinh(----) - 4a x sinh(---)sinh(a x) + 3a x sinh(---)
+--R                    2                2                         2
+--R     + 
+--R                 a x                       a x
+--R       2a x cosh(---)cosh(a x) - 2a x cosh(---)
+--R                  2                         2
+--R  /
+--R      2     3a x      2     a x               2     a x
+--R     a sinh(----) + 2a sinh(---)sinh(a x) - 3a sinh(---)
+--R              2              2                       2
+--R                                                     Type: Expression Integer
+--E
+
+--S 111
+sinhsinhrule:=rule(sinh(x)*sinh(y)==1/2*(cosh(x+y)-cosh(x-y)))
+--R
+--I                              %BK cosh(y + x) - %BK cosh(y - x)
+--I   (8)  %BK sinh(x)sinh(y) == ---------------------------------
+--R                                              2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 112
+ff:=sinhsinhrule ee
+--R
+--R   (9)
+--R                3a x          a x          3a x          a x
+--R         (2sinh(----) - 6sinh(---) + 2cosh(----) - 2cosh(---))
+--R                  2            2             2            2
+--R      *
+--R         log(sinh(a x) + cosh(a x) - 1)
+--R     + 
+--R                3a x          a x          3a x          a x           a x
+--R       (- 2sinh(----) + 6sinh(---) - 2cosh(----) + 2cosh(---))log(sinh(---))
+--R                  2            2             2            2             2
+--R     + 
+--R                  3a x              a x              3a x
+--R       - a x sinh(----) + 3a x sinh(---) - 2a x cosh(----)
+--R                    2                2                 2
+--R     + 
+--R                 a x
+--R       2a x cosh(---)cosh(a x)
+--R                  2
+--R  /
+--R      2     3a x      2     a x     2     3a x     2     a x
+--R     a sinh(----) - 3a sinh(---) + a cosh(----) - a cosh(---)
+--R              2              2              2             2
+--R                                                     Type: Expression Integer
+--E
+
+--S 113
+coshcoshrule:=rule(cosh(x)*cosh(y)==1/2*(cosh(x+y)+cosh(x-y)))
+--R
+--I                               %BL cosh(y + x) + %BL cosh(y - x)
+--I   (10)  %BL cosh(x)cosh(y) == ---------------------------------
+--R                                               2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 114
+gg:=coshcoshrule ff
+--R
+--R                                                     a x
+--R         2log(sinh(a x) + cosh(a x) - 1) - 2log(sinh(---)) - a x
+--R                                                      2
+--R   (11)  -------------------------------------------------------
+--R                                     2
+--R                                    a
+--R                                                     Type: Expression Integer
+--E
+
+--S 115    14:578 Schaums and Axiom differ by a constant
+hh:=complexNormalize gg
+--R
+--R         2log(2)
+--R   (12)  -------
+--R             2
+--R            a
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.579~~~~~$\displaystyle
@@ -379,7 +1534,7 @@ $$
 <<*>>=
 )clear all
 
---S 18 of 28
+--S 116
 aa:=integrate(1/(cosh(a*x)+1)^2,x)
 --R 
 --R
@@ -396,6 +1551,59 @@ aa:=integrate(1/(cosh(a*x)+1)^2,x)
 --R       9a cosh(a x)  + 9a cosh(a x) + 3a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 117
+bb:=1/(2*a)*tanh((a*x)/2)-1/(6*a)*tanh((a*x)/2)^3
+--R
+--R               a x 3         a x
+--R        - tanh(---)  + 3tanh(---)
+--R                2             2
+--R   (2)  -------------------------
+--R                    6a
+--R                                                     Type: Expression Integer
+--E
+
+--S 118    14:579 Axiom cannot compute this integral
+cc:=aa-bb
+--R
+--R   (3)
+--R                    3                            2
+--R           sinh(a x)  + (3cosh(a x) + 3)sinh(a x)
+--R         + 
+--R                      2                                       3             2
+--R           (3cosh(a x)  + 6cosh(a x) + 3)sinh(a x) + cosh(a x)  + 3cosh(a x)
+--R         + 
+--R           3cosh(a x) + 1
+--R      *
+--R              a x 3
+--R         tanh(---)
+--R               2
+--R     + 
+--R                       3                              2
+--R           - 3sinh(a x)  + (- 9cosh(a x) - 9)sinh(a x)
+--R         + 
+--R                        2                                         3
+--R           (- 9cosh(a x)  - 18cosh(a x) - 9)sinh(a x) - 3cosh(a x)
+--R         + 
+--R                       2
+--R           - 9cosh(a x)  - 9cosh(a x) - 3
+--R      *
+--R              a x
+--R         tanh(---)
+--R               2
+--R     + 
+--R       - 12sinh(a x) - 12cosh(a x) - 4
+--R  /
+--R                   3                                 2
+--R       6a sinh(a x)  + (18a cosh(a x) + 18a)sinh(a x)
+--R     + 
+--R                     2                                               3
+--R       (18a cosh(a x)  + 36a cosh(a x) + 18a)sinh(a x) + 6a cosh(a x)
+--R     + 
+--R                    2
+--R       18a cosh(a x)  + 18a cosh(a x) + 6a
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.580~~~~~$\displaystyle
@@ -406,7 +1614,7 @@ $$
 <<*>>=
 )clear all
 
---S 19 of 28
+--S 119
 aa:=integrate(1/(cosh(a*x)-1)^2,x)
 --R 
 --R
@@ -423,6 +1631,58 @@ aa:=integrate(1/(cosh(a*x)-1)^2,x)
 --R       - 9a cosh(a x)  + 9a cosh(a x) - 3a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 120
+bb:=1/(2*a)*coth((a*x)/2)-1/(6*a)*coth((a*x)/2)^3
+--R
+--R               a x 3         a x
+--R        - coth(---)  + 3coth(---)
+--R                2             2
+--R   (2)  -------------------------
+--R                    6a
+--R                                                     Type: Expression Integer
+--E
+
+--S 121    14:580 Axiom cannot compute this integral
+cc:=aa-bb
+--R
+--R   (3)
+--R             a x 3         a x           3
+--R       (coth(---)  - 3coth(---))sinh(a x)
+--R              2             2
+--R     + 
+--R                             a x 3                          a x           2
+--R       ((3cosh(a x) - 3)coth(---)  + (- 9cosh(a x) + 9)coth(---))sinh(a x)
+--R                              2                              2
+--R     + 
+--R                      2                       a x 3
+--R           (3cosh(a x)  - 6cosh(a x) + 3)coth(---)
+--R                                               2
+--R         + 
+--R                        2                        a x
+--R           (- 9cosh(a x)  + 18cosh(a x) - 9)coth(---) - 12
+--R                                                  2
+--R      *
+--R         sinh(a x)
+--R     + 
+--R                 3             2                       a x 3
+--R       (cosh(a x)  - 3cosh(a x)  + 3cosh(a x) - 1)coth(---)
+--R                                                        2
+--R     + 
+--R                  3             2                       a x
+--R     (- 3cosh(a x)  + 9cosh(a x)  - 9cosh(a x) + 3)coth(---) - 12cosh(a x) + 4
+--R                                                         2
+--R  /
+--R                   3                                 2
+--R       6a sinh(a x)  + (18a cosh(a x) - 18a)sinh(a x)
+--R     + 
+--R                     2                                               3
+--R       (18a cosh(a x)  - 36a cosh(a x) + 18a)sinh(a x) + 6a cosh(a x)
+--R     + 
+--R                      2
+--R       - 18a cosh(a x)  + 18a cosh(a x) - 6a
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.581~~~~~$\displaystyle
@@ -442,7 +1702,7 @@ $$
 <<*>>=
 )clear all
 
---S 20 of 28
+--S 122
 aa:=integrate(1/(p+q*cosh(a*x)),x)
 --R 
 --R
@@ -483,6 +1743,159 @@ aa:=integrate(1/(p+q*cosh(a*x)),x)
 --R                       a\|q  - p
 --R                                     Type: Union(List Expression Integer,...)
 --E 
+
+--S 123
+bb1:=2/(a*sqrt(q^2-p^2))*atan((q*%e^(a*x)+p)/sqrt(q^2-p^2))
+--R
+--R                  a x
+--R              q %e    + p
+--R        2atan(-----------)
+--R                +-------+
+--R                | 2    2
+--R               \|q  - p
+--R   (2)  ------------------
+--R              +-------+
+--R              | 2    2
+--R            a\|q  - p
+--R                                                     Type: Expression Integer
+--E
+
+--S 124
+bb2:=1/(a*sqrt(p^2-q^2))*log((q*%e^(a*x)+p-sqrt(p^2-q^2))/(q*%e^(a*x)+p+sqrt(p^2-q^2)))
+--R
+--R               +---------+
+--R               |   2    2        a x
+--R            - \|- q  + p   + q %e    + p
+--R        log(----------------------------)
+--R              +---------+
+--R              |   2    2        a x
+--R             \|- q  + p   + q %e    + p
+--R   (3)  ---------------------------------
+--R                    +---------+
+--R                    |   2    2
+--R                  a\|- q  + p
+--R                                                     Type: Expression Integer
+--E
+
+--S 125
+cc1:=aa.1-bb1
+--R
+--R   (4)
+--R          +-------+
+--R          | 2    2
+--R         \|q  - p
+--R      *
+--R         log
+--R                     2         2      2                              2         2
+--R                    q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
+--R                  + 
+--R                                      2     2
+--R                    2p q cosh(a x) - q  + 2p
+--R               *
+--R                   +---------+
+--R                   |   2    2
+--R                  \|- q  + p
+--R              + 
+--R                   3     2                 3     2                  2     3
+--R                (2q  - 2p q)sinh(a x) + (2q  - 2p q)cosh(a x) + 2p q  - 2p
+--R           /
+--R                           2                                             2
+--R                q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
+--R              + 
+--R                2p cosh(a x) + q
+--R     + 
+--R           +---------+         a x
+--R           |   2    2      q %e    + p
+--R       - 2\|- q  + p  atan(-----------)
+--R                             +-------+
+--R                             | 2    2
+--R                            \|q  - p
+--R  /
+--R       +---------+ +-------+
+--R       |   2    2  | 2    2
+--R     a\|- q  + p  \|q  - p
+--R                                                     Type: Expression Integer
+--E
+
+--S 126
+cc2:=aa.2-bb1
+--R
+--R                                              +-------+
+--R                                              | 2    2               a x
+--R              (q sinh(a x) + q cosh(a x) + p)\|q  - p            q %e    + p
+--R        2atan(-----------------------------------------) - 2atan(-----------)
+--R                                2    2                             +-------+
+--R                               q  - p                              | 2    2
+--R                                                                  \|q  - p
+--R   (5)  ---------------------------------------------------------------------
+--R                                       +-------+
+--R                                       | 2    2
+--R                                     a\|q  - p
+--R                                                     Type: Expression Integer
+--E
+
+--S 127
+cc3:=aa.1-bb2
+--R
+--R   (6)
+--R       log
+--R                   2         2      2                              2         2
+--R                  q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
+--R                + 
+--R                                    2     2
+--R                  2p q cosh(a x) - q  + 2p
+--R             *
+--R                 +---------+
+--R                 |   2    2
+--R                \|- q  + p
+--R            + 
+--R                 3     2                 3     2                  2     3
+--R              (2q  - 2p q)sinh(a x) + (2q  - 2p q)cosh(a x) + 2p q  - 2p
+--R         /
+--R                         2                                             2
+--R              q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
+--R            + 
+--R              2p cosh(a x) + q
+--R     + 
+--R                +---------+
+--R                |   2    2        a x
+--R             - \|- q  + p   + q %e    + p
+--R       - log(----------------------------)
+--R               +---------+
+--R               |   2    2        a x
+--R              \|- q  + p   + q %e    + p
+--R  /
+--R       +---------+
+--R       |   2    2
+--R     a\|- q  + p
+--R                                                     Type: Expression Integer
+--E
+
+--S 128    14:581 Axiom cannot simplify this expression
+cc4:=aa.2-bb2
+--R
+--R   (7)
+--R                          +---------+
+--R          +-------+       |   2    2        a x
+--R          | 2    2     - \|- q  + p   + q %e    + p
+--R       - \|q  - p  log(----------------------------)
+--R                         +---------+
+--R                         |   2    2        a x
+--R                        \|- q  + p   + q %e    + p
+--R     + 
+--R                                                         +-------+
+--R         +---------+                                     | 2    2
+--R         |   2    2      (q sinh(a x) + q cosh(a x) + p)\|q  - p
+--R       2\|- q  + p  atan(-----------------------------------------)
+--R                                           2    2
+--R                                          q  - p
+--R  /
+--R       +---------+ +-------+
+--R       |   2    2  | 2    2
+--R     a\|- q  + p  \|q  - p
+--R                                                     Type: Expression Integer
+--E
+
 @
 
 \section{\cite{1}:14.582~~~~~$\displaystyle
@@ -494,7 +1907,7 @@ $$
 <<*>>=
 )clear all
 
---S 21 of 28
+--S 129
 aa:=integrate(1/(p+q*cosh(a*x))^2,x)
 --R 
 --R
@@ -575,6 +1988,408 @@ aa:=integrate(1/(p+q*cosh(a*x))^2,x)
 --R     ]
 --R                                     Type: Union(List Expression Integer,...)
 --E 
+
+--S 130
+t1:=integrate(1/(p+q*cosh(a*x)),x)
+--R
+--R   (2)
+--R   [
+--R       log
+--R                   2         2      2                              2         2
+--R                  q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
+--R                + 
+--R                                    2     2
+--R                  2p q cosh(a x) - q  + 2p
+--R             *
+--R                 +---------+
+--R                 |   2    2
+--R                \|- q  + p
+--R            + 
+--R                 3     2                 3     2                  2     3
+--R              (2q  - 2p q)sinh(a x) + (2q  - 2p q)cosh(a x) + 2p q  - 2p
+--R         /
+--R                         2                                             2
+--R              q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
+--R            + 
+--R              2p cosh(a x) + q
+--R    /
+--R         +---------+
+--R         |   2    2
+--R       a\|- q  + p
+--R     ,
+--R                                          +-------+
+--R                                          | 2    2
+--R          (q sinh(a x) + q cosh(a x) + p)\|q  - p
+--R    2atan(-----------------------------------------)
+--R                            2    2
+--R                           q  - p
+--R    ------------------------------------------------]
+--R                         +-------+
+--R                         | 2    2
+--R                       a\|q  - p
+--R                                     Type: Union(List Expression Integer,...)
+--E
+
+--S 131
+bb1:=(q*sinh(a*x))/(a*(q^2-p^2)*(p+q*cosh(a*x)))-p/(q^2-p^2)*t1.1
+--R
+--R   (3)
+--R                             2
+--R         (- p q cosh(a x) - p )
+--R      *
+--R         log
+--R                     2         2      2                              2         2
+--R                    q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
+--R                  + 
+--R                                      2     2
+--R                    2p q cosh(a x) - q  + 2p
+--R               *
+--R                   +---------+
+--R                   |   2    2
+--R                  \|- q  + p
+--R              + 
+--R                   3     2                 3     2                  2     3
+--R                (2q  - 2p q)sinh(a x) + (2q  - 2p q)cosh(a x) + 2p q  - 2p
+--R           /
+--R                           2                                             2
+--R                q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
+--R              + 
+--R                2p cosh(a x) + q
+--R     + 
+--R                   +---------+
+--R                   |   2    2
+--R       q sinh(a x)\|- q  + p
+--R  /
+--R                                               +---------+
+--R          3      2                   2      3  |   2    2
+--R     ((a q  - a p q)cosh(a x) + a p q  - a p )\|- q  + p
+--R                                                     Type: Expression Integer
+--E
+
+--S 132
+bb2:=(q*sinh(a*x))/(a*(q^2-p^2)*(p+q*cosh(a*x)))-p/(q^2-p^2)*t1.2
+--R
+--R   (4)
+--R                                                                    +-------+
+--R                                                                    | 2    2
+--R                             2      (q sinh(a x) + q cosh(a x) + p)\|q  - p
+--R       (- 2p q cosh(a x) - 2p )atan(-----------------------------------------)
+--R                                                      2    2
+--R                                                     q  - p
+--R     + 
+--R                   +-------+
+--R                   | 2    2
+--R       q sinh(a x)\|q  - p
+--R  /
+--R                                               +-------+
+--R          3      2                   2      3  | 2    2
+--R     ((a q  - a p q)cosh(a x) + a p q  - a p )\|q  - p
+--R                                                     Type: Expression Integer
+--E
+
+--S 133
+cc1:=aa.1-bb1
+--R
+--R   (5)
+--R               2             2           2
+--R           (p q cosh(a x) + p q)sinh(a x)
+--R         + 
+--R                2         2     2                3                2         3
+--R           (2p q cosh(a x)  + 4p q cosh(a x) + 2p )sinh(a x) + p q cosh(a x)
+--R         + 
+--R             2           2       2     3              2
+--R           3p q cosh(a x)  + (p q  + 2p )cosh(a x) + p q
+--R      *
+--R         log
+--R                     2         2      2                              2         2
+--R                    q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
+--R                  + 
+--R                                      2     2
+--R                    2p q cosh(a x) - q  + 2p
+--R               *
+--R                   +---------+
+--R                   |   2    2
+--R                  \|- q  + p
+--R              + 
+--R                   3     2                 3     2                  2     3
+--R                (2q  - 2p q)sinh(a x) + (2q  - 2p q)cosh(a x) + 2p q  - 2p
+--R           /
+--R                           2                                             2
+--R                q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
+--R              + 
+--R                2p cosh(a x) + q
+--R     + 
+--R               2             2           2
+--R           (p q cosh(a x) + p q)sinh(a x)
+--R         + 
+--R                2         2     2                3                2         3
+--R           (2p q cosh(a x)  + 4p q cosh(a x) + 2p )sinh(a x) + p q cosh(a x)
+--R         + 
+--R             2           2       2     3              2
+--R           3p q cosh(a x)  + (p q  + 2p )cosh(a x) + p q
+--R      *
+--R         log
+--R                     2         2      2                              2         2
+--R                    q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
+--R                  + 
+--R                                      2     2
+--R                    2p q cosh(a x) - q  + 2p
+--R               *
+--R                   +---------+
+--R                   |   2    2
+--R                  \|- q  + p
+--R              + 
+--R                     3     2                   3     2                  2     3
+--R                (- 2q  + 2p q)sinh(a x) + (- 2q  + 2p q)cosh(a x) - 2p q  + 2p
+--R           /
+--R                           2                                             2
+--R                q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
+--R              + 
+--R                2p cosh(a x) + q
+--R     + 
+--R              2         3        2                          2
+--R           - q sinh(a x)  + (- 2q cosh(a x) - 2p q)sinh(a x)
+--R         + 
+--R               2         2                     2     2
+--R           (- q cosh(a x)  - 4p q cosh(a x) - q  - 2p )sinh(a x)
+--R         + 
+--R                           2        2     2
+--R           - 2p q cosh(a x)  + (- 2q  - 2p )cosh(a x) - 2p q
+--R      *
+--R          +---------+
+--R          |   2    2
+--R         \|- q  + p
+--R  /
+--R              4      2 2                  3      3           2
+--R         ((a q  - a p q )cosh(a x) + a p q  - a p q)sinh(a x)
+--R       + 
+--R                  4       2 2          2          3       3                  2 2
+--R             (2a q  - 2a p q )cosh(a x)  + (4a p q  - 4a p q)cosh(a x) + 2a p q
+--R           + 
+--R                   4
+--R             - 2a p
+--R        *
+--R           sinh(a x)
+--R       + 
+--R             4      2 2          3          3       3           2
+--R         (a q  - a p q )cosh(a x)  + (3a p q  - 3a p q)cosh(a x)
+--R       + 
+--R             4      2 2       4                  3      3
+--R         (a q  + a p q  - 2a p )cosh(a x) + a p q  - a p q
+--R    *
+--R        +---------+
+--R        |   2    2
+--R       \|- q  + p
+--R                                                     Type: Expression Integer
+--E
+
+--S 134
+cc2:=aa.2-bb1
+--R
+--R   (6)
+--R               2             2           2
+--R           (p q cosh(a x) + p q)sinh(a x)
+--R         + 
+--R                2         2     2                3                2         3
+--R           (2p q cosh(a x)  + 4p q cosh(a x) + 2p )sinh(a x) + p q cosh(a x)
+--R         + 
+--R             2           2       2     3              2
+--R           3p q cosh(a x)  + (p q  + 2p )cosh(a x) + p q
+--R      *
+--R          +-------+
+--R          | 2    2
+--R         \|q  - p
+--R      *
+--R         log
+--R                     2         2      2                              2         2
+--R                    q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
+--R                  + 
+--R                                      2     2
+--R                    2p q cosh(a x) - q  + 2p
+--R               *
+--R                   +---------+
+--R                   |   2    2
+--R                  \|- q  + p
+--R              + 
+--R                   3     2                 3     2                  2     3
+--R                (2q  - 2p q)sinh(a x) + (2q  - 2p q)cosh(a x) + 2p q  - 2p
+--R           /
+--R                           2                                             2
+--R                q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
+--R              + 
+--R                2p cosh(a x) + q
+--R     + 
+--R                  2              2           2
+--R           (- 2p q cosh(a x) - 2p q)sinh(a x)
+--R         + 
+--R                  2         2     2                3                 2         3
+--R           (- 4p q cosh(a x)  - 8p q cosh(a x) - 4p )sinh(a x) - 2p q cosh(a x)
+--R         + 
+--R               2           2          2     3               2
+--R           - 6p q cosh(a x)  + (- 2p q  - 4p )cosh(a x) - 2p q
+--R      *
+--R                                                          +-------+
+--R          +---------+                                     | 2    2
+--R          |   2    2      (q sinh(a x) + q cosh(a x) + p)\|q  - p
+--R         \|- q  + p  atan(-----------------------------------------)
+--R                                            2    2
+--R                                           q  - p
+--R     + 
+--R              2         3        2                          2
+--R           - q sinh(a x)  + (- 2q cosh(a x) - 2p q)sinh(a x)
+--R         + 
+--R               2         2                     2     2
+--R           (- q cosh(a x)  - 4p q cosh(a x) - q  - 2p )sinh(a x)
+--R         + 
+--R                           2        2     2
+--R           - 2p q cosh(a x)  + (- 2q  - 2p )cosh(a x) - 2p q
+--R      *
+--R          +---------+ +-------+
+--R          |   2    2  | 2    2
+--R         \|- q  + p  \|q  - p
+--R  /
+--R              4      2 2                  3      3           2
+--R         ((a q  - a p q )cosh(a x) + a p q  - a p q)sinh(a x)
+--R       + 
+--R                  4       2 2          2          3       3                  2 2
+--R             (2a q  - 2a p q )cosh(a x)  + (4a p q  - 4a p q)cosh(a x) + 2a p q
+--R           + 
+--R                   4
+--R             - 2a p
+--R        *
+--R           sinh(a x)
+--R       + 
+--R             4      2 2          3          3       3           2
+--R         (a q  - a p q )cosh(a x)  + (3a p q  - 3a p q)cosh(a x)
+--R       + 
+--R             4      2 2       4                  3      3
+--R         (a q  + a p q  - 2a p )cosh(a x) + a p q  - a p q
+--R    *
+--R        +---------+ +-------+
+--R        |   2    2  | 2    2
+--R       \|- q  + p  \|q  - p
+--R                                                     Type: Expression Integer
+--E
+
+--S 135
+cc3:=aa.1-bb2
+--R
+--R   (7)
+--R               2             2           2
+--R           (p q cosh(a x) + p q)sinh(a x)
+--R         + 
+--R                2         2     2                3                2         3
+--R           (2p q cosh(a x)  + 4p q cosh(a x) + 2p )sinh(a x) + p q cosh(a x)
+--R         + 
+--R             2           2       2     3              2
+--R           3p q cosh(a x)  + (p q  + 2p )cosh(a x) + p q
+--R      *
+--R          +-------+
+--R          | 2    2
+--R         \|q  - p
+--R      *
+--R         log
+--R                     2         2      2                              2         2
+--R                    q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
+--R                  + 
+--R                                      2     2
+--R                    2p q cosh(a x) - q  + 2p
+--R               *
+--R                   +---------+
+--R                   |   2    2
+--R                  \|- q  + p
+--R              + 
+--R                     3     2                   3     2                  2     3
+--R                (- 2q  + 2p q)sinh(a x) + (- 2q  + 2p q)cosh(a x) - 2p q  + 2p
+--R           /
+--R                           2                                             2
+--R                q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
+--R              + 
+--R                2p cosh(a x) + q
+--R     + 
+--R                2              2           2
+--R           (2p q cosh(a x) + 2p q)sinh(a x)
+--R         + 
+--R                2         2     2                3                 2         3
+--R           (4p q cosh(a x)  + 8p q cosh(a x) + 4p )sinh(a x) + 2p q cosh(a x)
+--R         + 
+--R             2           2        2     3               2
+--R           6p q cosh(a x)  + (2p q  + 4p )cosh(a x) + 2p q
+--R      *
+--R                                                          +-------+
+--R          +---------+                                     | 2    2
+--R          |   2    2      (q sinh(a x) + q cosh(a x) + p)\|q  - p
+--R         \|- q  + p  atan(-----------------------------------------)
+--R                                            2    2
+--R                                           q  - p
+--R     + 
+--R              2         3        2                          2
+--R           - q sinh(a x)  + (- 2q cosh(a x) - 2p q)sinh(a x)
+--R         + 
+--R               2         2                     2     2
+--R           (- q cosh(a x)  - 4p q cosh(a x) - q  - 2p )sinh(a x)
+--R         + 
+--R                           2        2     2
+--R           - 2p q cosh(a x)  + (- 2q  - 2p )cosh(a x) - 2p q
+--R      *
+--R          +---------+ +-------+
+--R          |   2    2  | 2    2
+--R         \|- q  + p  \|q  - p
+--R  /
+--R              4      2 2                  3      3           2
+--R         ((a q  - a p q )cosh(a x) + a p q  - a p q)sinh(a x)
+--R       + 
+--R                  4       2 2          2          3       3                  2 2
+--R             (2a q  - 2a p q )cosh(a x)  + (4a p q  - 4a p q)cosh(a x) + 2a p q
+--R           + 
+--R                   4
+--R             - 2a p
+--R        *
+--R           sinh(a x)
+--R       + 
+--R             4      2 2          3          3       3           2
+--R         (a q  - a p q )cosh(a x)  + (3a p q  - 3a p q)cosh(a x)
+--R       + 
+--R             4      2 2       4                  3      3
+--R         (a q  + a p q  - 2a p )cosh(a x) + a p q  - a p q
+--R    *
+--R        +---------+ +-------+
+--R        |   2    2  | 2    2
+--R       \|- q  + p  \|q  - p
+--R                                                     Type: Expression Integer
+--E
+
+--S 136    14:582 Axiom cannot simplify this expression
+cc4:=aa.2-bb2
+--R
+--R   (8)
+--R          2         3        2                          2
+--R       - q sinh(a x)  + (- 2q cosh(a x) - 2p q)sinh(a x)
+--R     + 
+--R           2         2                     2     2                           2
+--R       (- q cosh(a x)  - 4p q cosh(a x) - q  - 2p )sinh(a x) - 2p q cosh(a x)
+--R     + 
+--R            2     2
+--R       (- 2q  - 2p )cosh(a x) - 2p q
+--R  /
+--R            4      2 2                  3      3           2
+--R       ((a q  - a p q )cosh(a x) + a p q  - a p q)sinh(a x)
+--R     + 
+--R                4       2 2          2          3       3                  2 2
+--R           (2a q  - 2a p q )cosh(a x)  + (4a p q  - 4a p q)cosh(a x) + 2a p q
+--R         + 
+--R                 4
+--R           - 2a p
+--R      *
+--R         sinh(a x)
+--R     + 
+--R           4      2 2          3          3       3           2
+--R       (a q  - a p q )cosh(a x)  + (3a p q  - 3a p q)cosh(a x)
+--R     + 
+--R           4      2 2       4                  3      3
+--R       (a q  + a p q  - 2a p )cosh(a x) + a p q  - a p q
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.583~~~~~$\displaystyle
@@ -594,7 +2409,7 @@ $$
 <<*>>=
 )clear all
 
---S 22 of 28
+--S 137
 aa:=integrate(1/(p^2-q^2*cosh(a*x)^2),x)
 --R 
 --R
@@ -661,6 +2476,219 @@ aa:=integrate(1/(p^2-q^2*cosh(a*x)^2),x)
 --R     ]
 --R                                     Type: Union(List Expression Integer,...)
 --E 
+
+--S 138
+bb1:=1/(2*a*p*sqrt(p^2-q^2))*log((p*tanh(a*x)+sqrt(p^2-q^2))/(p*tanh(a*x)-sqrt(p^2-q^2)))
+--R
+--R               +---------+
+--R               |   2    2
+--R            - \|- q  + p   - p tanh(a x)
+--R        log(----------------------------)
+--R              +---------+
+--R              |   2    2
+--R             \|- q  + p   - p tanh(a x)
+--R   (2)  ---------------------------------
+--R                      +---------+
+--R                      |   2    2
+--R                 2a p\|- q  + p
+--R                                                     Type: Expression Integer
+--E
+
+--S 139
+bb2:=-1/(a*p*sqrt(q^2-p^2))*atan((p*tanh(a*x))/sqrt(q^2-p^2))
+--R
+--R               p tanh(a x)
+--R          atan(-----------)
+--R                 +-------+
+--R                 | 2    2
+--R                \|q  - p
+--R   (3)  - -----------------
+--R                +-------+
+--R                | 2    2
+--R            a p\|q  - p
+--R                                                     Type: Expression Integer
+--E
+
+--S 140
+cc1:=aa.1-bb1
+--R
+--R   (4)
+--R       log
+--R                   4         4     4                  3
+--R                  q sinh(a x)  + 4q cosh(a x)sinh(a x)
+--R                + 
+--R                     4         2     4     2 2          2
+--R                  (6q cosh(a x)  + 2q  - 4p q )sinh(a x)
+--R                + 
+--R                     4         3      4     2 2
+--R                  (4q cosh(a x)  + (4q  - 8p q )cosh(a x))sinh(a x)
+--R                + 
+--R                   4         4      4     2 2          2    4     2 2     4
+--R                  q cosh(a x)  + (2q  - 4p q )cosh(a x)  + q  - 8p q  + 8p
+--R             *
+--R                 +---------+
+--R                 |   2    2
+--R                \|- q  + p
+--R            + 
+--R                     4     3 2          2          4     3 2
+--R              (- 4p q  + 4p q )sinh(a x)  + (- 8p q  + 8p q )cosh(a x)sinh(a x)
+--R            + 
+--R                     4     3 2          2       4      3 2     5
+--R              (- 4p q  + 4p q )cosh(a x)  - 4p q  + 12p q  - 8p
+--R         /
+--R               2         4     2                  3
+--R              q sinh(a x)  + 4q cosh(a x)sinh(a x)
+--R            + 
+--R                 2         2     2     2          2
+--R              (6q cosh(a x)  + 2q  - 4p )sinh(a x)
+--R            + 
+--R                 2         3      2     2                        2         4
+--R              (4q cosh(a x)  + (4q  - 8p )cosh(a x))sinh(a x) + q cosh(a x)
+--R            + 
+--R                 2     2          2    2
+--R              (2q  - 4p )cosh(a x)  + q
+--R     + 
+--R                +---------+
+--R                |   2    2
+--R             - \|- q  + p   - p tanh(a x)
+--R       - log(----------------------------)
+--R               +---------+
+--R               |   2    2
+--R              \|- q  + p   - p tanh(a x)
+--R  /
+--R          +---------+
+--R          |   2    2
+--R     2a p\|- q  + p
+--R                                                     Type: Expression Integer
+--E
+
+--S 141
+cc2:=aa.2-bb1
+--R
+--R   (5)
+--R                          +---------+
+--R          +-------+       |   2    2
+--R          | 2    2     - \|- q  + p   - p tanh(a x)
+--R       - \|q  - p  log(----------------------------)
+--R                         +---------+
+--R                         |   2    2
+--R                        \|- q  + p   - p tanh(a x)
+--R     + 
+--R       -
+--R              +---------+
+--R              |   2    2
+--R            2\|- q  + p
+--R         *
+--R            atan
+--R                      2         2     2                      2         2    2
+--R                     q sinh(a x)  + 2q cosh(a x)sinh(a x) + q cosh(a x)  + q
+--R                   + 
+--R                         2
+--R                     - 2p
+--R                *
+--R                    +-------+
+--R                    | 2    2
+--R                   \|q  - p
+--R              /
+--R                     2     3
+--R                 2p q  - 2p
+--R  /
+--R          +---------+ +-------+
+--R          |   2    2  | 2    2
+--R     2a p\|- q  + p  \|q  - p
+--R                                                     Type: Expression Integer
+--E
+
+--S 142
+cc3:=aa.1-bb2
+--R
+--R   (6)
+--R          +-------+
+--R          | 2    2
+--R         \|q  - p
+--R      *
+--R         log
+--R                     4         4     4                  3
+--R                    q sinh(a x)  + 4q cosh(a x)sinh(a x)
+--R                  + 
+--R                       4         2     4     2 2          2
+--R                    (6q cosh(a x)  + 2q  - 4p q )sinh(a x)
+--R                  + 
+--R                       4         3      4     2 2
+--R                    (4q cosh(a x)  + (4q  - 8p q )cosh(a x))sinh(a x)
+--R                  + 
+--R                     4         4      4     2 2          2    4     2 2     4
+--R                    q cosh(a x)  + (2q  - 4p q )cosh(a x)  + q  - 8p q  + 8p
+--R               *
+--R                   +---------+
+--R                   |   2    2
+--R                  \|- q  + p
+--R              + 
+--R                       4     3 2          2
+--R                (- 4p q  + 4p q )sinh(a x)
+--R              + 
+--R                       4     3 2
+--R                (- 8p q  + 8p q )cosh(a x)sinh(a x)
+--R              + 
+--R                       4     3 2          2       4      3 2     5
+--R                (- 4p q  + 4p q )cosh(a x)  - 4p q  + 12p q  - 8p
+--R           /
+--R                 2         4     2                  3
+--R                q sinh(a x)  + 4q cosh(a x)sinh(a x)
+--R              + 
+--R                   2         2     2     2          2
+--R                (6q cosh(a x)  + 2q  - 4p )sinh(a x)
+--R              + 
+--R                   2         3      2     2                        2         4
+--R                (4q cosh(a x)  + (4q  - 8p )cosh(a x))sinh(a x) + q cosh(a x)
+--R              + 
+--R                   2     2          2    2
+--R                (2q  - 4p )cosh(a x)  + q
+--R     + 
+--R         +---------+
+--R         |   2    2      p tanh(a x)
+--R       2\|- q  + p  atan(-----------)
+--R                           +-------+
+--R                           | 2    2
+--R                          \|q  - p
+--R  /
+--R          +---------+ +-------+
+--R          |   2    2  | 2    2
+--R     2a p\|- q  + p  \|q  - p
+--R                                                     Type: Expression Integer
+--E
+
+--S 143    14:583 Axiom cannot simplify this expression
+cc4:=aa.2-bb2
+--R
+--R   (7)
+--R       -
+--R          atan
+--R                      2         2     2                      2         2    2
+--R                     q sinh(a x)  + 2q cosh(a x)sinh(a x) + q cosh(a x)  + q
+--R                   + 
+--R                         2
+--R                     - 2p
+--R              *
+--R                  +-------+
+--R                  | 2    2
+--R                 \|q  - p
+--R            /
+--R                   2     3
+--R               2p q  - 2p
+--R     + 
+--R            p tanh(a x)
+--R       atan(-----------)
+--R              +-------+
+--R              | 2    2
+--R             \|q  - p
+--R  /
+--R         +-------+
+--R         | 2    2
+--R     a p\|q  - p
+--R                                                     Type: Expression Integer
+--E
+
 @
 
 \section{\cite{1}:14.584~~~~~$\displaystyle
@@ -680,7 +2708,7 @@ $$
 <<*>>=
 )clear all
 
---S 23 of 28
+--S 144
 aa:=integrate(1/(p^2+q^2*cosh(a*x)^2),x)
 --R 
 --R
@@ -725,6 +2753,142 @@ aa:=integrate(1/(p^2+q^2*cosh(a*x)^2),x)
 --R     2a p\|q  + p
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 145
+bb1:=1/(2*a*p*sqrt(p^2+q^2))*log((p*tanh(a*x)+sqrt(p^2+q^2))/(p*tanh(a*x)-sqrt(p^2+q^2)))
+--R
+--R               +-------+
+--R               | 2    2
+--R            - \|q  + p   - p tanh(a x)
+--R        log(--------------------------)
+--R              +-------+
+--R              | 2    2
+--R             \|q  + p   - p tanh(a x)
+--R   (2)  -------------------------------
+--R                      +-------+
+--R                      | 2    2
+--R                 2a p\|q  + p
+--R                                                     Type: Expression Integer
+--E
+
+--S 146
+bb2:=1/(a*p*sqrt(p^2+q^2))*atan((p*tanh(a*x))/sqrt(p^2+q^2))
+--R
+--R             p tanh(a x)
+--R        atan(-----------)
+--R               +-------+
+--R               | 2    2
+--R              \|q  + p
+--R   (3)  -----------------
+--R              +-------+
+--R              | 2    2
+--R          a p\|q  + p
+--R                                                     Type: Expression Integer
+--E
+
+--S 147
+cc1:=aa-bb1
+--R
+--R   (4)
+--R       log
+--R                   4         4     4                  3
+--R                  q sinh(a x)  + 4q cosh(a x)sinh(a x)
+--R                + 
+--R                     4         2     4     2 2          2
+--R                  (6q cosh(a x)  + 2q  + 4p q )sinh(a x)
+--R                + 
+--R                     4         3      4     2 2
+--R                  (4q cosh(a x)  + (4q  + 8p q )cosh(a x))sinh(a x)
+--R                + 
+--R                   4         4      4     2 2          2    4     2 2     4
+--R                  q cosh(a x)  + (2q  + 4p q )cosh(a x)  + q  + 8p q  + 8p
+--R             *
+--R                 +-------+
+--R                 | 2    2
+--R                \|q  + p
+--R            + 
+--R                     4     3 2          2          4     3 2
+--R              (- 4p q  - 4p q )sinh(a x)  + (- 8p q  - 8p q )cosh(a x)sinh(a x)
+--R            + 
+--R                     4     3 2          2       4      3 2     5
+--R              (- 4p q  - 4p q )cosh(a x)  - 4p q  - 12p q  - 8p
+--R         /
+--R               2         4     2                  3
+--R              q sinh(a x)  + 4q cosh(a x)sinh(a x)
+--R            + 
+--R                 2         2     2     2          2
+--R              (6q cosh(a x)  + 2q  + 4p )sinh(a x)
+--R            + 
+--R                 2         3      2     2                        2         4
+--R              (4q cosh(a x)  + (4q  + 8p )cosh(a x))sinh(a x) + q cosh(a x)
+--R            + 
+--R                 2     2          2    2
+--R              (2q  + 4p )cosh(a x)  + q
+--R     + 
+--R                +-------+
+--R                | 2    2
+--R             - \|q  + p   - p tanh(a x)
+--R       - log(--------------------------)
+--R               +-------+
+--R               | 2    2
+--R              \|q  + p   - p tanh(a x)
+--R  /
+--R          +-------+
+--R          | 2    2
+--R     2a p\|q  + p
+--R                                                     Type: Expression Integer
+--E
+
+--S 148    14:584 Axiom cannot compute this integral
+cc2:=aa-bb2
+--R
+--R   (5)
+--R       log
+--R                   4         4     4                  3
+--R                  q sinh(a x)  + 4q cosh(a x)sinh(a x)
+--R                + 
+--R                     4         2     4     2 2          2
+--R                  (6q cosh(a x)  + 2q  + 4p q )sinh(a x)
+--R                + 
+--R                     4         3      4     2 2
+--R                  (4q cosh(a x)  + (4q  + 8p q )cosh(a x))sinh(a x)
+--R                + 
+--R                   4         4      4     2 2          2    4     2 2     4
+--R                  q cosh(a x)  + (2q  + 4p q )cosh(a x)  + q  + 8p q  + 8p
+--R             *
+--R                 +-------+
+--R                 | 2    2
+--R                \|q  + p
+--R            + 
+--R                     4     3 2          2          4     3 2
+--R              (- 4p q  - 4p q )sinh(a x)  + (- 8p q  - 8p q )cosh(a x)sinh(a x)
+--R            + 
+--R                     4     3 2          2       4      3 2     5
+--R              (- 4p q  - 4p q )cosh(a x)  - 4p q  - 12p q  - 8p
+--R         /
+--R               2         4     2                  3
+--R              q sinh(a x)  + 4q cosh(a x)sinh(a x)
+--R            + 
+--R                 2         2     2     2          2
+--R              (6q cosh(a x)  + 2q  + 4p )sinh(a x)
+--R            + 
+--R                 2         3      2     2                        2         4
+--R              (4q cosh(a x)  + (4q  + 8p )cosh(a x))sinh(a x) + q cosh(a x)
+--R            + 
+--R                 2     2          2    2
+--R              (2q  + 4p )cosh(a x)  + q
+--R     + 
+--R               p tanh(a x)
+--R       - 2atan(-----------)
+--R                 +-------+
+--R                 | 2    2
+--R                \|q  + p
+--R  /
+--R          +-------+
+--R          | 2    2
+--R     2a p\|q  + p
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.585~~~~~$\displaystyle
@@ -735,7 +2899,7 @@ $$
 <<*>>=
 )clear all
 
---S 24 of 28
+--S 149    14:585 Axiom cannot compute this integral
 aa:=integrate(x^m*cosh(a*x),x)
 --R 
 --R
@@ -755,7 +2919,7 @@ $$
 <<*>>=
 )clear all
 
---S 25 of 28
+--S 150    14:586 Axiom cannot compute this integral
 aa:=integrate(cosh(a*x)^n,x)
 --R 
 --R
@@ -776,7 +2940,7 @@ $$
 <<*>>=
 )clear all
 
---S 26 of 28
+--S 151    14:587 Axiom cannot compute this integral
 aa:=integrate(cosh(a*x)/x^n,x)
 --R 
 --R
@@ -798,7 +2962,7 @@ $$
 <<*>>=
 )clear all
 
---S 27 of 28
+--S 152    14:588 Axiom cannot compute this integral
 aa:=integrate(1/cosh(a*x)^n,x)
 --R 
 --R
@@ -821,7 +2985,7 @@ $$
 <<*>>=
 )clear all
 
---S 28 of 28
+--S 153    14:589 Axiom cannot compute this integral
 aa:=integrate(1/cosh(a*x)^n,x)
 --R 
 --R



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	Schaums-Axiom	equivalence testing (26-28))
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daly@axiom-developer.org wrote:
> On at least 2 of these problems Schaums and Axiom seem to disagree 
> on the results, namely:
>   14:569 SCHAUMS AND AXIOM DISAGREE?
>   14:571 SCHAUMS AND AXIOM DISAGREE?
> as the compute result is not constant but does not seem to have a 
> simplification that eliminates x.
> This needs to be studied further.
>
>   
> ---S 8 of 28
> +--S 17
>  aa:=integrate(cosh(a*x)^2,x)
>  --R 
>  --R
> @@ -170,6 +248,42 @@ aa:=integrate(cosh(a*x)^2,x)
>  --R                   2a
>  --R                                          Type: Union(Expression Integer,...)
>  --E
> +
> +--S 18
> +bb:=x/2+(sinh(a*x)*cosh(a*x))/2
>
>   

+bb:=x/2+(sinh(a*x)*cosh(a*x))/2

this should be

+bb:=x/2+(sinh(a*x)*cosh(a*x))/2a

I think your Schaums is out of date on this one.





> +--R
> +--R        cosh(a x)sinh(a x) + x
> +--R   (2)  ----------------------
> +--R                   2
> +--R                                                     Type: Expression Integer
> +--E
> +
> +--S 19
> +cc:=aa-bb
> +--R
> +--R        (- a + 1)cosh(a x)sinh(a x)
> +--R   (3)  ---------------------------
> +--R                     2a
> +--R                                                     Type: Expression Integer
> +--E
> +
> +--S 20
> +sinhcoshrule:=rule(sinh(x)*cosh(y) == 1/2*(sinh(x+y)+sinh(x-y)))
> +--R
> +--I                             %B sinh(y + x) - %B sinh(y - x)
> +--I   (4)  %B cosh(y)sinh(x) == -------------------------------
> +--R                                            2
> +--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
> +--E
> +
> +--S 21     14:569 SCHAUMS AND AXIOM DISAGREE?
> +dd:=sinhcoshrule cc
> +--R
> +--R        (- a + 1)sinh(2a x)
> +--R   (5)  -------------------
> +--R                 4a
> +--R                                                     Type: Expression Integer
> +--E
>  @
>   








For this next one Maxima gives

(%i6) integrate(1/cosh(a*x)^2,x);
(%o6) -4/(2*a*%e^(2*a*x)+2*a)




But if I try
(%i7) integrate(1/cos(a*x*i)^2,x);
(%o7) 
(2*sin(2*a*i*x))/(a*i*sin(2*a*i*x)^2+a*i*cos(2*a*i*x)^2+2*a*i*cos(2*a*i*x)+a*i)
(%i8) trigreduce(%);
(%o8) sin(2*a*i*x)/(a*i*cos(2*a*i*x)+a*i)
(%i9) trigrat(%);
(%o9) sin(a*i*x)/(a*i*cos(a*i*x))
(%i10) trigreduce(%);
(%o10) tan(a*i*x)/(a*i)

Now this can be written as
tanh(ax)  /ai
and this is different than Schaums

I think my logic is OK here But I am not an expert.






>  
>  \section{\cite{1}:14.571~~~~~$\displaystyle
> @@ -201,7 +396,7 @@ $$
>  <<*>>=
>  )clear all
>  
> ---S 10 of 28
> +--S 31
>  aa:=integrate(1/cosh(a*x)^2,x)
>  --R 
>  --R
> @@ -211,6 +406,176 @@ aa:=integrate(1/cosh(a*x)^2,x)
>  --R          a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  + a
>  --R                                          Type: Union(Expression Integer,...)
>  --E 
> +
> +--S 32
> +bb:=tanh(a*x)/a
> +--R
> +--R        tanh(a x)
> +--R   (2)  ---------
> +--R            a
> +--R                                                     Type: Expression Integer
> +--E
> +
> +--S 33
> +cc:=aa-bb
> +--R
> +--R                    2                                  2
> +--R        (- sinh(a x)  - 2cosh(a x)sinh(a x) - cosh(a x)  - 1)tanh(a x) - 2
> +--R   (3)  ------------------------------------------------------------------
> +--R                         2                                      2
> +--R              a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  + a
> +--R                                                     Type: Expression Integer
> +--E
> +
> +--S 34
> +tanhrule:=rule(tanh(x) == sinh(x)/cosh(x))
> +--R
> +--R                   sinh(x)
> +--R   (4)  tanh(x) == -------
> +--R                   cosh(x)
> +--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
> +--E
> +
> +--S 35
> +dd:=tanhrule cc
> +--R
> +--R   (5)
> +--R                  3                      2               2
> +--R       - sinh(a x)  - 2cosh(a x)sinh(a x)  + (- cosh(a x)  - 1)sinh(a x)
> +--R     + 
> +--R       - 2cosh(a x)
> +--R  /
> +--R                         2               2                       3
> +--R     a cosh(a x)sinh(a x)  + 2a cosh(a x) sinh(a x) + a cosh(a x)  + a cosh(a x)
> +--R                                                     Type: Expression Integer
> +--E
> +
> +--S 36
> +sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2)
> +--R
> +--R               2    cosh(2x) - 1
> +--R   (6)  sinh(x)  == ------------
> +--R                          2
> +--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
> +--E
> +
> +--S 37
> +ee:=sinhsqrrule dd
> +--R
> +--R   (7)
> +--R                   3                2
> +--R       - 2sinh(a x)  + (- 2cosh(a x)  - 2)sinh(a x) - 2cosh(a x)cosh(2a x)
> +--R     + 
> +--R       - 2cosh(a x)
> +--R  /
> +--R                   2                                                3
> +--R       4a cosh(a x) sinh(a x) + a cosh(a x)cosh(2a x) + 2a cosh(a x)
> +--R     + 
> +--R       a cosh(a x)
> +--R                                                     Type: Expression Integer
> +--E
> +
> +--S 38
> +coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2)
> +--R
> +--R               2    cosh(2x) + 1
> +--R   (8)  cosh(x)  == ------------
> +--R                          2
> +--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
> +--E
> +
> +--S 39
> +ff:=coshsqrrule ee
> +--R
> +--R   (9)
> +--R                   3
> +--R       - 2sinh(a x)  + (- cosh(2a x) - 3)sinh(a x) - 2cosh(a x)cosh(2a x)
> +--R     + 
> +--R       - 2cosh(a x)
> +--R  /
> +--R                                                                           3
> +--R       (2a cosh(2a x) + 2a)sinh(a x) + a cosh(a x)cosh(2a x) + 2a cosh(a x)
> +--R     + 
> +--R       a cosh(a x)
> +--R                                                     Type: Expression Integer
> +--E
> +
> +--S 40
> +sinhcuberule:=rule(sinh(x)^3 == 1/4*sinh(3*x)-3/4*sinh(x))
> +--R
> +--R                3    sinh(3x) - 3sinh(x)
> +--R   (10)  sinh(x)  == -------------------
> +--R                              4
> +--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
> +--E
> +
> +--S 41
> +gg:=sinhcuberule ff
> +--R
> +--R   (11)
> +--R       - sinh(3a x) + (- 2cosh(2a x) - 3)sinh(a x) - 4cosh(a x)cosh(2a x)
> +--R     + 
> +--R       - 4cosh(a x)
> +--R  /
> +--R                                                                            3
> +--R       (4a cosh(2a x) + 4a)sinh(a x) + 2a cosh(a x)cosh(2a x) + 4a cosh(a x)
> +--R     + 
> +--R       2a cosh(a x)
> +--R                                                     Type: Expression Integer
> +--E
> +
> +--S 42
> +coshcuberule:=rule(cosh(x)^3 == 1/4*cosh(3*x)-3/4*cosh(x))
> +--R
> +--R                3    cosh(3x) - 3cosh(x)
> +--R   (12)  cosh(x)  == -------------------
> +--R                              4
> +--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
> +--E
> +
> +--S 43
> +hh:=coshcuberule gg
> +--R
> +--R   (13)
> +--R       - sinh(3a x) + (- 2cosh(2a x) - 3)sinh(a x) - 4cosh(a x)cosh(2a x)
> +--R     + 
> +--R       - 4cosh(a x)
> +--R  /
> +--R       (4a cosh(2a x) + 4a)sinh(a x) + a cosh(3a x) + 2a cosh(a x)cosh(2a x)
> +--R     + 
> +--R       - a cosh(a x)
> +--R                                                     Type: Expression Integer
> +--E
> +
> +--S 44
> +coshcoshrule:=rule(cosh(x)*cosh(y)==1/2*(cosh(x+y)+cosh(x-y)))
> +--R
> +--I                              %U cosh(y + x) + %U cosh(y - x)
> +--I   (14)  %U cosh(x)cosh(y) == -------------------------------
> +--R                                             2
> +--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
> +--E
> +
> +--S 45
> +ii:=coshcoshrule hh
> +--R
> +--R   (15)
> +--R   - sinh(3a x) + (- 2cosh(2a x) - 3)sinh(a x) - 2cosh(3a x) - 6cosh(a x)
> +--R   ----------------------------------------------------------------------
> +--R                (4a cosh(2a x) + 4a)sinh(a x) + 2a cosh(3a x)
> +--R                                                     Type: Expression Integer
> +--E
> +
> +--S 46     14:571 SCHAUMS AND AXIOM DISAGREE?
> +jj:=complexNormalize ii
> +--R
> +--R               a x 2
> +--R         - 2(%e   )  - 2
> +--R   (16)  ---------------
> +--R               a x 2
> +--R         2a (%e   )  - a
> +--R                                                     Type: Expression Integer
> +--E
>   



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Subject: Re: [Axiom-developer] 20080426.01.tpd.patch (CATS Schaums-Axiom
	equivalence testing (26-28))
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> On at least 2 of these problems Schaums and Axiom seem to disagree 
> on the results, namely:
>   14:569 SCHAUMS AND AXIOM DISAGREE?
>   14:571 SCHAUMS AND AXIOM DISAGREE?
> as the compute result is not constant but does not seem to have a 
> simplification that eliminates x.
> This needs to be studied further.
> 

> ---S 10 of 28
> +--S 31
>  aa:=integrate(1/cosh(a*x)^2,x)
>  --R 
>  --R
> @@ -211,6 +406,176 @@ aa:=integrate(1/cosh(a*x)^2,x)
>  --R          a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  + a
>  --R                                          Type: Union(Expression Integer,...)
>  --E 
> +
> +--S 32
> +bb:=tanh(a*x)/a

I get:

normalize(integrate(1/cosh(a*x)^2,x) - tanh(a*x)/a)

           1
   (14)  - -
           a
                                                     Type: Expression Integer

so it seems that the difference really is a constant.

-- 
                              Waldek Hebisch
hebisch@math.uni.wroc.pl 



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	Sun, 27 Apr 2008 05:49:29 -0400)
Subject: Re: [Axiom-developer] 20080426.01.tpd.patch (CATS
	Schaums-Axiom	equivalence testing (26-28))
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>
>+bb:=x/2+(sinh(a*x)*cosh(a*x))/2
>
>this should be
>
>+bb:=x/2+(sinh(a*x)*cosh(a*x))/2a
>
>I think your Schaums is out of date on this one.

Thanks. It is a typo in my copy of Schaums.
No wonder they disagree.

Tim 




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	equivalence testing (26-28))
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>> On at least 2 of these problems Schaums and Axiom seem to disagree 
>> on the results, namely:
>>   14:569 SCHAUMS AND AXIOM DISAGREE?
>>   14:571 SCHAUMS AND AXIOM DISAGREE?
>> as the compute result is not constant but does not seem to have a 
>> simplification that eliminates x.
>> This needs to be studied further.
>> 
>
>> ---S 10 of 28
>> +--S 31
>>  aa:=integrate(1/cosh(a*x)^2,x)
>>  --R 
>>  --R
>> @@ -211,6 +406,176 @@ aa:=integrate(1/cosh(a*x)^2,x)
>>  --R          a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  + a
>>  --R                                          Type: Union(Expression Integer,...)
>>  --E 
>> +
>> +--S 32
>> +bb:=tanh(a*x)/a
>
>I get:
>
>normalize(integrate(1/cosh(a*x)^2,x) - tanh(a*x)/a)
>
>           1
>   (14)  - -
>           a
>                                                     Type: Expression Integer
>
>so it seems that the difference really is a constant.

You're right. It was probably just post-midnight stupidity on my part.
I'll fix it in the next update.

Thanks.
Tim



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Any help on this would really be appreciated.
Is it really a bug in complexNormalize?

--S 5 of 14
aa:=integrate(sinh(a*x)^2*cosh(a*x)^2,x)
--R 
--R
--R                          3            3
--R        cosh(a x)sinh(a x)  + cosh(a x) sinh(a x) - a x
--R   (1)  -----------------------------------------------
--R                               8a
--R                                          Type: Union(Expression Integer,...)
--E 

--S
bb:=sinh(4*a*x)/(32*a)-x/8

        sinh(4a x) - 4a x
   (2)  -----------------
               32a
                                                     Type: Expression Integer
--E

--S
cc:=complexNormalize(aa-bb)

   (3)  0
                                                     Type: Expression Integer
--E
@
{\bf NOTE}, that if we compute this ``same'' expression directly
we get a different answer. This appears to be a bug.
--S
dd:=complexNormalize(integrate(sinh(a*x)^2*cosh(a*x)^2,x)-sinh(4*a*x)/(32*a)-x/8)

          x
   (4)  - -
          4
                                                     Type: Expression Integer
--E
@



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Subject: Re: [Axiom-developer] bug in complexNormalize?
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> Any help on this would really be appreciated.
> Is it really a bug in complexNormalize?
> 
> --S 5 of 14
> aa:=integrate(sinh(a*x)^2*cosh(a*x)^2,x)
> --R 
> --R
> --R                          3            3
> --R        cosh(a x)sinh(a x)  + cosh(a x) sinh(a x) - a x
> --R   (1)  -----------------------------------------------
> --R                               8a
> --R                                          Type: Union(Expression Integer,...)
> --E 
> 
> --S
> bb:=sinh(4*a*x)/(32*a)-x/8
> 
>         sinh(4a x) - 4a x
>    (2)  -----------------
>                32a
>                                                      Type: Expression Integer
> --E
> 
> --S
> cc:=complexNormalize(aa-bb)
> 
>    (3)  0
>                                                      Type: Expression Integer
> --E
> @
> {\bf NOTE}, that if we compute this ``same'' expression directly
> we get a different answer. This appears to be a bug.
> --S
> dd:=complexNormalize(integrate(sinh(a*x)^2*cosh(a*x)^2,x)-sinh(4*a*x)/(32*a)-x/8)
> 
>           x
>    (4)  - -
>           4
>                                                      Type: Expression Integer
> --E
> @
> 

I get:

complexNormalize(integrate(sinh(a*x)^2*cosh(a*x)^2,x)-(sinh(4*a*x)/(32*a)-x/8))

   (5)  0
                                                     Type: Expression Integer

AFAICS the 'dd' expression lacks parentheses around copy of 'bb' term,
so you get 'x/8' with different sign.


-- 
                              Waldek Hebisch
hebisch@math.uni.wroc.pl 



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In 14.661 Schaums claims:

integral acoth(x/a) = x*acoth(x)+a/2*log(x^2-a^2)
                        ^^^^^^^^

Axiom claims

integral acoth(x/a) = x*acoth(x/a)+a/2*log(x^2-a^2)
                        ^^^^^^^^^^

Is this a Schaums typo?

Tim




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  14:668 SCHAUMS AND AXIOM DIFFER (Axiom has closed form)
  14:671 SCHAUMS AND AXIOM DIFFER (Axiom has closed form)
In these two problems Axiom constructs a closed form for the integral
whereas Schaums shows a series expansion. Axiom makes the claim that
if there exists a closed form for an integral in elementary terms then
Axiom will return that form. If it returns the original integral then 
no closed form exists. Thus, Axiom is a decision procedure. In these
two cases, Axiom has constructed a closed form.

Also, in 
  14:661 Schaums and Axiom agree
I believe that my copy of Schaums has a typo and that instead of
  integral acoth(x/a) = x*acoth(x)+a/2*log(x^2-a^2)
the correct result should be
  integral acoth(x/a) = x*acoth(x/a)+a/2*log(x^2-a^2)
This has been fixed proactively but needs to be verified against a
later copy of Schaums. It appears that I've gotten so old that the
equations have changed since my college mathematics education :-)

At this point I have checked Axiom against all of the indefinite 
integrals in Schaums. Frankly, I'm quite impressed with the Axiom
team (Trager, Bronstein, et.al.) that created this code (Note that
I did not author any of the integration code). By any measure this
is an impressive showing.

Of the forms that Axiom could not simplify I have two further approaches.
The first approach will be to check the answers using Maxima/MMA/Maple.
Note that I believe the problems are mostly simplification issues.

The second approach is to spend some time thinking about a better,
more general method for automating the simplification, including using
proviso forms to capture assumptions. I have a graph-based procedure
that I'll explain and codify in a different pamphlet.

Another point is that there were a couple simplifications that ended
up with x only in the imaginary portion of the answer. This indicates
to me that there is a sign assumption in the code (see 14.666, around
-S 124 where I expand this more fully in a clearer example). These
assumptions need to be pushed forward in provisos.

Much remains to be done with CATS but this exercise has left me with
the impression that Axiom's integration routines are rock solid and
can be relied on with confidence. The 4Ms could benefit from doing
the same exercise but I don't have the time available to do that yet.
Ideally it could be shown that all of the CASs are "plug-compatible",
giving known-good answers to published problems.


schaum29.input.pamphlet
  14:590 Schaums and Axiom agree
  14:591 Axiom cannot simplify this expression
  14:592 Axiom cannot simplify this expression
  14:593 Axiom cannot simplify this expression
  14:594 Schaums and Axiom agree
  14:595 Schaums and Axiom agree
  14:596 Axiom cannot simplify this expression
  14:597 Schaums and Axiom agree
  14:598 Axiom cannot simplify this expression
  14:599 Axiom cannot simplify this expression
  14:600 Axiom cannot simplify this expression
  14:601 Schaums and Axiom agree
  14:602 Schaums and Axiom agree
  14:603 Schaums and Axiom agree

schaum30.input.pamphlet
  14:604 Schaums and Axiom differ by a constant
  14:605 Schaums and Axiom differ by a constant
  14:606 Axiom cannot simplify this expression
  14:607 Axiom cannot simplify this expression
  14:608 Schaums and Axiom agree
  14:609 Schaums and Axiom differ by a constant
  14:610 Axiom cannot compute this integral
  14:611 Schaums and Axiom differ by a constant
  14:612 Axiom cannot compute this integral
  14:613 Schaums and Axiom differ by a constant
  14:614 Axiom cannot compute this integral

schaum31.input.pamphlet
  14:615 Schaums and Axiom differ by a constant
  14:616 Schaums and Axiom differ by a constant
  14:617 Axiom cannot simplify this expression
  14:618 Schaums and Axiom agree
  14:619 Schaums and Axiom agree
  14:620 Schaums and Axiom differ by a constant
  14:621 Axiom cannot compute this integral
  14:622 Schaums and Axiom differ by a constant
  14:623 Axiom cannot compute this integral
  14:624 Schaums and Axiom differ by a constant
  14:625 Axiom cannot compute this integral

schaum32.input.pamphlet
  14:626 Schaums and Axiom agree
  14:627 Schaums and Axiom differ by a constant
  14:628 Axiom cannot simplify this expression
  14:629 Schaums and Axiom agree
  14:630 Schaums and Axiom agree
  14:631 Axiom cannot compute this integral
  14:632 Schaums and Axiom differ by a constant
  14:633 Axiom cannot compute this integral
  14:634 Schaums and Axiom agree
  14:635 Axiom cannot compute this integral

schaum33.input.pamphlet
  14:636 Schaums and Axiom agree
  14:637 Axiom cannot simplify this expression
  14:638 Axiom cannot simplify this expression
  14:639 Schaums and Axiom agree
  14:640 Schaums and Axiom agree
  14:641 Axiom cannot compute this integral
  14:642 Axiom cannot simplify this expression
  14:643 Axiom cannot compute this integral
  14:644 Schaums and Axiom differ by a constant
  14:645 Axiom cannot compute this integral

schaum34.input.pamphlet
  14:646 Schaums and Axiom agree
  14:647 Schaums and Axiom agree
  14:648 Schaums and Axiom agree
  14:649 Axiom cannot compute this integral
  14:650 Schaums and Axiom differ by a constant
  14:651 Schaums and Axiom agree
  14:652 Schaums and Axiom agree
  14:653 Schaums and Axiom agree
  14:654 Axiom cannot compute this integral
  14:655 Axiom cannot simplify these expressions
  14:656 Schaums and Axiom differ by a constant
  14:657 Schaums and Axiom agree
  14:658 Schaums and Axiom differ by a constant
  14:659 Axiom cannot compute this integral
  14:660 Schaums and Axiom agree
  14:661 Schaums and Axiom agree
  14:662 Schaums and Axiom agree
  14:663 Schaums and Axiom agree
  14:664 Axiom cannot compute this integral
  14:665 Schaums and Axiom agree
  14:666 Schaums and Axiom agree
  14:667 Schaums and Axiom differ by a constant
  14:668 SCHAUMS AND AXIOM DIFFER (Axiom has closed form)
  14:669 Axiom cannot simplify these expressions
  14:670 Axiom cannot simplify these expressions
  14:671 SCHAUMS AND AXIOM DIFFER (Axiom has closed form)
  14:672 Axiom cannot compute this integral
  14:673 Axiom cannot compute this integral
  14:674 Axiom cannot compute this integral
  14:675 Axiom cannot compute this integral
  14:676 Axiom cannot compute this integral
  14:677 Axiom cannot compute this integral

===========================================================================
diff --git a/src/input/schaum28.input.pamphlet b/src/input/schaum28.input.pamphlet
index 5c68b06..3ba0bfc 100644
--- a/src/input/schaum28.input.pamphlet
+++ b/src/input/schaum28.input.pamphlet
@@ -234,6 +234,10 @@ aa:=integrate(x/cosh(a*x),x)
 \section{\cite{1}:14.569~~~~~$\displaystyle
 \int{\cosh^2{ax}}~dx$}
 $$\int{\cosh^2{ax}}=
+\frac{x}{2}+\frac{\sinh{ax}\cosh{ax}}{2a}
+$$
+Note that the Schaums print edition (1968 printing 3) has a typo:
+$$\int{\cosh^2{ax}}=
 \frac{x}{2}+\frac{\sinh{ax}\cosh{ax}}{2}
 $$
 <<*>>=
@@ -250,40 +254,21 @@ aa:=integrate(cosh(a*x)^2,x)
 --E
 
 --S 18
-bb:=x/2+(sinh(a*x)*cosh(a*x))/2
+bb:=x/2+(sinh(a*x)*cosh(a*x))/(2*a)
 --R
---R        cosh(a x)sinh(a x) + x
---R   (2)  ----------------------
---R                   2
+--R        cosh(a x)sinh(a x) + a x
+--R   (2)  ------------------------
+--R                   2a
 --R                                                     Type: Expression Integer
 --E
 
---S 19
+--S 19     14:569 Schaums and Axiom agree
 cc:=aa-bb
 --R
---R        (- a + 1)cosh(a x)sinh(a x)
---R   (3)  ---------------------------
---R                     2a
+--R   (3)  0
 --R                                                     Type: Expression Integer
 --E
 
---S 20
-sinhcoshrule:=rule(sinh(x)*cosh(y) == 1/2*(sinh(x+y)+sinh(x-y)))
---R
---I                             %B sinh(y + x) - %B sinh(y - x)
---I   (4)  %B cosh(y)sinh(x) == -------------------------------
---R                                            2
---R                        Type: RewriteRule(Integer,Integer,Expression Integer)
---E
-
---S 21     14:569 SCHAUMS AND AXIOM DISAGREE?
-dd:=sinhcoshrule cc
---R
---R        (- a + 1)sinh(2a x)
---R   (5)  -------------------
---R                 4a
---R                                                     Type: Expression Integer
---E
 @
 
 \section{\cite{1}:14.570~~~~~$\displaystyle
@@ -294,7 +279,7 @@ $$
 <<*>>=
 )clear all
 
---S 22
+--S 20
 aa:=integrate(x*cosh(a*x)^2,x)
 --R 
 --R
@@ -306,7 +291,7 @@ aa:=integrate(x*cosh(a*x)^2,x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
 
---S 23
+--S 21
 bb:=x^2/4+(x*sinh(2*a*x))/(4*a)-cosh(2*a*x)/(8*a^2)
 --R
 --R                                         2 2
@@ -317,7 +302,7 @@ bb:=x^2/4+(x*sinh(2*a*x))/(4*a)-cosh(2*a*x)/(8*a^2)
 --R                                                     Type: Expression Integer
 --E
 
---S 24
+--S 22
 cc:=aa-bb
 --R
 --R   (3)
@@ -332,7 +317,7 @@ cc:=aa-bb
 --R                                                     Type: Expression Integer
 --E
 
---S 25
+--S 23
 sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2)
 --R
 --R               2    cosh(2x) - 1
@@ -341,7 +326,7 @@ sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2)
 --R                        Type: RewriteRule(Integer,Integer,Expression Integer)
 --E
 
---S 26
+--S 24
 dd:=sinhsqrrule cc
 --R
 --R   (5)
@@ -353,7 +338,7 @@ dd:=sinhsqrrule cc
 --R                                                     Type: Expression Integer
 --E
 
---S 27
+--S 25
 coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2)
 --R
 --R               2    cosh(2x) + 1
@@ -362,7 +347,7 @@ coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2)
 --R                        Type: RewriteRule(Integer,Integer,Expression Integer)
 --E
 
---S 28
+--S 26
 ee:=coshsqrrule dd
 --R
 --R        - x sinh(2a x) + 2x cosh(a x)sinh(a x)
@@ -371,7 +356,7 @@ ee:=coshsqrrule dd
 --R                                                     Type: Expression Integer
 --E
 
---S 29
+--S 27
 sinhcoshrule:=rule(sinh(x)*cosh(y) == 1/2*(sinh(x+y)+sinh(x-y)))
 --R
 --I                             %S sinh(y + x) - %S sinh(y - x)
@@ -380,7 +365,7 @@ sinhcoshrule:=rule(sinh(x)*cosh(y) == 1/2*(sinh(x+y)+sinh(x-y)))
 --R                        Type: RewriteRule(Integer,Integer,Expression Integer)
 --E
 
---S 30     14:570 Schaums and Axiom agree
+--S 28     14:570 Schaums and Axiom agree
 ff:=sinhcoshrule ee
 --R
 --R   (9)  0
@@ -396,7 +381,7 @@ $$
 <<*>>=
 )clear all
 
---S 31
+--S 29
 aa:=integrate(1/cosh(a*x)^2,x)
 --R 
 --R
@@ -407,7 +392,7 @@ aa:=integrate(1/cosh(a*x)^2,x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
 
---S 32
+--S 30
 bb:=tanh(a*x)/a
 --R
 --R        tanh(a x)
@@ -416,7 +401,7 @@ bb:=tanh(a*x)/a
 --R                                                     Type: Expression Integer
 --E
 
---S 33
+--S 31
 cc:=aa-bb
 --R
 --R                    2                                  2
@@ -425,155 +410,12 @@ cc:=aa-bb
 --R                         2                                      2
 --R              a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  + a
 --R                                                     Type: Expression Integer
---E
-
---S 34
-tanhrule:=rule(tanh(x) == sinh(x)/cosh(x))
---R
---R                   sinh(x)
---R   (4)  tanh(x) == -------
---R                   cosh(x)
---R                        Type: RewriteRule(Integer,Integer,Expression Integer)
---E
-
---S 35
-dd:=tanhrule cc
---R
---R   (5)
---R                  3                      2               2
---R       - sinh(a x)  - 2cosh(a x)sinh(a x)  + (- cosh(a x)  - 1)sinh(a x)
---R     + 
---R       - 2cosh(a x)
---R  /
---R                         2               2                       3
---R     a cosh(a x)sinh(a x)  + 2a cosh(a x) sinh(a x) + a cosh(a x)  + a cosh(a x)
---R                                                     Type: Expression Integer
---E
-
---S 36
-sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2)
---R
---R               2    cosh(2x) - 1
---R   (6)  sinh(x)  == ------------
---R                          2
---R                        Type: RewriteRule(Integer,Integer,Expression Integer)
---E
-
---S 37
-ee:=sinhsqrrule dd
---R
---R   (7)
---R                   3                2
---R       - 2sinh(a x)  + (- 2cosh(a x)  - 2)sinh(a x) - 2cosh(a x)cosh(2a x)
---R     + 
---R       - 2cosh(a x)
---R  /
---R                   2                                                3
---R       4a cosh(a x) sinh(a x) + a cosh(a x)cosh(2a x) + 2a cosh(a x)
---R     + 
---R       a cosh(a x)
---R                                                     Type: Expression Integer
---E
-
---S 38
-coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2)
---R
---R               2    cosh(2x) + 1
---R   (8)  cosh(x)  == ------------
---R                          2
---R                        Type: RewriteRule(Integer,Integer,Expression Integer)
---E
-
---S 39
-ff:=coshsqrrule ee
---R
---R   (9)
---R                   3
---R       - 2sinh(a x)  + (- cosh(2a x) - 3)sinh(a x) - 2cosh(a x)cosh(2a x)
---R     + 
---R       - 2cosh(a x)
---R  /
---R                                                                           3
---R       (2a cosh(2a x) + 2a)sinh(a x) + a cosh(a x)cosh(2a x) + 2a cosh(a x)
---R     + 
---R       a cosh(a x)
---R                                                     Type: Expression Integer
---E
-
---S 40
-sinhcuberule:=rule(sinh(x)^3 == 1/4*sinh(3*x)-3/4*sinh(x))
---R
---R                3    sinh(3x) - 3sinh(x)
---R   (10)  sinh(x)  == -------------------
---R                              4
---R                        Type: RewriteRule(Integer,Integer,Expression Integer)
---E
-
---S 41
-gg:=sinhcuberule ff
---R
---R   (11)
---R       - sinh(3a x) + (- 2cosh(2a x) - 3)sinh(a x) - 4cosh(a x)cosh(2a x)
---R     + 
---R       - 4cosh(a x)
---R  /
---R                                                                            3
---R       (4a cosh(2a x) + 4a)sinh(a x) + 2a cosh(a x)cosh(2a x) + 4a cosh(a x)
---R     + 
---R       2a cosh(a x)
---R                                                     Type: Expression Integer
---E
-
---S 42
-coshcuberule:=rule(cosh(x)^3 == 1/4*cosh(3*x)-3/4*cosh(x))
---R
---R                3    cosh(3x) - 3cosh(x)
---R   (12)  cosh(x)  == -------------------
---R                              4
---R                        Type: RewriteRule(Integer,Integer,Expression Integer)
---E
-
---S 43
-hh:=coshcuberule gg
---R
---R   (13)
---R       - sinh(3a x) + (- 2cosh(2a x) - 3)sinh(a x) - 4cosh(a x)cosh(2a x)
---R     + 
---R       - 4cosh(a x)
---R  /
---R       (4a cosh(2a x) + 4a)sinh(a x) + a cosh(3a x) + 2a cosh(a x)cosh(2a x)
---R     + 
---R       - a cosh(a x)
---R                                                     Type: Expression Integer
---E
-
---S 44
-coshcoshrule:=rule(cosh(x)*cosh(y)==1/2*(cosh(x+y)+cosh(x-y)))
---R
---I                              %U cosh(y + x) + %U cosh(y - x)
---I   (14)  %U cosh(x)cosh(y) == -------------------------------
---R                                             2
---R                        Type: RewriteRule(Integer,Integer,Expression Integer)
---E
-
---S 45
-ii:=coshcoshrule hh
---R
---R   (15)
---R   - sinh(3a x) + (- 2cosh(2a x) - 3)sinh(a x) - 2cosh(3a x) - 6cosh(a x)
---R   ----------------------------------------------------------------------
---R                (4a cosh(2a x) + 4a)sinh(a x) + 2a cosh(3a x)
---R                                                     Type: Expression Integer
---E
-
---S 46     14:571 SCHAUMS AND AXIOM DISAGREE?
-jj:=complexNormalize ii
+--S 32
+dd:=complexNormalize cc
 --R
---R               a x 2
---R         - 2(%e   )  - 2
---R   (16)  ---------------
---R               a x 2
---R         2a (%e   )  - a
+--R          1
+--R   (4)  - -
+--R          a
 --R                                                     Type: Expression Integer
 --E
 @
@@ -586,7 +428,7 @@ $$
 <<*>>=
 )clear all
 
---S 47
+--S 33 
 aa:=integrate(cosh(a*x)*cosh(p*x),x)
 --R 
 --R
@@ -597,7 +439,7 @@ aa:=integrate(cosh(a*x)*cosh(p*x),x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
 
---S 48
+--S 34
 bb:=(sinh(a-p)*x)/(2*(a-p))+(sinh(a+p)*x)/(2*(a+p))
 --R
 --R        (p - a)x sinh(p + a) + (p + a)x sinh(p - a)
@@ -607,7 +449,7 @@ bb:=(sinh(a-p)*x)/(2*(a-p))+(sinh(a+p)*x)/(2*(a+p))
 --R                                                     Type: Expression Integer
 --E
 
---S 49
+--S 35
 cc:=aa-bb
 --R
 --R   (3)
@@ -627,7 +469,7 @@ cc:=aa-bb
 --R                                                     Type: Expression Integer
 --E
 
---S 50
+--S 36
 sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2)
 --R
 --R               2    cosh(2x) - 1
@@ -636,7 +478,7 @@ sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2)
 --R                        Type: RewriteRule(Integer,Integer,Expression Integer)
 --E
 
---S 51
+--S 37
 dd:=sinhsqrrule cc
 --R
 --R   (5)
@@ -653,7 +495,7 @@ dd:=sinhsqrrule cc
 --R                                                     Type: Expression Integer
 --E
 
---S 52
+--S 38
 coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2)
 --R
 --R               2    cosh(2x) + 1
@@ -662,7 +504,7 @@ coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2)
 --R                        Type: RewriteRule(Integer,Integer,Expression Integer)
 --E
 
---S 53
+--S 39
 ee:=coshsqrrule dd
 --R
 --R   (7)
@@ -675,7 +517,7 @@ ee:=coshsqrrule dd
 --R                                                     Type: Expression Integer
 --E
 
---S 54
+--S 40
 sinhcoshrule:=rule(sinh(x)*cosh(y) == 1/2*(sinh(x+y)+sinh(x-y)))
 --R
 --I                             %V sinh(y + x) - %V sinh(y - x)
@@ -684,7 +526,7 @@ sinhcoshrule:=rule(sinh(x)*cosh(y) == 1/2*(sinh(x+y)+sinh(x-y)))
 --R                        Type: RewriteRule(Integer,Integer,Expression Integer)
 --E
 
---S 55     14:572 Schaums and Axiom agree
+--S 41     14:572 Schaums and Axiom agree
 ff:=sinhcoshrule ee
 --R
 --R   (9)
@@ -706,7 +548,7 @@ $$
 <<*>>=
 )clear all
 
---S 56
+--S 42
 aa:=integrate(cosh(a*x)*sin(p*x),x)
 --R 
 --R
@@ -724,7 +566,7 @@ aa:=integrate(cosh(a*x)*sin(p*x),x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
 
---S 57
+--S 43
 bb:=(a*sinh(a*x)*sin(p*x)-p*cosh(a*x)*cos(p*x))/(a^2+p^2)
 --R
 --R        a sin(p x)sinh(a x) - p cos(p x)cosh(a x)
@@ -734,7 +576,7 @@ bb:=(a*sinh(a*x)*sin(p*x)-p*cosh(a*x)*cos(p*x))/(a^2+p^2)
 --R                                                     Type: Expression Integer
 --E
 
---S 58
+--S 44
 cc:=aa-bb
 --R
 --R   (3)
@@ -749,7 +591,7 @@ cc:=aa-bb
 --R                                                     Type: Expression Integer
 --E
 
---S 59
+--S 45
 coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2)
 --R
 --R               2    cosh(2x) + 1
@@ -758,7 +600,7 @@ coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2)
 --R                        Type: RewriteRule(Integer,Integer,Expression Integer)
 --E
 
---S 60
+--S 46
 dd:=coshsqrrule cc
 --R
 --R   (5)
@@ -772,7 +614,7 @@ dd:=coshsqrrule cc
 --R                                                     Type: Expression Integer
 --E
 
---S 61
+--S 47
 sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2)
 --R
 --R               2    cosh(2x) - 1
@@ -781,7 +623,7 @@ sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2)
 --R                        Type: RewriteRule(Integer,Integer,Expression Integer)
 --E
 
---S 62     14:573 Schaums and Axiom agree
+--S 48     14:573 Schaums and Axiom agree
 ee:=sinhsqrrule dd
 --R
 --R   (7)  0
@@ -797,7 +639,7 @@ $$
 <<*>>=
 )clear all
 
---S 63
+--S 49
 aa:=integrate(cosh(a*x)*cos(p*x),x)
 --R 
 --R
@@ -815,7 +657,7 @@ aa:=integrate(cosh(a*x)*cos(p*x),x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
 
---S 64
+--S 50
 bb:=(a*sinh(a*x)*cos(p*x)+p*cosh(a*x)*sin(p*x))/(a^2+p^2)
 --R
 --R        a cos(p x)sinh(a x) + p cosh(a x)sin(p x)
@@ -825,7 +667,7 @@ bb:=(a*sinh(a*x)*cos(p*x)+p*cosh(a*x)*sin(p*x))/(a^2+p^2)
 --R                                                     Type: Expression Integer
 --E
 
---S 65
+--S 51
 cc:=aa-bb
 --R
 --R   (3)
@@ -840,7 +682,7 @@ cc:=aa-bb
 --R                                                     Type: Expression Integer
 --E
 
---S 66
+--S 52
 coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2)
 --R
 --R               2    cosh(2x) + 1
@@ -849,7 +691,7 @@ coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2)
 --R                        Type: RewriteRule(Integer,Integer,Expression Integer)
 --E
 
---S 67
+--S 53
 dd:=coshsqrrule cc
 --R
 --R   (5)
@@ -863,7 +705,7 @@ dd:=coshsqrrule cc
 --R                                                     Type: Expression Integer
 --E
 
---S 68
+--S 54
 sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2)
 --R
 --R               2    cosh(2x) - 1
@@ -872,7 +714,7 @@ sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2)
 --R                        Type: RewriteRule(Integer,Integer,Expression Integer)
 --E
 
---S 69     14:574 Schaums and Axiom agree
+--S 55     14:574 Schaums and Axiom agree
 ee:=sinhsqrrule dd
 --R
 --R   (7)  0
@@ -888,7 +730,7 @@ $$
 <<*>>=
 )clear all
 
---S 70
+--S 56
 aa:=integrate(1/(cosh(a*x)+1),x)
 --R 
 --R
@@ -898,7 +740,7 @@ aa:=integrate(1/(cosh(a*x)+1),x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
 
---S 71
+--S 57
 bb:=1/a*tanh((a*x)/2)
 --R
 --R             a x
@@ -909,7 +751,7 @@ bb:=1/a*tanh((a*x)/2)
 --R                                                     Type: Expression Integer
 --E
 
---S 72
+--S 58
 cc:=aa-bb
 --R
 --R                                          a x
@@ -920,7 +762,7 @@ cc:=aa-bb
 --R                                                     Type: Expression Integer
 --E
 
---S 73
+--S 59
 tanhrule:=rule(tanh(x) == sinh(x)/cosh(x))
 --R
 --R                   sinh(x)
@@ -929,7 +771,7 @@ tanhrule:=rule(tanh(x) == sinh(x)/cosh(x))
 --R                        Type: RewriteRule(Integer,Integer,Expression Integer)
 --E
 
---S 74
+--S 60
 dd:=tanhrule cc
 --R
 --R               a x                                   a x          a x
@@ -942,7 +784,7 @@ dd:=tanhrule cc
 --R                                                     Type: Expression Integer
 --E
 
---S 75
+--S 61
 sinhcoshrule:=rule(sinh(x)*cosh(y) == 1/2*(sinh(x+y)+sinh(x-y)))
 --R
 --I                             %B sinh(y + x) - %B sinh(y - x)
@@ -951,7 +793,7 @@ sinhcoshrule:=rule(sinh(x)*cosh(y) == 1/2*(sinh(x+y)+sinh(x-y)))
 --R                        Type: RewriteRule(Integer,Integer,Expression Integer)
 --E
 
---S 76
+--S 62
 ee:=sinhcoshrule dd
 --R
 --R                  3a x          a x                  a x          a x
@@ -964,7 +806,7 @@ ee:=sinhcoshrule dd
 --R                                                     Type: Expression Integer
 --E
 
---S 77
+--S 63
 sinhsinhrule:=rule(sinh(x)*sinh(y)==1/2*(cosh(x+y)-cosh(x-y)))
 --R
 --I                             %B cosh(y + x) - %B cosh(y - x)
@@ -973,7 +815,7 @@ sinhsinhrule:=rule(sinh(x)*sinh(y)==1/2*(cosh(x+y)-cosh(x-y)))
 --R                        Type: RewriteRule(Integer,Integer,Expression Integer)
 --E
 
---S 78
+--S 64
 ff:=sinhsinhrule ee
 --R
 --R                       3a x         a x         3a x          a x
@@ -986,7 +828,7 @@ ff:=sinhsinhrule ee
 --R                                                     Type: Expression Integer
 --E
 
---S 79
+--S 65
 coshcoshrule:=rule(cosh(x)*cosh(y)==1/2*(cosh(x+y)+cosh(x-y)))
 --R
 --I                               %BC cosh(y + x) + %BC cosh(y - x)
@@ -995,7 +837,7 @@ coshcoshrule:=rule(cosh(x)*cosh(y)==1/2*(cosh(x+y)+cosh(x-y)))
 --R                        Type: RewriteRule(Integer,Integer,Expression Integer)
 --E
 
---S 80     14:575 Schaums and Axiom differ by a constant
+--S 66     14:575 Schaums and Axiom differ by a constant
 gg:=coshcoshrule ff
 --R
 --R           1
@@ -1013,7 +855,7 @@ $$
 <<*>>=
 )clear all
 
---S 81
+--S 67
 aa:=integrate(1/(cosh(a*x)-1),x)
 --R 
 --R
@@ -1023,7 +865,7 @@ aa:=integrate(1/(cosh(a*x)-1),x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
 
---S 82
+--S 68
 bb:=-1/a*coth((a*x)/2)
 --R
 --R               a x
@@ -1034,7 +876,7 @@ bb:=-1/a*coth((a*x)/2)
 --R                                                     Type: Expression Integer
 --E
 
---S 83
+--S 69
 cc:=aa-bb
 --R
 --R             a x                                 a x
@@ -1045,7 +887,7 @@ cc:=aa-bb
 --R                                                     Type: Expression Integer
 --E
 
---S 84
+--S 70
 cothrule:=rule(coth(x) == cosh(x)/sinh(x))
 --R
 --R                   cosh(x)
@@ -1054,7 +896,7 @@ cothrule:=rule(coth(x) == cosh(x)/sinh(x))
 --R                        Type: RewriteRule(Integer,Integer,Expression Integer)
 --E
 
---S 85
+--S 71
 dd:=cothrule cc
 --R
 --R             a x                   a x         a x                  a x
@@ -1067,7 +909,7 @@ dd:=cothrule cc
 --R                                                     Type: Expression Integer
 --E
 
---S 86
+--S 72
 sinhcoshrule:=rule(sinh(x)*cosh(y) == 1/2*(sinh(x+y)+sinh(x-y)))
 --R
 --I                              %BD sinh(y + x) - %BD sinh(y - x)
@@ -1076,7 +918,7 @@ sinhcoshrule:=rule(sinh(x)*cosh(y) == 1/2*(sinh(x+y)+sinh(x-y)))
 --R                        Type: RewriteRule(Integer,Integer,Expression Integer)
 --E
 
---S 87
+--S 73
 ee:=sinhcoshrule dd
 --R
 --R             3a x          a x          a x                   a x
@@ -1089,7 +931,7 @@ ee:=sinhcoshrule dd
 --R                                                     Type: Expression Integer
 --E
 
---S 88
+--S 74
 sinhsinhrule:=rule(sinh(x)*sinh(y)==1/2*(cosh(x+y)-cosh(x-y)))
 --R
 --I                              %BE cosh(y + x) - %BE cosh(y - x)
@@ -1098,7 +940,7 @@ sinhsinhrule:=rule(sinh(x)*sinh(y)==1/2*(cosh(x+y)-cosh(x-y)))
 --R                        Type: RewriteRule(Integer,Integer,Expression Integer)
 --E
 
---S 89
+--S 75
 ff:=sinhsinhrule ee
 --R
 --R             3a x          a x          a x                   a x
@@ -1111,7 +953,7 @@ ff:=sinhsinhrule ee
 --R                                                     Type: Expression Integer
 --E
 
---S 90
+--S 76
 coshcoshrule:=rule(cosh(x)*cosh(y)==1/2*(cosh(x+y)+cosh(x-y)))
 --R
 --I                               %BF cosh(y + x) + %BF cosh(y - x)
@@ -1120,7 +962,7 @@ coshcoshrule:=rule(cosh(x)*cosh(y)==1/2*(cosh(x+y)+cosh(x-y)))
 --R                        Type: RewriteRule(Integer,Integer,Expression Integer)
 --E
 
---S 91     14:576 Schaums and Axiom differ by a constant
+--S 77     14:576 Schaums and Axiom differ by a constant
 gg:=coshcoshrule ff
 --R
 --R         1
@@ -1138,7 +980,7 @@ $$
 <<*>>=
 )clear all
 
---S 92
+--S 78
 aa:=integrate(x/(cosh(a*x)+1),x)
 --R 
 --R
@@ -1152,7 +994,7 @@ aa:=integrate(x/(cosh(a*x)+1),x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
 
---S 93
+--S 79
 bb:=x/a*tanh((a*x)/2)-2/a^2*log(cosh((a*x)/2))
 --R
 --R                    a x              a x
@@ -1164,7 +1006,7 @@ bb:=x/a*tanh((a*x)/2)-2/a^2*log(cosh((a*x)/2))
 --R                                                     Type: Expression Integer
 --E
 
---S 94
+--S 80
 cc:=aa-bb
 --R
 --R   (3)
@@ -1185,7 +1027,7 @@ cc:=aa-bb
 --R                                                     Type: Expression Integer
 --E
 
---S 95
+--S 81
 tanhrule:=rule(tanh(x) == sinh(x)/cosh(x))
 --R
 --R                   sinh(x)
@@ -1194,7 +1036,7 @@ tanhrule:=rule(tanh(x) == sinh(x)/cosh(x))
 --R                        Type: RewriteRule(Integer,Integer,Expression Integer)
 --E
 
---S 96
+--S 82
 dd:=tanhrule cc
 --R
 --R   (5)
@@ -1222,7 +1064,7 @@ dd:=tanhrule cc
 --R                                                     Type: Expression Integer
 --E
 
---S 97
+--S 83
 coshcoshrule:=rule(cosh(x)*cosh(y)==1/2*(cosh(x+y)+cosh(x-y)))
 --R
 --I                              %BG cosh(y + x) + %BG cosh(y - x)
@@ -1231,7 +1073,7 @@ coshcoshrule:=rule(cosh(x)*cosh(y)==1/2*(cosh(x+y)+cosh(x-y)))
 --R                        Type: RewriteRule(Integer,Integer,Expression Integer)
 --E
 
---S 98
+--S 84
 ee:=coshcoshrule dd
 --R
 --R   (7)
@@ -1259,7 +1101,7 @@ ee:=coshcoshrule dd
 --R                                                     Type: Expression Integer
 --E
 
---S 99
+--S 85
 sinhcoshrule:=rule(sinh(x)*cosh(y) == 1/2*(sinh(x+y)+sinh(x-y)))
 --R
 --I                              %BH sinh(y + x) - %BH sinh(y - x)
@@ -1268,7 +1110,7 @@ sinhcoshrule:=rule(sinh(x)*cosh(y) == 1/2*(sinh(x+y)+sinh(x-y)))
 --R                        Type: RewriteRule(Integer,Integer,Expression Integer)
 --E
 
---S 100
+--S 86
 ff:=sinhcoshrule ee
 --R
 --R   (9)
@@ -1296,7 +1138,7 @@ ff:=sinhcoshrule ee
 --R                                                     Type: Expression Integer
 --E
 
---S 101
+--S 87
 sinhsinhrule:=rule(sinh(x)*sinh(y)==1/2*(cosh(x+y)-cosh(x-y)))
 --R
 --I                               %BI cosh(y + x) - %BI cosh(y - x)
@@ -1305,7 +1147,7 @@ sinhsinhrule:=rule(sinh(x)*sinh(y)==1/2*(cosh(x+y)-cosh(x-y)))
 --R                        Type: RewriteRule(Integer,Integer,Expression Integer)
 --E
 
---S 102
+--S 88
 gg:=sinhsinhrule ff
 --R
 --R                                                       a x
@@ -1317,7 +1159,7 @@ gg:=sinhsinhrule ff
 --R                                                     Type: Expression Integer
 --E
 
---S 103    14:577 Schaums and Axiom differ by a constant
+--S 89     14:577 Schaums and Axiom differ by a constant
 complexNormalize gg
 --R
 --R           2log(2)
@@ -1336,7 +1178,7 @@ $$
 <<*>>=
 )clear all
 
---S 104
+--S 90
 aa:=integrate(x/(cosh(a*x)-1),x)
 --R 
 --R
@@ -1350,7 +1192,7 @@ aa:=integrate(x/(cosh(a*x)-1),x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
 
---S 105
+--S 91
 bb:=-x/a*coth((a*x)/2)+2/a^2*log(sinh((a*x)/2))
 --R
 --R                  a x              a x
@@ -1362,7 +1204,7 @@ bb:=-x/a*coth((a*x)/2)+2/a^2*log(sinh((a*x)/2))
 --R                                                     Type: Expression Integer
 --E
 
---S 106
+--S 92
 cc:=aa-bb
 --R
 --R   (3)
@@ -1383,7 +1225,7 @@ cc:=aa-bb
 --R                                                     Type: Expression Integer
 --E
 
---S 107
+--S 93
 cothrule:=rule(coth(x) == cosh(x)/sinh(x))
 --R
 --R                   cosh(x)
@@ -1392,7 +1234,7 @@ cothrule:=rule(coth(x) == cosh(x)/sinh(x))
 --R                        Type: RewriteRule(Integer,Integer,Expression Integer)
 --E
 
---S 108
+--S 94
 dd:=cothrule cc
 --R
 --R   (5)
@@ -1420,7 +1262,7 @@ dd:=cothrule cc
 --R                                                     Type: Expression Integer
 --E
 
---S 109
+--S 95
 sinhcoshrule:=rule(sinh(x)*cosh(y) == 1/2*(sinh(x+y)+sinh(x-y)))
 --R
 --I                              %BJ sinh(y + x) - %BJ sinh(y - x)
@@ -1429,7 +1271,7 @@ sinhcoshrule:=rule(sinh(x)*cosh(y) == 1/2*(sinh(x+y)+sinh(x-y)))
 --R                        Type: RewriteRule(Integer,Integer,Expression Integer)
 --E
 
---S 110
+--S 96
 ee:=sinhcoshrule dd
 --R
 --R   (7)
@@ -1457,7 +1299,7 @@ ee:=sinhcoshrule dd
 --R                                                     Type: Expression Integer
 --E
 
---S 111
+--S 97
 sinhsinhrule:=rule(sinh(x)*sinh(y)==1/2*(cosh(x+y)-cosh(x-y)))
 --R
 --I                              %BK cosh(y + x) - %BK cosh(y - x)
@@ -1466,7 +1308,7 @@ sinhsinhrule:=rule(sinh(x)*sinh(y)==1/2*(cosh(x+y)-cosh(x-y)))
 --R                        Type: RewriteRule(Integer,Integer,Expression Integer)
 --E
 
---S 112
+--S 98
 ff:=sinhsinhrule ee
 --R
 --R   (9)
@@ -1494,7 +1336,7 @@ ff:=sinhsinhrule ee
 --R                                                     Type: Expression Integer
 --E
 
---S 113
+--S 99
 coshcoshrule:=rule(cosh(x)*cosh(y)==1/2*(cosh(x+y)+cosh(x-y)))
 --R
 --I                               %BL cosh(y + x) + %BL cosh(y - x)
@@ -1503,7 +1345,7 @@ coshcoshrule:=rule(cosh(x)*cosh(y)==1/2*(cosh(x+y)+cosh(x-y)))
 --R                        Type: RewriteRule(Integer,Integer,Expression Integer)
 --E
 
---S 114
+--S 100
 gg:=coshcoshrule ff
 --R
 --R                                                     a x
@@ -1515,7 +1357,7 @@ gg:=coshcoshrule ff
 --R                                                     Type: Expression Integer
 --E
 
---S 115    14:578 Schaums and Axiom differ by a constant
+--S 101    14:578 Schaums and Axiom differ by a constant
 hh:=complexNormalize gg
 --R
 --R         2log(2)
@@ -1534,7 +1376,7 @@ $$
 <<*>>=
 )clear all
 
---S 116
+--S 102
 aa:=integrate(1/(cosh(a*x)+1)^2,x)
 --R 
 --R
@@ -1552,7 +1394,7 @@ aa:=integrate(1/(cosh(a*x)+1)^2,x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
 
---S 117
+--S 103
 bb:=1/(2*a)*tanh((a*x)/2)-1/(6*a)*tanh((a*x)/2)^3
 --R
 --R               a x 3         a x
@@ -1563,7 +1405,7 @@ bb:=1/(2*a)*tanh((a*x)/2)-1/(6*a)*tanh((a*x)/2)^3
 --R                                                     Type: Expression Integer
 --E
 
---S 118    14:579 Axiom cannot compute this integral
+--S 104    14:579 Axiom cannot compute this integral
 cc:=aa-bb
 --R
 --R   (3)
@@ -1614,7 +1456,7 @@ $$
 <<*>>=
 )clear all
 
---S 119
+--S 105
 aa:=integrate(1/(cosh(a*x)-1)^2,x)
 --R 
 --R
@@ -1632,7 +1474,7 @@ aa:=integrate(1/(cosh(a*x)-1)^2,x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
 
---S 120
+--S 106
 bb:=1/(2*a)*coth((a*x)/2)-1/(6*a)*coth((a*x)/2)^3
 --R
 --R               a x 3         a x
@@ -1643,7 +1485,7 @@ bb:=1/(2*a)*coth((a*x)/2)-1/(6*a)*coth((a*x)/2)^3
 --R                                                     Type: Expression Integer
 --E
 
---S 121    14:580 Axiom cannot compute this integral
+--S 107    14:580 Axiom cannot compute this integral
 cc:=aa-bb
 --R
 --R   (3)
@@ -1702,7 +1544,7 @@ $$
 <<*>>=
 )clear all
 
---S 122
+--S 108
 aa:=integrate(1/(p+q*cosh(a*x)),x)
 --R 
 --R
@@ -1744,7 +1586,7 @@ aa:=integrate(1/(p+q*cosh(a*x)),x)
 --R                                     Type: Union(List Expression Integer,...)
 --E 
 
---S 123
+--S 109
 bb1:=2/(a*sqrt(q^2-p^2))*atan((q*%e^(a*x)+p)/sqrt(q^2-p^2))
 --R
 --R                  a x
@@ -1760,7 +1602,7 @@ bb1:=2/(a*sqrt(q^2-p^2))*atan((q*%e^(a*x)+p)/sqrt(q^2-p^2))
 --R                                                     Type: Expression Integer
 --E
 
---S 124
+--S 110
 bb2:=1/(a*sqrt(p^2-q^2))*log((q*%e^(a*x)+p-sqrt(p^2-q^2))/(q*%e^(a*x)+p+sqrt(p^2-q^2)))
 --R
 --R               +---------+
@@ -1777,7 +1619,7 @@ bb2:=1/(a*sqrt(p^2-q^2))*log((q*%e^(a*x)+p-sqrt(p^2-q^2))/(q*%e^(a*x)+p+sqrt(p^2
 --R                                                     Type: Expression Integer
 --E
 
---S 125
+--S 111
 cc1:=aa.1-bb1
 --R
 --R   (4)
@@ -1817,7 +1659,7 @@ cc1:=aa.1-bb1
 --R                                                     Type: Expression Integer
 --E
 
---S 126
+--S 112
 cc2:=aa.2-bb1
 --R
 --R                                              +-------+
@@ -1834,7 +1676,7 @@ cc2:=aa.2-bb1
 --R                                                     Type: Expression Integer
 --E
 
---S 127
+--S 113
 cc3:=aa.1-bb2
 --R
 --R   (6)
@@ -1871,7 +1713,7 @@ cc3:=aa.1-bb2
 --R                                                     Type: Expression Integer
 --E
 
---S 128    14:581 Axiom cannot simplify this expression
+--S 114    14:581 Axiom cannot simplify this expression
 cc4:=aa.2-bb2
 --R
 --R   (7)
@@ -1907,7 +1749,7 @@ $$
 <<*>>=
 )clear all
 
---S 129
+--S 115
 aa:=integrate(1/(p+q*cosh(a*x))^2,x)
 --R 
 --R
@@ -1989,7 +1831,7 @@ aa:=integrate(1/(p+q*cosh(a*x))^2,x)
 --R                                     Type: Union(List Expression Integer,...)
 --E 
 
---S 130
+--S 116
 t1:=integrate(1/(p+q*cosh(a*x)),x)
 --R
 --R   (2)
@@ -2030,7 +1872,7 @@ t1:=integrate(1/(p+q*cosh(a*x)),x)
 --R                                     Type: Union(List Expression Integer,...)
 --E
 
---S 131
+--S 117
 bb1:=(q*sinh(a*x))/(a*(q^2-p^2)*(p+q*cosh(a*x)))-p/(q^2-p^2)*t1.1
 --R
 --R   (3)
@@ -2066,7 +1908,7 @@ bb1:=(q*sinh(a*x))/(a*(q^2-p^2)*(p+q*cosh(a*x)))-p/(q^2-p^2)*t1.1
 --R                                                     Type: Expression Integer
 --E
 
---S 132
+--S 118
 bb2:=(q*sinh(a*x))/(a*(q^2-p^2)*(p+q*cosh(a*x)))-p/(q^2-p^2)*t1.2
 --R
 --R   (4)
@@ -2087,7 +1929,7 @@ bb2:=(q*sinh(a*x))/(a*(q^2-p^2)*(p+q*cosh(a*x)))-p/(q^2-p^2)*t1.2
 --R                                                     Type: Expression Integer
 --E
 
---S 133
+--S 119
 cc1:=aa.1-bb1
 --R
 --R   (5)
@@ -2183,7 +2025,7 @@ cc1:=aa.1-bb1
 --R                                                     Type: Expression Integer
 --E
 
---S 134
+--S 120
 cc2:=aa.2-bb1
 --R
 --R   (6)
@@ -2271,7 +2113,7 @@ cc2:=aa.2-bb1
 --R                                                     Type: Expression Integer
 --E
 
---S 135
+--S 121
 cc3:=aa.1-bb2
 --R
 --R   (7)
@@ -2359,7 +2201,7 @@ cc3:=aa.1-bb2
 --R                                                     Type: Expression Integer
 --E
 
---S 136    14:582 Axiom cannot simplify this expression
+--S 122    14:582 Axiom cannot simplify this expression
 cc4:=aa.2-bb2
 --R
 --R   (8)
@@ -2409,7 +2251,7 @@ $$
 <<*>>=
 )clear all
 
---S 137
+--S 123
 aa:=integrate(1/(p^2-q^2*cosh(a*x)^2),x)
 --R 
 --R
@@ -2477,7 +2319,7 @@ aa:=integrate(1/(p^2-q^2*cosh(a*x)^2),x)
 --R                                     Type: Union(List Expression Integer,...)
 --E 
 
---S 138
+--S 124
 bb1:=1/(2*a*p*sqrt(p^2-q^2))*log((p*tanh(a*x)+sqrt(p^2-q^2))/(p*tanh(a*x)-sqrt(p^2-q^2)))
 --R
 --R               +---------+
@@ -2494,7 +2336,7 @@ bb1:=1/(2*a*p*sqrt(p^2-q^2))*log((p*tanh(a*x)+sqrt(p^2-q^2))/(p*tanh(a*x)-sqrt(p
 --R                                                     Type: Expression Integer
 --E
 
---S 139
+--S 125
 bb2:=-1/(a*p*sqrt(q^2-p^2))*atan((p*tanh(a*x))/sqrt(q^2-p^2))
 --R
 --R               p tanh(a x)
@@ -2509,7 +2351,7 @@ bb2:=-1/(a*p*sqrt(q^2-p^2))*atan((p*tanh(a*x))/sqrt(q^2-p^2))
 --R                                                     Type: Expression Integer
 --E
 
---S 140
+--S 126
 cc1:=aa.1-bb1
 --R
 --R   (4)
@@ -2562,7 +2404,7 @@ cc1:=aa.1-bb1
 --R                                                     Type: Expression Integer
 --E
 
---S 141
+--S 127
 cc2:=aa.2-bb1
 --R
 --R   (5)
@@ -2599,7 +2441,7 @@ cc2:=aa.2-bb1
 --R                                                     Type: Expression Integer
 --E
 
---S 142
+--S 128
 cc3:=aa.1-bb2
 --R
 --R   (6)
@@ -2658,7 +2500,7 @@ cc3:=aa.1-bb2
 --R                                                     Type: Expression Integer
 --E
 
---S 143    14:583 Axiom cannot simplify this expression
+--S 129    14:583 Axiom cannot simplify this expression
 cc4:=aa.2-bb2
 --R
 --R   (7)
@@ -2708,7 +2550,7 @@ $$
 <<*>>=
 )clear all
 
---S 144
+--S 130
 aa:=integrate(1/(p^2+q^2*cosh(a*x)^2),x)
 --R 
 --R
@@ -2754,7 +2596,7 @@ aa:=integrate(1/(p^2+q^2*cosh(a*x)^2),x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
 
---S 145
+--S 131
 bb1:=1/(2*a*p*sqrt(p^2+q^2))*log((p*tanh(a*x)+sqrt(p^2+q^2))/(p*tanh(a*x)-sqrt(p^2+q^2)))
 --R
 --R               +-------+
@@ -2771,7 +2613,7 @@ bb1:=1/(2*a*p*sqrt(p^2+q^2))*log((p*tanh(a*x)+sqrt(p^2+q^2))/(p*tanh(a*x)-sqrt(p
 --R                                                     Type: Expression Integer
 --E
 
---S 146
+--S 132
 bb2:=1/(a*p*sqrt(p^2+q^2))*atan((p*tanh(a*x))/sqrt(p^2+q^2))
 --R
 --R             p tanh(a x)
@@ -2786,7 +2628,7 @@ bb2:=1/(a*p*sqrt(p^2+q^2))*atan((p*tanh(a*x))/sqrt(p^2+q^2))
 --R                                                     Type: Expression Integer
 --E
 
---S 147
+--S 133
 cc1:=aa-bb1
 --R
 --R   (4)
@@ -2839,7 +2681,7 @@ cc1:=aa-bb1
 --R                                                     Type: Expression Integer
 --E
 
---S 148    14:584 Axiom cannot compute this integral
+--S 134    14:584 Axiom cannot compute this integral
 cc2:=aa-bb2
 --R
 --R   (5)
@@ -2899,7 +2741,7 @@ $$
 <<*>>=
 )clear all
 
---S 149    14:585 Axiom cannot compute this integral
+--S 135    14:585 Axiom cannot compute this integral
 aa:=integrate(x^m*cosh(a*x),x)
 --R 
 --R
@@ -2919,7 +2761,7 @@ $$
 <<*>>=
 )clear all
 
---S 150    14:586 Axiom cannot compute this integral
+--S 136    14:586 Axiom cannot compute this integral
 aa:=integrate(cosh(a*x)^n,x)
 --R 
 --R
@@ -2940,7 +2782,7 @@ $$
 <<*>>=
 )clear all
 
---S 151    14:587 Axiom cannot compute this integral
+--S 137    14:587 Axiom cannot compute this integral
 aa:=integrate(cosh(a*x)/x^n,x)
 --R 
 --R
@@ -2962,7 +2804,7 @@ $$
 <<*>>=
 )clear all
 
---S 152    14:588 Axiom cannot compute this integral
+--S 138    14:588 Axiom cannot compute this integral
 aa:=integrate(1/cosh(a*x)^n,x)
 --R 
 --R
@@ -2985,7 +2827,7 @@ $$
 <<*>>=
 )clear all
 
---S 153    14:589 Axiom cannot compute this integral
+--S 139    14:589 Axiom cannot compute this integral
 aa:=integrate(1/cosh(a*x)^n,x)
 --R 
 --R
diff --git a/src/input/schaum29.input.pamphlet b/src/input/schaum29.input.pamphlet
index 37e2800..1aff49f 100644
--- a/src/input/schaum29.input.pamphlet
+++ b/src/input/schaum29.input.pamphlet
@@ -18,7 +18,7 @@ $$
 )set message auto off
 )clear all
 
---S 1 of 14
+--S 1
 aa:=integrate(sinh(a*x)*cosh(a*x),x)
 --R 
 --R
@@ -28,6 +28,63 @@ aa:=integrate(sinh(a*x)*cosh(a*x),x)
 --R                   4a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 2
+bb:=sinh(a*x)^2/(2*a)
+--R
+--R                 2
+--R        sinh(a x)
+--R   (2)  ----------
+--R            2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 3
+cc:=aa-bb
+--R
+--R                   2            2
+--R        - sinh(a x)  + cosh(a x)
+--R   (3)  -------------------------
+--R                    4a
+--R                                                     Type: Expression Integer
+--E
+
+--S 4
+sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2)
+--R
+--R               2    cosh(2x) - 1
+--R   (4)  sinh(x)  == ------------
+--R                          2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 5
+dd:=sinhsqrrule cc
+--R
+--R                                 2
+--R        - cosh(2a x) + 2cosh(a x)  + 1
+--R   (5)  ------------------------------
+--R                      8a
+--R                                                     Type: Expression Integer
+--E
+
+--S 6
+coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2)
+--R
+--R               2    cosh(2x) + 1
+--R   (6)  cosh(x)  == ------------
+--R                          2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 7      14:590 Schaums and Axiom agree
+ee:=coshsqrrule dd
+--R
+--R         1
+--R   (7)  --
+--R        4a
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.591~~~~~$\displaystyle
@@ -38,7 +95,7 @@ $$
 <<*>>=
 )clear all
 
---S 2 of 14
+--S 8
 aa:=integrate(sinh(p*x)*cosh(q*x),x)
 --R 
 --R
@@ -48,6 +105,35 @@ aa:=integrate(sinh(p*x)*cosh(q*x),x)
 --R         (q  - p )sinh(p x)  + (- q  + p )cosh(p x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 9
+bb:=(cosh(p+q)*x)/(2*(p+q))+(cosh(p-q)*x)/(2*(p-q))
+--R
+--R        (q - p)x cosh(q + p) + (- q - p)x cosh(q - p)
+--R   (2)  ---------------------------------------------
+--R                            2     2
+--R                          2q  - 2p
+--R                                                     Type: Expression Integer
+--E
+
+--S 10     14:591 Axiom cannot simplify this expression
+cc:=aa-bb
+--R
+--R   (3)
+--R       - 2q sinh(p x)sinh(q x)
+--R     + 
+--R                                                               2
+--R       ((- q + p)x cosh(q + p) + (q + p)x cosh(q - p))sinh(p x)
+--R     + 
+--R       2p cosh(p x)cosh(q x)
+--R     + 
+--R                                                               2
+--R       ((q - p)x cosh(q + p) + (- q - p)x cosh(q - p))cosh(p x)
+--R  /
+--R        2     2          2        2     2          2
+--R     (2q  - 2p )sinh(p x)  + (- 2q  + 2p )cosh(p x)
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.592~~~~~$\displaystyle
@@ -58,7 +144,7 @@ $$
 <<*>>=
 )clear all
 
---S 3 of 14
+--S 11
 aa:=integrate(sinh(a*x)^n*cosh(a*x),x)
 --R 
 --R
@@ -68,6 +154,29 @@ aa:=integrate(sinh(a*x)^n*cosh(a*x),x)
 --R                    (a n + a)sinh(a x)  + (- a n - a)cosh(a x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 12
+bb:=sinh(a*x)/((n+1)*a)
+--R
+--R        sinh(a x)
+--R   (2)  ---------
+--R         a n + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 13     14:592 Axiom cannot simplify this expression
+cc:=aa-bb
+--R
+--R   (3)
+--R       - sinh(a x)sinh(n log(sinh(a x))) - sinh(a x)cosh(n log(sinh(a x)))
+--R     + 
+--R                  3            2
+--R       - sinh(a x)  + cosh(a x) sinh(a x)
+--R  /
+--R                       2                       2
+--R     (a n + a)sinh(a x)  + (- a n - a)cosh(a x)
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.593~~~~~$\displaystyle
@@ -78,7 +187,7 @@ $$
 <<*>>=
 )clear all
 
---S 4 of 14
+--S 14
 aa:=integrate(cosh(a*x)^n*sinh(a*x),x)
 --R 
 --R
@@ -88,6 +197,29 @@ aa:=integrate(cosh(a*x)^n*sinh(a*x),x)
 --R                    (a n + a)sinh(a x)  + (- a n - a)cosh(a x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 15
+bb:=cosh(a*x)^(n+1)/((n+1)*a)
+--R
+--R                 n + 1
+--R        cosh(a x)
+--R   (2)  --------------
+--R            a n + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 16     14:593 Axiom cannot simplify this expression
+--R
+--R   (3)
+--R       - cosh(a x)sinh(n log(cosh(a x))) - cosh(a x)cosh(n log(cosh(a x)))
+--R     + 
+--R                   2            2          n + 1
+--R       (- sinh(a x)  + cosh(a x) )cosh(a x)
+--R  /
+--R                       2                       2
+--R     (a n + a)sinh(a x)  + (- a n - a)cosh(a x)
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.594~~~~~$\displaystyle
@@ -98,7 +230,7 @@ $$
 <<*>>=
 )clear all
 
---S 5 of 14
+--S 17
 aa:=integrate(sinh(a*x)^2*cosh(a*x)^2,x)
 --R 
 --R
@@ -108,6 +240,22 @@ aa:=integrate(sinh(a*x)^2*cosh(a*x)^2,x)
 --R                               8a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 18
+bb:=sinh(4*a*x)/(32*a)-x/8
+--R
+--R        sinh(4a x) - 4a x
+--R   (2)  -----------------
+--R               32a
+--R                                                     Type: Expression Integer
+--E
+
+--S 19     14:594 Schaums and Axiom agree
+cc:=complexNormalize(aa-bb)
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.595~~~~~$\displaystyle
@@ -118,7 +266,7 @@ $$
 <<*>>=
 )clear all
 
---S 6 of 14
+--S 20
 aa:=integrate(1/(sinh(a*x)*cosh(a*x)),x)
 --R 
 --R
@@ -129,6 +277,67 @@ aa:=integrate(1/(sinh(a*x)*cosh(a*x)),x)
 --R                                      a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 21
+bb:=1/a*log(tanh(a*x))
+--R
+--R        log(tanh(a x))
+--R   (2)  --------------
+--R               a
+--R                                                     Type: Expression Integer
+--E
+
+--S 22
+cc:=aa-bb
+--R
+--R   (3)
+--R                                      2cosh(a x)
+--R       - log(tanh(a x)) - log(- ---------------------)
+--R                                sinh(a x) - cosh(a x)
+--R     + 
+--R                   2sinh(a x)
+--R       log(- ---------------------)
+--R             sinh(a x) - cosh(a x)
+--R  /
+--R     a
+--R                                                     Type: Expression Integer
+--E
+
+--S 23
+dd:=expandLog cc
+--R
+--R        - log(tanh(a x)) + log(sinh(a x)) - log(cosh(a x))
+--R   (4)  --------------------------------------------------
+--R                                 a
+--R                                                     Type: Expression Integer
+--E
+
+--S 24
+tanhrule:=rule(tanh(x) == sinh(x)/cosh(x))
+--R
+--R                   sinh(x)
+--R   (5)  tanh(x) == -------
+--R                   cosh(x)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 25
+ee:=tanhrule dd
+--R
+--R                             sinh(a x)
+--R        log(sinh(a x)) - log(---------) - log(cosh(a x))
+--R                             cosh(a x)
+--R   (6)  ------------------------------------------------
+--R                                a
+--R                                                     Type: Expression Integer
+--E
+
+--S 26     14:595 Schaums and Axiom agree
+ff:=expandLog ee
+--R
+--R   (7)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.596~~~~~$\displaystyle
@@ -139,17 +348,52 @@ $$
 <<*>>=
 )clear all
 
---S 7 of 14
-aa:=integrate(1/(sinh(a*x)^2*cos(a*x)),x)
---R 
+--S 27
+aa:=integrate(1/(sinh(a*x)^2*cosh(a*x)),x)
 --R
---R           x
---R         ++            1
---I   (1)   |   -------------------- d%R
---R        ++                      2
---I             cos(%R a)sinh(%R a)
+--R   (1)
+--R                      2                                   2
+--R         (- 2sinh(a x)  - 4cosh(a x)sinh(a x) - 2cosh(a x)  + 2)
+--R      *
+--R         atan(sinh(a x) + cosh(a x))
+--R     + 
+--R       - 2sinh(a x) - 2cosh(a x)
+--R  /
+--R                2                                      2
+--R     a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  - a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 28
+bb:=-1/a*atan(sinh(a*x)-csch(a*x))/a
+--R
+--R          atan(sinh(a x) - csch(a x))
+--R   (2)  - ---------------------------
+--R                        2
+--R                       a
+--R                                                     Type: Expression Integer
+--E
+
+--S 29     14:596 Axiom cannot simplify this expression
+cc:=aa-bb
+--R
+--R   (3)
+--R                        2                                       2
+--R         (- 2a sinh(a x)  - 4a cosh(a x)sinh(a x) - 2a cosh(a x)  + 2a)
+--R      *
+--R         atan(sinh(a x) + cosh(a x))
+--R     + 
+--R                   2                                  2
+--R         (sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  - 1)
+--R      *
+--R         atan(sinh(a x) - csch(a x))
+--R     + 
+--R       - 2a sinh(a x) - 2a cosh(a x)
+--R  /
+--R      2         2     2                      2         2    2
+--R     a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  - a
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.597~~~~~$\displaystyle
@@ -160,7 +404,7 @@ $$
 <<*>>=
 )clear all
 
---S 8 of 14
+--S 30
 aa:=integrate(1/(sinh(a*x)*cosh(a*x)^2),x)
 --R 
 --R
@@ -181,6 +425,272 @@ aa:=integrate(1/(sinh(a*x)*cosh(a*x)^2),x)
 --R     a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  + a
 --R                                          Type: Union(Expression Integer,...)
 --E
+
+--S 31
+bb:=sech(a*x)/a+1/a*log(tanh((a*x)/2))
+--R
+--R                 a x
+--R        log(tanh(---)) + sech(a x)
+--R                  2
+--R   (2)  --------------------------
+--R                     a
+--R                                                     Type: Expression Integer
+--E
+
+--S 32
+cc:=aa-bb
+--R
+--R   (3)
+--R                   2                                  2              a x
+--R       (- sinh(a x)  - 2cosh(a x)sinh(a x) - cosh(a x)  - 1)log(tanh(---))
+--R                                                                      2
+--R     + 
+--R                     2                                  2
+--R         (- sinh(a x)  - 2cosh(a x)sinh(a x) - cosh(a x)  - 1)
+--R      *
+--R         log(sinh(a x) + cosh(a x) + 1)
+--R     + 
+--R                   2                                  2
+--R         (sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  + 1)
+--R      *
+--R         log(sinh(a x) + cosh(a x) - 1)
+--R     + 
+--R                           2
+--R       - sech(a x)sinh(a x)  + (- 2cosh(a x)sech(a x) + 2)sinh(a x)
+--R     + 
+--R                   2
+--R       (- cosh(a x)  - 1)sech(a x) + 2cosh(a x)
+--R  /
+--R                2                                      2
+--R     a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 33
+sechrule:=rule(sech(x) == 1/cosh(x))
+--R
+--R                      1
+--R   (4)  sech(x) == -------
+--R                   cosh(x)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 34
+dd:=sechrule cc
+--R
+--R   (5)
+--R                              2             2                     3
+--R         (- cosh(a x)sinh(a x)  - 2cosh(a x) sinh(a x) - cosh(a x)  - cosh(a x))
+--R      *
+--R                  a x
+--R         log(tanh(---))
+--R                   2
+--R     + 
+--R                              2             2                     3
+--R         (- cosh(a x)sinh(a x)  - 2cosh(a x) sinh(a x) - cosh(a x)  - cosh(a x))
+--R      *
+--R         log(sinh(a x) + cosh(a x) + 1)
+--R     + 
+--R                            2             2                     3
+--R         (cosh(a x)sinh(a x)  + 2cosh(a x) sinh(a x) + cosh(a x)  + cosh(a x))
+--R      *
+--R         log(sinh(a x) + cosh(a x) - 1)
+--R     + 
+--R                  2            2
+--R       - sinh(a x)  + cosh(a x)  - 1
+--R  /
+--R                         2               2                       3
+--R     a cosh(a x)sinh(a x)  + 2a cosh(a x) sinh(a x) + a cosh(a x)  + a cosh(a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 35
+tanhrule:=rule(tanh(x) == sinh(x)/cosh(x))
+--R
+--R                   sinh(x)
+--R   (6)  tanh(x) == -------
+--R                   cosh(x)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 36
+ee:=tanhrule dd
+--R
+--R   (7)
+--R                              2             2                     3
+--R         (- cosh(a x)sinh(a x)  - 2cosh(a x) sinh(a x) - cosh(a x)  - cosh(a x))
+--R      *
+--R         log(sinh(a x) + cosh(a x) + 1)
+--R     + 
+--R                            2             2                     3
+--R         (cosh(a x)sinh(a x)  + 2cosh(a x) sinh(a x) + cosh(a x)  + cosh(a x))
+--R      *
+--R         log(sinh(a x) + cosh(a x) - 1)
+--R     + 
+--R                              2             2                     3
+--R         (- cosh(a x)sinh(a x)  - 2cosh(a x) sinh(a x) - cosh(a x)  - cosh(a x))
+--R      *
+--R                  a x
+--R             sinh(---)
+--R                   2
+--R         log(---------)
+--R                  a x
+--R             cosh(---)
+--R                   2
+--R     + 
+--R                  2            2
+--R       - sinh(a x)  + cosh(a x)  - 1
+--R  /
+--R                         2               2                       3
+--R     a cosh(a x)sinh(a x)  + 2a cosh(a x) sinh(a x) + a cosh(a x)  + a cosh(a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 37
+coshcuberule:=rule(cosh(x)^3 == 1/4*cosh(3*x)-3/4*cosh(x))
+--R
+--R               3    cosh(3x) - 3cosh(x)
+--R   (8)  cosh(x)  == -------------------
+--R                             4
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 38
+ff:=coshcuberule ee
+--R
+--R   (9)
+--R                                  2             2
+--R             - 4cosh(a x)sinh(a x)  - 8cosh(a x) sinh(a x) - cosh(3a x)
+--R           + 
+--R             - cosh(a x)
+--R      *
+--R         log(sinh(a x) + cosh(a x) + 1)
+--R     + 
+--R                             2             2
+--R         (4cosh(a x)sinh(a x)  + 8cosh(a x) sinh(a x) + cosh(3a x) + cosh(a x))
+--R      *
+--R         log(sinh(a x) + cosh(a x) - 1)
+--R     + 
+--R                                  2             2
+--R             - 4cosh(a x)sinh(a x)  - 8cosh(a x) sinh(a x) - cosh(3a x)
+--R           + 
+--R             - cosh(a x)
+--R      *
+--R                  a x
+--R             sinh(---)
+--R                   2
+--R         log(---------)
+--R                  a x
+--R             cosh(---)
+--R                   2
+--R     + 
+--R                   2             2
+--R       - 4sinh(a x)  + 4cosh(a x)  - 4
+--R  /
+--R                            2               2
+--R       4a cosh(a x)sinh(a x)  + 8a cosh(a x) sinh(a x) + a cosh(3a x)
+--R     + 
+--R       a cosh(a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 39
+coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2)
+--R
+--R                2    cosh(2x) + 1
+--R   (10)  cosh(x)  == ------------
+--R                           2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 40
+gg:=coshsqrrule ff
+--R
+--R   (11)
+--R                                2
+--R           - 4cosh(a x)sinh(a x)  + (- 4cosh(2a x) - 4)sinh(a x) - cosh(3a x)
+--R         + 
+--R           - cosh(a x)
+--R      *
+--R         log(sinh(a x) + cosh(a x) + 1)
+--R     + 
+--R                              2
+--R           4cosh(a x)sinh(a x)  + (4cosh(2a x) + 4)sinh(a x) + cosh(3a x)
+--R         + 
+--R           cosh(a x)
+--R      *
+--R         log(sinh(a x) + cosh(a x) - 1)
+--R     + 
+--R                                2
+--R           - 4cosh(a x)sinh(a x)  + (- 4cosh(2a x) - 4)sinh(a x) - cosh(3a x)
+--R         + 
+--R           - cosh(a x)
+--R      *
+--R                  a x
+--R             sinh(---)
+--R                   2
+--R         log(---------)
+--R                  a x
+--R             cosh(---)
+--R                   2
+--R     + 
+--R                   2
+--R       - 4sinh(a x)  + 2cosh(2a x) - 2
+--R  /
+--R                            2
+--R       4a cosh(a x)sinh(a x)  + (4a cosh(2a x) + 4a)sinh(a x) + a cosh(3a x)
+--R     + 
+--R       a cosh(a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 41
+sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2)
+--R
+--R                2    cosh(2x) - 1
+--R   (12)  sinh(x)  == ------------
+--R                           2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 42
+hh:=sinhsqrrule gg
+--R
+--R   (13)
+--R       - log(sinh(a x) + cosh(a x) + 1) + log(sinh(a x) + cosh(a x) - 1)
+--R     + 
+--R                  a x
+--R             sinh(---)
+--R                   2
+--R       - log(---------)
+--R                  a x
+--R             cosh(---)
+--R                   2
+--R  /
+--R     a
+--R                                                     Type: Expression Integer
+--E
+
+--S 43
+ii:=expandLog hh
+--R
+--R   (14)
+--R       - log(sinh(a x) + cosh(a x) + 1) + log(sinh(a x) + cosh(a x) - 1)
+--R     + 
+--R                  a x              a x
+--R       - log(sinh(---)) + log(cosh(---))
+--R                   2                2
+--R  /
+--R     a
+--R                                                     Type: Expression Integer
+--E
+
+--S 44     14:597 Schaums and Axiom agree
+jj:=complexNormalize ii
+--R
+--R   (15)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.598~~~~~$\displaystyle
@@ -191,7 +701,7 @@ $$
 <<*>>=
 )clear all
 
---S 9 of 14
+--S 45
 aa:=integrate(1/(sinh(a*x)^2*cosh(a*x)^2),x)
 --R 
 --R
@@ -206,6 +716,35 @@ aa:=integrate(1/(sinh(a*x)^2*cosh(a*x)^2),x)
 --R          4a cosh(a x) sinh(a x) + a cosh(a x)  - a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 46
+bb:=-(2*coth(2*a*x))/a
+--R
+--R          2coth(2a x)
+--R   (2)  - -----------
+--R               a
+--R                                                     Type: Expression Integer
+--E
+
+--S 47     14:598 Axiom cannot simplify this expression
+--R
+--R   (3)
+--R                           4                                3
+--R       2coth(2a x)sinh(a x)  + 8cosh(a x)coth(2a x)sinh(a x)
+--R     + 
+--R                  2                   2             3
+--R       12cosh(a x) coth(2a x)sinh(a x)  + 8cosh(a x) coth(2a x)sinh(a x)
+--R     + 
+--R                  4
+--R       (2cosh(a x)  - 2)coth(2a x) - 4
+--R  /
+--R                  4                        3               2         2
+--R       a sinh(a x)  + 4a cosh(a x)sinh(a x)  + 6a cosh(a x) sinh(a x)
+--R     + 
+--R                   3                       4
+--R       4a cosh(a x) sinh(a x) + a cosh(a x)  - a
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.599~~~~~$\displaystyle
@@ -216,7 +755,7 @@ $$
 <<*>>=
 )clear all
 
---S 10 of 14
+--S 48
 aa:=integrate(sinh(a*x)^2/cosh(a*x),x)
 --R 
 --R
@@ -230,6 +769,28 @@ aa:=integrate(sinh(a*x)^2/cosh(a*x),x)
 --R     2a sinh(a x) + 2a cosh(a x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 49
+bb:=sinh(a*x)/a-1/a*atan(sinh(a*x))
+--R
+--R        - atan(sinh(a x)) + sinh(a x)
+--R   (2)  -----------------------------
+--R                      a
+--R                                                     Type: Expression Integer
+--E
+
+--S 50     14:599 Axiom cannot simplify this expression
+cc:=aa-bb
+--R
+--R   (3)
+--R       (- 4sinh(a x) - 4cosh(a x))atan(sinh(a x) + cosh(a x))
+--R     + 
+--R                                                           2            2
+--R       (2sinh(a x) + 2cosh(a x))atan(sinh(a x)) - sinh(a x)  + cosh(a x)  - 1
+--R  /
+--R     2a sinh(a x) + 2a cosh(a x)
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.600~~~~~$\displaystyle
@@ -240,7 +801,7 @@ $$
 <<*>>=
 )clear all
 
---S 11 of 14
+--S 51
 aa:=integrate(cosh(a*x)^2/sinh(a*x),x)
 --R 
 --R
@@ -256,6 +817,37 @@ aa:=integrate(cosh(a*x)^2/sinh(a*x),x)
 --R     2a sinh(a x) + 2a cosh(a x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 52
+bb:=cosh(a*x)/a+1/a*log(tanh((a*x)/2))
+--R
+--R                 a x
+--R        log(tanh(---)) + cosh(a x)
+--R                  2
+--R   (2)  --------------------------
+--R                     a
+--R                                                     Type: Expression Integer
+--E
+
+--S 53     14:600 Axiom cannot simplify this expression
+cc:=aa-bb
+--R
+--R   (3)
+--R                                           a x
+--R       (- 2sinh(a x) - 2cosh(a x))log(tanh(---))
+--R                                            2
+--R     + 
+--R       (- 2sinh(a x) - 2cosh(a x))log(sinh(a x) + cosh(a x) + 1)
+--R     + 
+--R                                                                          2
+--R       (2sinh(a x) + 2cosh(a x))log(sinh(a x) + cosh(a x) - 1) + sinh(a x)
+--R     + 
+--R                  2
+--R       - cosh(a x)  + 1
+--R  /
+--R     2a sinh(a x) + 2a cosh(a x)
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.601~~~~~$\displaystyle
@@ -267,7 +859,7 @@ $$
 <<*>>=
 )clear all
 
---S 12 of 14
+--S 54
 aa:=integrate(1/(cosh(a*x)*(1+sinh(a*x))),x)
 --R 
 --R
@@ -281,6 +873,87 @@ aa:=integrate(1/(cosh(a*x)*(1+sinh(a*x))),x)
 --R     2a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 55
+bb:=1/(2*a)*log((1+sinh(a*x))/cosh(a*x))+1/a*atan(%e^(a*x))
+--R
+--R            sinh(a x) + 1            a x
+--R        log(-------------) + 2atan(%e   )
+--R              cosh(a x)
+--R   (2)  ---------------------------------
+--R                        2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 56
+cc:=aa-bb
+--R
+--R   (3)
+--R             sinh(a x) + 1                2cosh(a x)
+--R       - log(-------------) - log(- ---------------------)
+--R               cosh(a x)            sinh(a x) - cosh(a x)
+--R     + 
+--R              - 2sinh(a x) - 2                                             a x
+--R       log(---------------------) + 2atan(sinh(a x) + cosh(a x)) - 2atan(%e   )
+--R           sinh(a x) - cosh(a x)
+--R  /
+--R     2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 57
+dd:=expandLog cc
+--R
+--R                                             a x
+--R        atan(sinh(a x) + cosh(a x)) - atan(%e   )
+--R   (4)  -----------------------------------------
+--R                            a
+--R                                                     Type: Expression Integer
+--E
+
+--S 58
+atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
+--R
+--R                            - x + %i
+--R                     %i log(--------)
+--R                             x + %i
+--R   (5)  atan(x) == - ----------------
+--R                             2
+--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
+--E
+
+--S 59
+ee:=atanrule dd
+--R
+--R                   a x
+--R               - %e    + %i           - sinh(a x) - cosh(a x) + %i
+--R        %i log(------------) - %i log(----------------------------)
+--R                  a x                  sinh(a x) + cosh(a x) + %i
+--R                %e    + %i
+--R   (6)  -----------------------------------------------------------
+--R                                     2a
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 60
+ff:=expandLog ee
+--R
+--R   (7)
+--R       %i log(sinh(a x) + cosh(a x) + %i) - %i log(sinh(a x) + cosh(a x) - %i)
+--R     + 
+--R                  a x                  a x
+--R       - %i log(%e    + %i) + %i log(%e    - %i)
+--R  /
+--R     2a
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 61     14:601 Schaums and Axiom agree
+gg:=complexNormalize ff
+--R
+--R   (8)  0
+--R                                             Type: Expression Complex Integer
+--E
 @
 
 \section{\cite{1}:14.602~~~~~$\displaystyle
@@ -291,7 +964,7 @@ $$
 <<*>>=
 )clear all
 
---S 13 of 14
+--S 62
 aa:=integrate(1/(sinh(a*x)*(cosh(a*x)+1)),x)
 --R 
 --R
@@ -316,6 +989,204 @@ aa:=integrate(1/(sinh(a*x)*(cosh(a*x)+1)),x)
 --R       4a cosh(a x) + 2a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 63
+bb:=1/(2*a)*log(tanh((a*x)/2))+1/(2*a*(cosh(a*x)+1))
+--R
+--R                                a x
+--R        (cosh(a x) + 1)log(tanh(---)) + 1
+--R                                 2
+--R   (2)  ---------------------------------
+--R                2a cosh(a x) + 2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 64
+cc:=aa-bb
+--R
+--R   (3)
+--R                                     2
+--R           (- cosh(a x) - 1)sinh(a x)
+--R         + 
+--R                        2                                       3             2
+--R           (- 2cosh(a x)  - 4cosh(a x) - 2)sinh(a x) - cosh(a x)  - 3cosh(a x)
+--R         + 
+--R           - 3cosh(a x) - 1
+--R      *
+--R                  a x
+--R         log(tanh(---))
+--R                   2
+--R     + 
+--R                                     2
+--R           (- cosh(a x) - 1)sinh(a x)
+--R         + 
+--R                        2                                       3             2
+--R           (- 2cosh(a x)  - 4cosh(a x) - 2)sinh(a x) - cosh(a x)  - 3cosh(a x)
+--R         + 
+--R           - 3cosh(a x) - 1
+--R      *
+--R         log(sinh(a x) + cosh(a x) + 1)
+--R     + 
+--R                                   2              2
+--R           (cosh(a x) + 1)sinh(a x)  + (2cosh(a x)  + 4cosh(a x) + 2)sinh(a x)
+--R         + 
+--R                    3             2
+--R           cosh(a x)  + 3cosh(a x)  + 3cosh(a x) + 1
+--R      *
+--R         log(sinh(a x) + cosh(a x) - 1)
+--R     + 
+--R                  2            2
+--R       - sinh(a x)  + cosh(a x)  - 1
+--R  /
+--R                                   2
+--R       (2a cosh(a x) + 2a)sinh(a x)
+--R     + 
+--R                    2                                             3
+--R       (4a cosh(a x)  + 8a cosh(a x) + 4a)sinh(a x) + 2a cosh(a x)
+--R     + 
+--R                   2
+--R       6a cosh(a x)  + 6a cosh(a x) + 2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 65
+coshcuberule:=rule(cosh(x)^3 == 1/4*cosh(3*x)-3/4*cosh(x))
+--R
+--R               3    cosh(3x) - 3cosh(x)
+--R   (4)  cosh(x)  == -------------------
+--R                             4
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 66
+dd:=coshcuberule cc
+--R
+--R   (5)
+--R                                      2
+--R           (- 4cosh(a x) - 4)sinh(a x)
+--R         + 
+--R                        2
+--R           (- 8cosh(a x)  - 16cosh(a x) - 8)sinh(a x) - cosh(3a x)
+--R         + 
+--R                        2
+--R           - 12cosh(a x)  - 9cosh(a x) - 4
+--R      *
+--R                  a x
+--R         log(tanh(---))
+--R                   2
+--R     + 
+--R                                      2
+--R           (- 4cosh(a x) - 4)sinh(a x)
+--R         + 
+--R                        2
+--R           (- 8cosh(a x)  - 16cosh(a x) - 8)sinh(a x) - cosh(3a x)
+--R         + 
+--R                        2
+--R           - 12cosh(a x)  - 9cosh(a x) - 4
+--R      *
+--R         log(sinh(a x) + cosh(a x) + 1)
+--R     + 
+--R                                    2              2
+--R           (4cosh(a x) + 4)sinh(a x)  + (8cosh(a x)  + 16cosh(a x) + 8)sinh(a x)
+--R         + 
+--R                                   2
+--R           cosh(3a x) + 12cosh(a x)  + 9cosh(a x) + 4
+--R      *
+--R         log(sinh(a x) + cosh(a x) - 1)
+--R     + 
+--R                   2             2
+--R       - 4sinh(a x)  + 4cosh(a x)  - 4
+--R  /
+--R                                   2
+--R       (8a cosh(a x) + 8a)sinh(a x)
+--R     + 
+--R                     2
+--R       (16a cosh(a x)  + 32a cosh(a x) + 16a)sinh(a x) + 2a cosh(3a x)
+--R     + 
+--R                    2
+--R       24a cosh(a x)  + 18a cosh(a x) + 8a
+--R                                                     Type: Expression Integer
+--E
+
+--S 67
+sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2)
+--R
+--R               2    cosh(2x) - 1
+--R   (6)  sinh(x)  == ------------
+--R                          2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 68
+ee:=sinhsqrrule dd
+--R
+--R   (7)
+--R                        2
+--R           (- 8cosh(a x)  - 16cosh(a x) - 8)sinh(a x) - cosh(3a x)
+--R         + 
+--R                                                     2
+--R           (- 2cosh(a x) - 2)cosh(2a x) - 12cosh(a x)  - 7cosh(a x) - 2
+--R      *
+--R                  a x
+--R         log(tanh(---))
+--R                   2
+--R     + 
+--R                        2
+--R           (- 8cosh(a x)  - 16cosh(a x) - 8)sinh(a x) - cosh(3a x)
+--R         + 
+--R                                                     2
+--R           (- 2cosh(a x) - 2)cosh(2a x) - 12cosh(a x)  - 7cosh(a x) - 2
+--R      *
+--R         log(sinh(a x) + cosh(a x) + 1)
+--R     + 
+--R                      2
+--R           (8cosh(a x)  + 16cosh(a x) + 8)sinh(a x) + cosh(3a x)
+--R         + 
+--R                                                   2
+--R           (2cosh(a x) + 2)cosh(2a x) + 12cosh(a x)  + 7cosh(a x) + 2
+--R      *
+--R         log(sinh(a x) + cosh(a x) - 1)
+--R     + 
+--R                                 2
+--R       - 2cosh(2a x) + 4cosh(a x)  - 2
+--R  /
+--R                     2
+--R       (16a cosh(a x)  + 32a cosh(a x) + 16a)sinh(a x) + 2a cosh(3a x)
+--R     + 
+--R                                                    2
+--R       (4a cosh(a x) + 4a)cosh(2a x) + 24a cosh(a x)  + 14a cosh(a x) + 4a
+--R                                                     Type: Expression Integer
+--E
+
+--S 69
+coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2)
+--R
+--R               2    cosh(2x) + 1
+--R   (8)  cosh(x)  == ------------
+--R                          2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 70
+ff:=coshsqrrule ee
+--R
+--R   (9)
+--R                  a x
+--R       - log(tanh(---)) - log(sinh(a x) + cosh(a x) + 1)
+--R                   2
+--R     + 
+--R       log(sinh(a x) + cosh(a x) - 1)
+--R  /
+--R     2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 71     14:602 Schaums and Axiom agree
+gg:=complexNormalize ff
+--R
+--R   (10)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.603~~~~~$\displaystyle
@@ -326,7 +1197,7 @@ $$
 <<*>>=
 )clear all
 
---S 14 of 14
+--S 72
 aa:=integrate(1/(sinh(a*x)*(cosh(a*x)-1)),x)
 --R 
 --R
@@ -352,6 +1223,199 @@ aa:=integrate(1/(sinh(a*x)*(cosh(a*x)-1)),x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
 
+--S 73
+bb:=-1/(2*a)*log(tanh((a*x)/2))-1/(2*a*(cosh(a*x)-1))
+--R
+--R                                  a x
+--R        (- cosh(a x) + 1)log(tanh(---)) - 1
+--R                                   2
+--R   (2)  -----------------------------------
+--R                 2a cosh(a x) - 2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 74
+cc:=aa-bb
+--R
+--R   (3)
+--R                                   2              2
+--R           (cosh(a x) - 1)sinh(a x)  + (2cosh(a x)  - 4cosh(a x) + 2)sinh(a x)
+--R         + 
+--R                    3             2
+--R           cosh(a x)  - 3cosh(a x)  + 3cosh(a x) - 1
+--R      *
+--R                  a x
+--R         log(tanh(---))
+--R                   2
+--R     + 
+--R                                   2              2
+--R           (cosh(a x) - 1)sinh(a x)  + (2cosh(a x)  - 4cosh(a x) + 2)sinh(a x)
+--R         + 
+--R                    3             2
+--R           cosh(a x)  - 3cosh(a x)  + 3cosh(a x) - 1
+--R      *
+--R         log(sinh(a x) + cosh(a x) + 1)
+--R     + 
+--R                                     2
+--R           (- cosh(a x) + 1)sinh(a x)
+--R         + 
+--R                        2                                       3             2
+--R           (- 2cosh(a x)  + 4cosh(a x) - 2)sinh(a x) - cosh(a x)  + 3cosh(a x)
+--R         + 
+--R           - 3cosh(a x) + 1
+--R      *
+--R         log(sinh(a x) + cosh(a x) - 1)
+--R     + 
+--R                2            2
+--R       sinh(a x)  - cosh(a x)  + 1
+--R  /
+--R                                   2
+--R       (2a cosh(a x) - 2a)sinh(a x)
+--R     + 
+--R                    2                                             3
+--R       (4a cosh(a x)  - 8a cosh(a x) + 4a)sinh(a x) + 2a cosh(a x)
+--R     + 
+--R                     2
+--R       - 6a cosh(a x)  + 6a cosh(a x) - 2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 75
+coshcuberule:=rule(cosh(x)^3 == 1/4*cosh(3*x)-3/4*cosh(x))
+--R
+--R               3    cosh(3x) - 3cosh(x)
+--R   (4)  cosh(x)  == -------------------
+--R                             4
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 76
+dd:=coshcuberule cc
+--R
+--R   (5)
+--R                                    2              2
+--R           (4cosh(a x) - 4)sinh(a x)  + (8cosh(a x)  - 16cosh(a x) + 8)sinh(a x)
+--R         + 
+--R                                   2
+--R           cosh(3a x) - 12cosh(a x)  + 9cosh(a x) - 4
+--R      *
+--R                  a x
+--R         log(tanh(---))
+--R                   2
+--R     + 
+--R                                    2              2
+--R           (4cosh(a x) - 4)sinh(a x)  + (8cosh(a x)  - 16cosh(a x) + 8)sinh(a x)
+--R         + 
+--R                                   2
+--R           cosh(3a x) - 12cosh(a x)  + 9cosh(a x) - 4
+--R      *
+--R         log(sinh(a x) + cosh(a x) + 1)
+--R     + 
+--R                                      2
+--R           (- 4cosh(a x) + 4)sinh(a x)
+--R         + 
+--R                        2
+--R           (- 8cosh(a x)  + 16cosh(a x) - 8)sinh(a x) - cosh(3a x)
+--R         + 
+--R                      2
+--R           12cosh(a x)  - 9cosh(a x) + 4
+--R      *
+--R         log(sinh(a x) + cosh(a x) - 1)
+--R     + 
+--R                 2             2
+--R       4sinh(a x)  - 4cosh(a x)  + 4
+--R  /
+--R                                   2
+--R       (8a cosh(a x) - 8a)sinh(a x)
+--R     + 
+--R                     2
+--R       (16a cosh(a x)  - 32a cosh(a x) + 16a)sinh(a x) + 2a cosh(3a x)
+--R     + 
+--R                      2
+--R       - 24a cosh(a x)  + 18a cosh(a x) - 8a
+--R                                                     Type: Expression Integer
+--E
+
+--S 77
+sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2)
+--R
+--R               2    cosh(2x) - 1
+--R   (6)  sinh(x)  == ------------
+--R                          2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 78
+ee:=sinhsqrrule dd
+--R
+--R   (7)
+--R                      2
+--R           (8cosh(a x)  - 16cosh(a x) + 8)sinh(a x) + cosh(3a x)
+--R         + 
+--R                                                   2
+--R           (2cosh(a x) - 2)cosh(2a x) - 12cosh(a x)  + 7cosh(a x) - 2
+--R      *
+--R                  a x
+--R         log(tanh(---))
+--R                   2
+--R     + 
+--R                      2
+--R           (8cosh(a x)  - 16cosh(a x) + 8)sinh(a x) + cosh(3a x)
+--R         + 
+--R                                                   2
+--R           (2cosh(a x) - 2)cosh(2a x) - 12cosh(a x)  + 7cosh(a x) - 2
+--R      *
+--R         log(sinh(a x) + cosh(a x) + 1)
+--R     + 
+--R                        2
+--R           (- 8cosh(a x)  + 16cosh(a x) - 8)sinh(a x) - cosh(3a x)
+--R         + 
+--R                                                     2
+--R           (- 2cosh(a x) + 2)cosh(2a x) + 12cosh(a x)  - 7cosh(a x) + 2
+--R      *
+--R         log(sinh(a x) + cosh(a x) - 1)
+--R     + 
+--R                               2
+--R       2cosh(2a x) - 4cosh(a x)  + 2
+--R  /
+--R                     2
+--R       (16a cosh(a x)  - 32a cosh(a x) + 16a)sinh(a x) + 2a cosh(3a x)
+--R     + 
+--R                                                    2
+--R       (4a cosh(a x) - 4a)cosh(2a x) - 24a cosh(a x)  + 14a cosh(a x) - 4a
+--R                                                     Type: Expression Integer
+--E
+
+--S 79
+coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2)
+--R
+--R               2    cosh(2x) + 1
+--R   (8)  cosh(x)  == ------------
+--R                          2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 80
+ff:=coshsqrrule ee
+--R
+--R   (9)
+--R                a x
+--R       log(tanh(---)) + log(sinh(a x) + cosh(a x) + 1)
+--R                 2
+--R     + 
+--R       - log(sinh(a x) + cosh(a x) - 1)
+--R  /
+--R     2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 81     14:603 Schaums and Axiom agree
+gg:=complexNormalize ff
+--R
+--R   (10)  0
+--R                                                     Type: Expression Integer
+--E
+
 )spool
 )lisp (bye)
 @
diff --git a/src/input/schaum30.input.pamphlet b/src/input/schaum30.input.pamphlet
index 0e1aaf4..5df48bc 100644
--- a/src/input/schaum30.input.pamphlet
+++ b/src/input/schaum30.input.pamphlet
@@ -18,7 +18,7 @@ $$
 )set message auto off
 )clear all
 
---S 1 of 11
+--S 1
 aa:=integrate(tanh(a*x),x)
 --R 
 --R
@@ -29,6 +29,44 @@ aa:=integrate(tanh(a*x),x)
 --R                         a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 2
+bb:=1/a*log(cosh(a*x))
+--R
+--R        log(cosh(a x))
+--R   (2)  --------------
+--R               a
+--R                                                     Type: Expression Integer
+--E
+
+--S 3
+cc:=aa-bb
+--R
+--R                                       2cosh(a x)
+--R        - log(cosh(a x)) + log(- ---------------------) - a x
+--R                                 sinh(a x) - cosh(a x)
+--R   (3)  -----------------------------------------------------
+--R                                  a
+--R                                                     Type: Expression Integer
+--E
+
+--S 4
+dd:=expandLog cc
+--R
+--R        - log(sinh(a x) - cosh(a x)) + log(- 2) - a x
+--R   (4)  ---------------------------------------------
+--R                              a
+--R                                                     Type: Expression Integer
+--E
+
+--S 5      14:604 Schaums and Axiom differ by a constant
+ee:=complexNormalize dd
+--R
+--R        - log(- 1) + log(- 2)
+--R   (5)  ---------------------
+--R                  a
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.605~~~~~$\displaystyle
@@ -39,7 +77,7 @@ $$
 <<*>>=
 )clear all
 
---S 2 of 11
+--S 6
 aa:=integrate(tanh(a*x)^2,x)
 --R 
 --R
@@ -48,6 +86,42 @@ aa:=integrate(tanh(a*x)^2,x)
 --R                   a cosh(a x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 7
+bb:=x-tanh(a*x)/a
+--R
+--R        - tanh(a x) + a x
+--R   (2)  -----------------
+--R                a
+--R                                                     Type: Expression Integer
+--E
+
+--S 8
+cc:=aa-bb
+--R
+--R        cosh(a x)tanh(a x) - sinh(a x) + cosh(a x)
+--R   (3)  ------------------------------------------
+--R                        a cosh(a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 9
+tanhrule:=rule(tanh(x) == sinh(x)/cosh(x))
+--R
+--R                   sinh(x)
+--R   (4)  tanh(x) == -------
+--R                   cosh(x)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 10     14:605 Schaums and Axiom differ by a constant
+dd:=tanhrule cc
+--R
+--R        1
+--R   (5)  -
+--R        a
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.606~~~~~$\displaystyle
@@ -58,7 +132,7 @@ $$
 <<*>>=
 )clear all
 
---S 3 of 11
+--S 11
 aa:=integrate(tanh(a*x)^3,x)
 --R 
 --R
@@ -92,6 +166,69 @@ aa:=integrate(tanh(a*x)^3,x)
 --R     (4a cosh(a x)  + 4a cosh(a x))sinh(a x) + a cosh(a x)  + 2a cosh(a x)  + a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 12
+bb:=1/a*log(cosh(a*x))-tanh(a*x)^2/(2*a)
+--R
+--R                                   2
+--R        2log(cosh(a x)) - tanh(a x)
+--R   (2)  ----------------------------
+--R                     2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 13     14:606 Axiom cannot simplify this expression
+cc:=aa-bb
+--R
+--R   (3)
+--R                       4                      3                 2              2
+--R           - 2sinh(a x)  - 8cosh(a x)sinh(a x)  + (- 12cosh(a x)  - 4)sinh(a x)
+--R         + 
+--R                      3                                    4             2
+--R         (- 8cosh(a x)  - 8cosh(a x))sinh(a x) - 2cosh(a x)  - 4cosh(a x)  - 2
+--R      *
+--R         log(cosh(a x))
+--R     + 
+--R                     4                      3               2              2
+--R           2sinh(a x)  + 8cosh(a x)sinh(a x)  + (12cosh(a x)  + 4)sinh(a x)
+--R         + 
+--R                      3                                    4             2
+--R           (8cosh(a x)  + 8cosh(a x))sinh(a x) + 2cosh(a x)  + 4cosh(a x)  + 2
+--R      *
+--R                     2cosh(a x)
+--R         log(- ---------------------)
+--R               sinh(a x) - cosh(a x)
+--R     + 
+--R                    4                      3              2              2
+--R           sinh(a x)  + 4cosh(a x)sinh(a x)  + (6cosh(a x)  + 2)sinh(a x)
+--R         + 
+--R                      3                                   4             2
+--R           (4cosh(a x)  + 4cosh(a x))sinh(a x) + cosh(a x)  + 2cosh(a x)  + 1
+--R      *
+--R                  2
+--R         tanh(a x)
+--R     + 
+--R                       4                          3
+--R       - 2a x sinh(a x)  - 8a x cosh(a x)sinh(a x)
+--R     + 
+--R                         2                     2
+--R       (- 12a x cosh(a x)  - 4a x + 4)sinh(a x)
+--R     + 
+--R                        3                                                   4
+--R       (- 8a x cosh(a x)  + (- 8a x + 8)cosh(a x))sinh(a x) - 2a x cosh(a x)
+--R     + 
+--R                            2
+--R       (- 4a x + 4)cosh(a x)  - 2a x
+--R  /
+--R                   4                        3                 2               2
+--R       2a sinh(a x)  + 8a cosh(a x)sinh(a x)  + (12a cosh(a x)  + 4a)sinh(a x)
+--R     + 
+--R                    3                                        4               2
+--R       (8a cosh(a x)  + 8a cosh(a x))sinh(a x) + 2a cosh(a x)  + 4a cosh(a x)
+--R     + 
+--R       2a
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.607~~~~~$\displaystyle
@@ -102,7 +239,7 @@ $$
 <<*>>=
 )clear all
 
---S 4 of 11
+--S 14
 aa:=integrate(tanh(a*x)^n*sech(a*x)^2,x)
 --R 
 --R
@@ -113,6 +250,31 @@ aa:=integrate(tanh(a*x)^n*sech(a*x)^2,x)
 --R                                (a n + a)cosh(a x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 15
+bb:=tanh(a*x)^(n+1)/((n+1)*a)
+--R
+--R                 n + 1
+--R        tanh(a x)
+--R   (2)  --------------
+--R            a n + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 16     14:607 Axiom cannot simplify this expression
+cc:=aa-bb
+--R
+--R   (3)
+--R                           sinh(a x)                         sinh(a x)
+--R       sinh(a x)sinh(n log(---------)) + sinh(a x)cosh(n log(---------))
+--R                           cosh(a x)                         cosh(a x)
+--R     + 
+--R                           n + 1
+--R       - cosh(a x)tanh(a x)
+--R  /
+--R     (a n + a)cosh(a x)
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.608~~~~~$\displaystyle
@@ -123,7 +285,7 @@ $$
 <<*>>=
 )clear all
 
---S 5 of 11
+--S 17
 aa:=integrate(sech(a*x)^2/tanh(a*x),x)
 --R 
 --R
@@ -134,6 +296,63 @@ aa:=integrate(sech(a*x)^2/tanh(a*x),x)
 --R                                      a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 18
+bb:=1/a*log(tanh(a*x))
+--R
+--R        log(tanh(a x))
+--R   (2)  --------------
+--R               a
+--R                                                     Type: Expression Integer
+--E
+
+--S 19
+cc:=aa-bb
+--R
+--R   (3)
+--R                                      2cosh(a x)
+--R       - log(tanh(a x)) - log(- ---------------------)
+--R                                sinh(a x) - cosh(a x)
+--R     + 
+--R                   2sinh(a x)
+--R       log(- ---------------------)
+--R             sinh(a x) - cosh(a x)
+--R  /
+--R     a
+--R                                                     Type: Expression Integer
+--E
+
+--S 20
+tanhrule:=rule(tanh(x) == sinh(x)/cosh(x))
+--R
+--R                   sinh(x)
+--R   (4)  tanh(x) == -------
+--R                   cosh(x)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 21
+dd:=tanhrule cc
+--R
+--R   (5)
+--R             sinh(a x)                2cosh(a x)
+--R       - log(---------) - log(- ---------------------)
+--R             cosh(a x)          sinh(a x) - cosh(a x)
+--R     + 
+--R                   2sinh(a x)
+--R       log(- ---------------------)
+--R             sinh(a x) - cosh(a x)
+--R  /
+--R     a
+--R                                                     Type: Expression Integer
+--E
+
+--S 22     14:608 Schaums and Axiom agree
+ee:=expandLog dd
+--R
+--R   (6)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.609~~~~~$\displaystyle
@@ -144,7 +363,7 @@ $$
 <<*>>=
 )clear all
 
---S 6 of 11
+--S 23
 aa:=integrate(1/tanh(a*x),x)
 --R 
 --R
@@ -155,6 +374,44 @@ aa:=integrate(1/tanh(a*x),x)
 --R                         a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 24
+bb:=1/a*log(sinh(a*x))
+--R
+--R        log(sinh(a x))
+--R   (2)  --------------
+--R               a
+--R                                                     Type: Expression Integer
+--E
+
+--S 25
+cc:=aa-bb
+--R
+--R                                       2sinh(a x)
+--R        - log(sinh(a x)) + log(- ---------------------) - a x
+--R                                 sinh(a x) - cosh(a x)
+--R   (3)  -----------------------------------------------------
+--R                                  a
+--R                                                     Type: Expression Integer
+--E
+
+--S 26
+dd:=expandLog cc
+--R
+--R        - log(sinh(a x) - cosh(a x)) + log(- 2) - a x
+--R   (4)  ---------------------------------------------
+--R                              a
+--R                                                     Type: Expression Integer
+--E
+
+--S 27     14:609 Schaums and Axiom differ by a constant
+ee:=complexNormalize dd
+--R
+--R        - log(- 1) + log(- 2)
+--R   (5)  ---------------------
+--R                  a
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.610~~~~~$\displaystyle
@@ -167,7 +424,7 @@ $$
 <<*>>=
 )clear all
 
---S 7 of 11
+--S 28     14:610 Axiom cannot compute this integral
 aa:=integrate(x*tanh(a*x),x)
 --R 
 --R
@@ -187,7 +444,7 @@ $$
 <<*>>=
 )clear all
 
---S 8 of 11
+--S 29
 aa:=integrate(x*tanh(a*x)^2,x)
 --R 
 --R
@@ -209,6 +466,159 @@ aa:=integrate(x*tanh(a*x)^2,x)
 --R     2a sinh(a x)  + 4a cosh(a x)sinh(a x) + 2a cosh(a x)  + 2a
 --R                                          Type: Union(Expression Integer,...)
 --E
+
+--S 30
+bb:=x^2/2-(x*tanh(a*x))/a+1/a^2*log(cosh(a*x))
+--R
+--R                                            2 2
+--R        2log(cosh(a x)) - 2a x tanh(a x) + a x
+--R   (2)  ---------------------------------------
+--R                            2
+--R                          2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 31
+cc:=aa-bb
+--R
+--R   (3)
+--R                   2                                  2
+--R       (- sinh(a x)  - 2cosh(a x)sinh(a x) - cosh(a x)  - 1)log(cosh(a x))
+--R     + 
+--R                   2                                  2
+--R         (sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  + 1)
+--R      *
+--R                     2cosh(a x)
+--R         log(- ---------------------)
+--R               sinh(a x) - cosh(a x)
+--R     + 
+--R                       2                                          2
+--R         (a x sinh(a x)  + 2a x cosh(a x)sinh(a x) + a x cosh(a x)  + a x)
+--R      *
+--R         tanh(a x)
+--R     + 
+--R                       2                                           2
+--R       - 2a x sinh(a x)  - 4a x cosh(a x)sinh(a x) - 2a x cosh(a x)
+--R  /
+--R      2         2     2                      2         2    2
+--R     a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 32
+sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2)
+--R
+--R               2    cosh(2x) - 1
+--R   (4)  sinh(x)  == ------------
+--R                          2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 33
+dd:=sinhsqrrule cc
+--R
+--R   (5)
+--R                                                       2
+--R       (- 4cosh(a x)sinh(a x) - cosh(2a x) - 2cosh(a x)  - 1)log(cosh(a x))
+--R     + 
+--R                                                       2
+--R         (4cosh(a x)sinh(a x) + cosh(2a x) + 2cosh(a x)  + 1)
+--R      *
+--R                     2cosh(a x)
+--R         log(- ---------------------)
+--R               sinh(a x) - cosh(a x)
+--R     + 
+--R                                                                   2
+--R         (4a x cosh(a x)sinh(a x) + a x cosh(2a x) + 2a x cosh(a x)  + a x)
+--R      *
+--R         tanh(a x)
+--R     + 
+--R                                                                   2
+--R       - 8a x cosh(a x)sinh(a x) - 2a x cosh(2a x) - 4a x cosh(a x)  + 2a x
+--R  /
+--R       2                      2               2         2    2
+--R     4a cosh(a x)sinh(a x) + a cosh(2a x) + 2a cosh(a x)  + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 34
+coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2)
+--R
+--R               2    cosh(2x) + 1
+--R   (6)  cosh(x)  == ------------
+--R                          2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 35
+ee:=coshsqrrule dd
+--R
+--R   (7)
+--R       (- 2cosh(a x)sinh(a x) - cosh(2a x) - 1)log(cosh(a x))
+--R     + 
+--R                                                         2cosh(a x)
+--R       (2cosh(a x)sinh(a x) + cosh(2a x) + 1)log(- ---------------------)
+--R                                                   sinh(a x) - cosh(a x)
+--R     + 
+--R       (2a x cosh(a x)sinh(a x) + a x cosh(2a x) + a x)tanh(a x)
+--R     + 
+--R       - 4a x cosh(a x)sinh(a x) - 2a x cosh(2a x)
+--R  /
+--R       2                      2              2
+--R     2a cosh(a x)sinh(a x) + a cosh(2a x) + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 36
+ff:=expandLog ee
+--R
+--R   (8)
+--R       (- 2cosh(a x)sinh(a x) - cosh(2a x) - 1)log(sinh(a x) - cosh(a x))
+--R     + 
+--R       (2a x cosh(a x)sinh(a x) + a x cosh(2a x) + a x)tanh(a x)
+--R     + 
+--R       (2log(- 2) - 4a x)cosh(a x)sinh(a x) + (log(- 2) - 2a x)cosh(2a x)
+--R     + 
+--R       log(- 2)
+--R  /
+--R       2                      2              2
+--R     2a cosh(a x)sinh(a x) + a cosh(2a x) + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 37
+sinhcoshrule:=rule(sinh(x)*cosh(y) == 1/2*(sinh(x+y)+sinh(x-y)))
+--R
+--I                             %N sinh(y + x) - %N sinh(y - x)
+--I   (9)  %N cosh(y)sinh(x) == -------------------------------
+--R                                            2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 38
+gg:=sinhcoshrule ff
+--R
+--R   (10)
+--R       (- sinh(2a x) - cosh(2a x) - 1)log(sinh(a x) - cosh(a x))
+--R     + 
+--R       (a x sinh(2a x) + a x cosh(2a x) + a x)tanh(a x)
+--R     + 
+--R       (log(- 2) - 2a x)sinh(2a x) + (log(- 2) - 2a x)cosh(2a x) + log(- 2)
+--R  /
+--R      2              2              2
+--R     a sinh(2a x) + a cosh(2a x) + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 39     14:611 Schaums and Axiom differ by a constant
+hh:=complexNormalize gg
+--R
+--R         - log(- 1) + log(- 2)
+--R   (11)  ---------------------
+--R                    2
+--R                   a
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.612~~~~~$\displaystyle
@@ -220,7 +630,7 @@ $$
 <<*>>=
 )clear all
 
---S 9 of 11
+--S 40     14:612 Axiom cannot compute this integral
 aa:=integrate(tanh(a*x)/x,x)
 --R 
 --R
@@ -240,7 +650,7 @@ $$
 <<*>>=
 )clear all
 
---S 10 of 11
+--S 41
 aa:=integrate(1/(p+q*tanh(a*x)),x)
 --R 
 --R
@@ -252,6 +662,54 @@ aa:=integrate(1/(p+q*tanh(a*x)),x)
 --R                             a q  - a p
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 42
+bb:=(p*x)/(p^2-q^2)-q/(a*(p^2-q^2))*log(q*sinh(a*x)+p*cosh(a*x))
+--R
+--R        q log(q sinh(a x) + p cosh(a x)) - a p x
+--R   (2)  ----------------------------------------
+--R                          2      2
+--R                       a q  - a p
+--R                                                     Type: Expression Integer
+--E
+
+--S 43
+cc:=aa-bb
+--R
+--R   (3)
+--R                                                  - 2q sinh(a x) - 2p cosh(a x)
+--R       - q log(q sinh(a x) + p cosh(a x)) + q log(-----------------------------)
+--R                                                      sinh(a x) - cosh(a x)
+--R     + 
+--R       - a q x
+--R  /
+--R        2      2
+--R     a q  - a p
+--R                                                     Type: Expression Integer
+--E
+
+--S 44
+dd:=expandLog cc
+--R
+--R   (4)
+--R       - q log(q sinh(a x) + p cosh(a x)) - q log(sinh(a x) - cosh(a x))
+--R     + 
+--R       q log(- q sinh(a x) - p cosh(a x)) + q log(2) - a q x
+--R  /
+--R        2      2
+--R     a q  - a p
+--R                                                     Type: Expression Integer
+--E
+
+--S 45     14:613 Schaums and Axiom differ by a constant
+ee:=complexNormalize dd
+--R
+--R        q log(2) - 2q log(- 1)
+--R   (5)  ----------------------
+--R                 2      2
+--R              a q  - a p
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.614~~~~~$\displaystyle
@@ -262,7 +720,7 @@ $$
 <<*>>=
 )clear all
 
---S 11 of 11
+--S 46     14:614 Axiom cannot compute this integral
 aa:=integrate(tanh(a*x)^n,x)
 --R 
 --R
diff --git a/src/input/schaum31.input.pamphlet b/src/input/schaum31.input.pamphlet
index 3e81bf2..343aa2a 100644
--- a/src/input/schaum31.input.pamphlet
+++ b/src/input/schaum31.input.pamphlet
@@ -18,7 +18,7 @@ $$
 )set message auto off
 )clear all
 
---S 1 of 11
+--S 1
 aa:=integrate(coth(a*x),x)
 --R 
 --R
@@ -29,6 +29,44 @@ aa:=integrate(coth(a*x),x)
 --R                         a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 2
+bb:=1/a*log(sinh(a*x))
+--R
+--R        log(sinh(a x))
+--R   (2)  --------------
+--R               a
+--R                                                     Type: Expression Integer
+--E
+
+--S 3
+cc:=aa-bb
+--R
+--R                                       2sinh(a x)
+--R        - log(sinh(a x)) + log(- ---------------------) - a x
+--R                                 sinh(a x) - cosh(a x)
+--R   (3)  -----------------------------------------------------
+--R                                  a
+--R                                                     Type: Expression Integer
+--E
+
+--S 4
+dd:=expandLog cc
+--R
+--R        - log(sinh(a x) - cosh(a x)) + log(- 2) - a x
+--R   (4)  ---------------------------------------------
+--R                              a
+--R                                                     Type: Expression Integer
+--E
+
+--S 5      14:615 Schaums and Axiom differ by a constant
+ee:=complexNormalize dd
+--R
+--R        - log(- 1) + log(- 2)
+--R   (5)  ---------------------
+--R                  a
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.616~~~~~$\displaystyle
@@ -39,7 +77,7 @@ $$
 <<*>>=
 )clear all
 
---S 2 of 11
+--S 6
 aa:=integrate(coth(a*x)^2,x)
 --R 
 --R
@@ -48,6 +86,33 @@ aa:=integrate(coth(a*x)^2,x)
 --R                  a sinh(a x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 7
+bb:=x-coth(a*x)/a
+--R
+--R        - coth(a x) + a x
+--R   (2)  -----------------
+--R                a
+--R                                                     Type: Expression Integer
+--E
+
+--S 8
+cc:=aa-bb
+--R
+--R        (coth(a x) + 1)sinh(a x) - cosh(a x)
+--R   (3)  ------------------------------------
+--R                     a sinh(a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 9      14:616 Schaums and Axiom differ by a constant
+dd:=complexNormalize cc
+--R
+--R        1
+--R   (4)  -
+--R        a
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.617~~~~~$\displaystyle
@@ -58,7 +123,7 @@ $$
 <<*>>=
 )clear all
 
---S 3 of 11
+--S 10
 aa:=integrate(coth(a*x)^3,x)
 --R 
 --R
@@ -92,6 +157,69 @@ aa:=integrate(coth(a*x)^3,x)
 --R     (4a cosh(a x)  - 4a cosh(a x))sinh(a x) + a cosh(a x)  - 2a cosh(a x)  + a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 11
+bb:=1/a*log(sinh(a*x)-coth(a*x)^2)/(2*a)
+--R
+--R                                 2
+--R        log(sinh(a x) - coth(a x) )
+--R   (2)  ---------------------------
+--R                      2
+--R                    2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 12     14:617 Axiom cannot simplify this expression
+cc:=aa-bb
+--R
+--R   (3)
+--R                      4                      3                2              2
+--R           - sinh(a x)  - 4cosh(a x)sinh(a x)  + (- 6cosh(a x)  + 2)sinh(a x)
+--R         + 
+--R                        3                                   4             2
+--R           (- 4cosh(a x)  + 4cosh(a x))sinh(a x) - cosh(a x)  + 2cosh(a x)  - 1
+--R      *
+--R                                  2
+--R         log(sinh(a x) - coth(a x) )
+--R     + 
+--R                       4                        3
+--R           2a sinh(a x)  + 8a cosh(a x)sinh(a x)
+--R         + 
+--R                         2               2
+--R           (12a cosh(a x)  - 4a)sinh(a x)
+--R         + 
+--R                        3                                        4
+--R           (8a cosh(a x)  - 8a cosh(a x))sinh(a x) + 2a cosh(a x)
+--R         + 
+--R                         2
+--R           - 4a cosh(a x)  + 2a
+--R      *
+--R                     2sinh(a x)
+--R         log(- ---------------------)
+--R               sinh(a x) - cosh(a x)
+--R     + 
+--R           2           4     2                    3
+--R       - 2a x sinh(a x)  - 8a x cosh(a x)sinh(a x)
+--R     + 
+--R             2           2     2                2
+--R       (- 12a x cosh(a x)  + 4a x - 4a)sinh(a x)
+--R     + 
+--R            2           3      2                               2           4
+--R       (- 8a x cosh(a x)  + (8a x - 8a)cosh(a x))sinh(a x) - 2a x cosh(a x)
+--R     + 
+--R          2                2     2
+--R       (4a x - 4a)cosh(a x)  - 2a x
+--R  /
+--R         2         4     2                  3       2         2     2          2
+--R       2a sinh(a x)  + 8a cosh(a x)sinh(a x)  + (12a cosh(a x)  - 4a )sinh(a x)
+--R     + 
+--R          2         3     2                        2         4     2         2
+--R       (8a cosh(a x)  - 8a cosh(a x))sinh(a x) + 2a cosh(a x)  - 4a cosh(a x)
+--R     + 
+--R         2
+--R       2a
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.618~~~~~$\displaystyle
@@ -102,7 +230,7 @@ $$
 <<*>>=
 )clear all
 
---S 4 of 11
+--S 13
 aa:=integrate(coth(a*x)^n*csch(a*x)^2,x)
 --R 
 --R
@@ -113,6 +241,53 @@ aa:=integrate(coth(a*x)^n*csch(a*x)^2,x)
 --R                                 (a n + a)sinh(a x)
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 14
+bb:=-coth(a*x)^(n+1)/((n+1)*a)
+--R
+--R                   n + 1
+--R          coth(a x)
+--R   (2)  - --------------
+--R              a n + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 15
+cc:=aa-bb
+--R
+--R   (3)
+--R                             cosh(a x)                         cosh(a x)
+--R       - cosh(a x)sinh(n log(---------)) - cosh(a x)cosh(n log(---------))
+--R                             sinh(a x)                         sinh(a x)
+--R     + 
+--R                         n + 1
+--R       sinh(a x)coth(a x)
+--R  /
+--R     (a n + a)sinh(a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 16
+dd:=expandLog cc
+--R
+--R   (4)
+--R       cosh(a x)sinh(n log(sinh(a x)) - n log(cosh(a x)))
+--R     + 
+--R       - cosh(a x)cosh(n log(sinh(a x)) - n log(cosh(a x)))
+--R     + 
+--R                         n + 1
+--R       sinh(a x)coth(a x)
+--R  /
+--R     (a n + a)sinh(a x)
+--R                                                     Type: Expression Integer
+--E
+
+--S 17     14:618 Schaums and Axiom agree
+ee:=complexNormalize dd
+--R
+--R   (5)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.619~~~~~$\displaystyle
@@ -123,7 +298,7 @@ $$
 <<*>>=
 )clear all
 
---S 5 of 11
+--S 18
 aa:=integrate(csch(a*x)^2/coth(a*x),x)
 --R 
 --R
@@ -134,6 +309,43 @@ aa:=integrate(csch(a*x)^2/coth(a*x),x)
 --R                                      a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 19
+bb:=-1/a*log(coth(a*x))
+--R
+--R          log(coth(a x))
+--R   (2)  - --------------
+--R                 a
+--R                                                     Type: Expression Integer
+--E
+
+--S 20
+cc:=aa-bb
+--R
+--R   (3)
+--R                                2cosh(a x)                     2sinh(a x)
+--R   log(coth(a x)) - log(- ---------------------) + log(- ---------------------)
+--R                          sinh(a x) - cosh(a x)          sinh(a x) - cosh(a x)
+--R   ----------------------------------------------------------------------------
+--R                                         a
+--R                                                     Type: Expression Integer
+--E
+
+--S 21
+dd:=expandLog cc
+--R
+--R        log(sinh(a x)) + log(coth(a x)) - log(cosh(a x))
+--R   (4)  ------------------------------------------------
+--R                                a
+--R                                                     Type: Expression Integer
+--E
+
+--S 22     14:619 Schaums and Axiom agree
+ee:=complexNormalize dd
+--R
+--R   (5)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.620~~~~~$\displaystyle
@@ -144,7 +356,7 @@ $$
 <<*>>=
 )clear all
 
---S 6 of 11
+--S 23
 aa:=integrate(1/coth(a*x),x)
 --R 
 --R
@@ -155,6 +367,44 @@ aa:=integrate(1/coth(a*x),x)
 --R                         a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 24
+bb:=1/a*log(cosh(a*x))
+--R
+--R        log(cosh(a x))
+--R   (2)  --------------
+--R               a
+--R                                                     Type: Expression Integer
+--E
+
+--S 25
+cc:=aa-bb
+--R
+--R                                       2cosh(a x)
+--R        - log(cosh(a x)) + log(- ---------------------) - a x
+--R                                 sinh(a x) - cosh(a x)
+--R   (3)  -----------------------------------------------------
+--R                                  a
+--R                                                     Type: Expression Integer
+--E
+
+--S 26
+dd:=expandLog cc
+--R
+--R        - log(sinh(a x) - cosh(a x)) + log(- 2) - a x
+--R   (4)  ---------------------------------------------
+--R                              a
+--R                                                     Type: Expression Integer
+--E
+
+--S 27     14:620 Schaums and Axiom differ by a constant
+ee:=complexNormalize dd
+--R
+--R        - log(- 1) + log(- 2)
+--R   (5)  ---------------------
+--R                  a
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.621~~~~~$\displaystyle
@@ -167,7 +417,7 @@ $$
 <<*>>=
 )clear all
 
---S 7 of 11
+--S 28     14:621 Axiom cannot compute this integral
 aa:=integrate(x*coth(a*x),x)
 --R 
 --R
@@ -187,7 +437,7 @@ $$
 <<*>>=
 )clear all
 
---S 8 of 11
+--S 29
 aa:=integrate(x*coth(a*x)^2,x)
 --R 
 --R
@@ -209,6 +459,157 @@ aa:=integrate(x*coth(a*x)^2,x)
 --R     2a sinh(a x)  + 4a cosh(a x)sinh(a x) + 2a cosh(a x)  - 2a
 --R                                          Type: Union(Expression Integer,...)
 --E
+
+--S 30
+bb:=x^2/2-(x*coth(a*x)/a)+1/a^2*log(sinh(a*x))
+--R
+--R                                            2 2
+--R        2log(sinh(a x)) - 2a x coth(a x) + a x
+--R   (2)  ---------------------------------------
+--R                            2
+--R                          2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 31
+cc:=aa-bb
+--R
+--R   (3)
+--R                   2                                  2
+--R       (- sinh(a x)  - 2cosh(a x)sinh(a x) - cosh(a x)  + 1)log(sinh(a x))
+--R     + 
+--R                   2                                  2
+--R         (sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  - 1)
+--R      *
+--R                     2sinh(a x)
+--R         log(- ---------------------)
+--R               sinh(a x) - cosh(a x)
+--R     + 
+--R                                      2
+--R       (a x coth(a x) - 2a x)sinh(a x)
+--R     + 
+--R       (2a x cosh(a x)coth(a x) - 4a x cosh(a x))sinh(a x)
+--R     + 
+--R                     2                                 2
+--R       (a x cosh(a x)  - a x)coth(a x) - 2a x cosh(a x)
+--R  /
+--R      2         2     2                      2         2    2
+--R     a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  - a
+--R                                                     Type: Expression Integer
+--E
+
+--S 32
+dd:=expandLog cc
+--R
+--R   (4)
+--R                     2                                  2
+--R         (- sinh(a x)  - 2cosh(a x)sinh(a x) - cosh(a x)  + 1)
+--R      *
+--R         log(sinh(a x) - cosh(a x))
+--R     + 
+--R                                                 2
+--R       (a x coth(a x) + log(- 2) - 2a x)sinh(a x)
+--R     + 
+--R       (2a x cosh(a x)coth(a x) + (2log(- 2) - 4a x)cosh(a x))sinh(a x)
+--R     + 
+--R                     2                                             2
+--R       (a x cosh(a x)  - a x)coth(a x) + (log(- 2) - 2a x)cosh(a x)  - log(- 2)
+--R  /
+--R      2         2     2                      2         2    2
+--R     a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  - a
+--R                                                     Type: Expression Integer
+--E
+
+--S 33
+sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2)
+--R
+--R               2    cosh(2x) - 1
+--R   (5)  sinh(x)  == ------------
+--R                          2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 34
+ee:=sinhsqrrule dd
+--R
+--R   (6)
+--R                                                         2
+--R         (- 4cosh(a x)sinh(a x) - cosh(2a x) - 2cosh(a x)  + 3)
+--R      *
+--R         log(sinh(a x) - cosh(a x))
+--R     + 
+--R       (4a x cosh(a x)coth(a x) + (4log(- 2) - 8a x)cosh(a x))sinh(a x)
+--R     + 
+--R                                       2
+--R       (a x cosh(2a x) + 2a x cosh(a x)  - 3a x)coth(a x)
+--R     + 
+--R                                                                2
+--R       (log(- 2) - 2a x)cosh(2a x) + (2log(- 2) - 4a x)cosh(a x)  - 3log(- 2)
+--R     + 
+--R       2a x
+--R  /
+--R       2                      2               2         2     2
+--R     4a cosh(a x)sinh(a x) + a cosh(2a x) + 2a cosh(a x)  - 3a
+--R                                                     Type: Expression Integer
+--E
+
+--S 35
+coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2)
+--R
+--R               2    cosh(2x) + 1
+--R   (7)  cosh(x)  == ------------
+--R                          2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 36
+ff:=coshsqrrule ee
+--R
+--R   (8)
+--R       (- 2cosh(a x)sinh(a x) - cosh(2a x) + 1)log(sinh(a x) - cosh(a x))
+--R     + 
+--R       (2a x cosh(a x)coth(a x) + (2log(- 2) - 4a x)cosh(a x))sinh(a x)
+--R     + 
+--R       (a x cosh(2a x) - a x)coth(a x) + (log(- 2) - 2a x)cosh(2a x) - log(- 2)
+--R  /
+--R       2                      2              2
+--R     2a cosh(a x)sinh(a x) + a cosh(2a x) - a
+--R                                                     Type: Expression Integer
+--E
+
+--S 37
+sinhcoshrule:=rule(sinh(x)*cosh(y) == 1/2*(sinh(x+y)+sinh(x-y)))
+--R
+--I                             %L sinh(y + x) - %L sinh(y - x)
+--I   (9)  %L cosh(y)sinh(x) == -------------------------------
+--R                                            2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 38
+gg:=sinhcoshrule ff
+--R
+--R   (10)
+--R       (- sinh(2a x) - cosh(2a x) + 1)log(sinh(a x) - cosh(a x))
+--R     + 
+--R       (a x coth(a x) + log(- 2) - 2a x)sinh(2a x)
+--R     + 
+--R       (a x cosh(2a x) - a x)coth(a x) + (log(- 2) - 2a x)cosh(2a x) - log(- 2)
+--R  /
+--R      2              2              2
+--R     a sinh(2a x) + a cosh(2a x) - a
+--R                                                     Type: Expression Integer
+--E
+
+--S 39     14:622 Schaums and Axiom differ by a constant
+hh:=complexNormalize gg
+--R
+--R         - log(- 1) + log(- 2)
+--R   (11)  ---------------------
+--R                    2
+--R                   a
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.623~~~~~$\displaystyle
@@ -220,7 +621,7 @@ $$
 <<*>>=
 )clear all
 
---S 9 of 11
+--S 40     14:623 Axiom cannot compute this integral
 aa:=integrate(coth(a*x)/x,x)
 --R 
 --R
@@ -240,7 +641,7 @@ $$
 <<*>>=
 )clear all
 
---S 10 of 11
+--S 41
 aa:=integrate(1/(p+q*coth(a*x)),x)
 --R 
 --R
@@ -252,6 +653,54 @@ aa:=integrate(1/(p+q*coth(a*x)),x)
 --R                             a q  - a p
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 42
+bb:=(p*x)/(p^2-q^2)-q/(a*(p^2-q^2))*log(p*sinh(a*x)+q*cosh(a*x))
+--R
+--R        q log(p sinh(a x) + q cosh(a x)) - a p x
+--R   (2)  ----------------------------------------
+--R                          2      2
+--R                       a q  - a p
+--R                                                     Type: Expression Integer
+--E
+
+--S 43
+cc:=aa-bb
+--R
+--R   (3)
+--R                                                  - 2p sinh(a x) - 2q cosh(a x)
+--R       - q log(p sinh(a x) + q cosh(a x)) + q log(-----------------------------)
+--R                                                      sinh(a x) - cosh(a x)
+--R     + 
+--R       - a q x
+--R  /
+--R        2      2
+--R     a q  - a p
+--R                                                     Type: Expression Integer
+--E
+
+--S 44
+dd:=expandLog cc
+--R
+--R   (4)
+--R       - q log(p sinh(a x) + q cosh(a x)) - q log(sinh(a x) - cosh(a x))
+--R     + 
+--R       q log(- p sinh(a x) - q cosh(a x)) + q log(2) - a q x
+--R  /
+--R        2      2
+--R     a q  - a p
+--R                                                     Type: Expression Integer
+--E
+
+--S 45     14:624 Schaums and Axiom differ by a constant
+ee:=complexNormalize dd
+--R
+--R        q log(2) - 2q log(- 1)
+--R   (5)  ----------------------
+--R                 2      2
+--R              a q  - a p
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.625~~~~~$\displaystyle
@@ -262,7 +711,7 @@ $$
 <<*>>=
 )clear all
 
---S 11 of 11
+--S 46     14:625 Axiom cannot compute this integral
 aa:=integrate(coth(a*x)^n,x)
 --R 
 --R
diff --git a/src/input/schaum32.input.pamphlet b/src/input/schaum32.input.pamphlet
index 085ddf0..e5b2409 100644
--- a/src/input/schaum32.input.pamphlet
+++ b/src/input/schaum32.input.pamphlet
@@ -18,7 +18,7 @@ $$
 )set message auto off
 )clear all
 
---S 1 of 10
+--S 1
 aa:=integrate(sech(a*x),x)
 --R 
 --R
@@ -27,6 +27,70 @@ aa:=integrate(sech(a*x),x)
 --R                      a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 2
+bb:=2/a*atan(%e^(a*x))
+--R
+--R                a x
+--R        2atan(%e   )
+--R   (2)  ------------
+--R              a
+--R                                                     Type: Expression Integer
+--E
+
+--S 3
+cc:=aa-bb
+--R
+--R                                               a x
+--R        2atan(sinh(a x) + cosh(a x)) - 2atan(%e   )
+--R   (3)  -------------------------------------------
+--R                             a
+--R                                                     Type: Expression Integer
+--E
+
+--S 4
+atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
+--R
+--R                            - x + %i
+--R                     %i log(--------)
+--R                             x + %i
+--R   (4)  atan(x) == - ----------------
+--R                             2
+--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
+--E
+
+--S 5
+dd:=atanrule cc
+--R
+--R                   a x
+--R               - %e    + %i           - sinh(a x) - cosh(a x) + %i
+--R        %i log(------------) - %i log(----------------------------)
+--R                  a x                  sinh(a x) + cosh(a x) + %i
+--R                %e    + %i
+--R   (5)  -----------------------------------------------------------
+--R                                     a
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 6
+ee:=expandLog dd
+--R
+--R   (6)
+--R       %i log(sinh(a x) + cosh(a x) + %i) - %i log(sinh(a x) + cosh(a x) - %i)
+--R     + 
+--R                  a x                  a x
+--R       - %i log(%e    + %i) + %i log(%e    - %i)
+--R  /
+--R     a
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 7      14:626 Schaums and Axiom agree
+ff:=complexNormalize ee
+--R
+--R   (7)  0
+--R                                             Type: Expression Complex Integer
+--E
 @
 
 \section{\cite{1}:14.627~~~~~$\displaystyle
@@ -37,7 +101,7 @@ $$
 <<*>>=
 )clear all
 
---S 2 of 10
+--S 8
 aa:=integrate(sech(a*x)^2,x)
 --R 
 --R
@@ -47,6 +111,91 @@ aa:=integrate(sech(a*x)^2,x)
 --R          a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  + a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 9
+bb:=tanh(a*x)/a
+--R
+--R        tanh(a x)
+--R   (2)  ---------
+--R            a
+--R                                                     Type: Expression Integer
+--E
+
+--S 10
+cc:=aa-bb
+--R
+--R                    2                                  2
+--R        (- sinh(a x)  - 2cosh(a x)sinh(a x) - cosh(a x)  - 1)tanh(a x) - 2
+--R   (3)  ------------------------------------------------------------------
+--R                         2                                      2
+--R              a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 11
+sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2)
+--R
+--R               2    cosh(2x) - 1
+--R   (4)  sinh(x)  == ------------
+--R                          2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 12
+dd:=sinhsqrrule cc
+--R
+--R                                                        2
+--R        (- 4cosh(a x)sinh(a x) - cosh(2a x) - 2cosh(a x)  - 1)tanh(a x) - 4
+--R   (5)  -------------------------------------------------------------------
+--R                                                                 2
+--R              4a cosh(a x)sinh(a x) + a cosh(2a x) + 2a cosh(a x)  + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 13
+coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2)
+--R
+--R               2    cosh(2x) + 1
+--R   (6)  cosh(x)  == ------------
+--R                          2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 14
+ee:=coshsqrrule dd
+--R
+--R        (- 2cosh(a x)sinh(a x) - cosh(2a x) - 1)tanh(a x) - 2
+--R   (7)  -----------------------------------------------------
+--R               2a cosh(a x)sinh(a x) + a cosh(2a x) + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 15
+sinhcoshrule:=rule(sinh(x)*cosh(y) == 1/2*(sinh(x+y)+sinh(x-y)))
+--R
+--I                             %L sinh(y + x) - %L sinh(y - x)
+--I   (8)  %L cosh(y)sinh(x) == -------------------------------
+--R                                            2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 16
+ff:=sinhcoshrule ee
+--R
+--R        (- sinh(2a x) - cosh(2a x) - 1)tanh(a x) - 2
+--R   (9)  --------------------------------------------
+--R               a sinh(2a x) + a cosh(2a x) + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 17     14:627 Schaums and Axiom differ by a constant
+gg:=complexNormalize ff
+--R
+--R           1
+--R   (10)  - -
+--R           a
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.628~~~~~$\displaystyle
@@ -57,7 +206,7 @@ $$
 <<*>>=
 )clear all
 
---S 3 of 10
+--S 18
 aa:=integrate(sech(a*x)^3,x)
 --R 
 --R
@@ -83,6 +232,65 @@ aa:=integrate(sech(a*x)^3,x)
 --R     (4a cosh(a x)  + 4a cosh(a x))sinh(a x) + a cosh(a x)  + 2a cosh(a x)  + a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 19
+bb:=(sech(a*x)*tanh(a*x))/(2*a)+1/(2*a)*atan(sinh(a*x))
+--R
+--R        atan(sinh(a x)) + sech(a x)tanh(a x)
+--R   (2)  ------------------------------------
+--R                         2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 20     14:628 Axiom cannot simplify this expression
+cc:=aa-bb
+--R
+--R   (3)
+--R                     4                      3               2              2
+--R           2sinh(a x)  + 8cosh(a x)sinh(a x)  + (12cosh(a x)  + 4)sinh(a x)
+--R         + 
+--R                      3                                    4             2
+--R           (8cosh(a x)  + 8cosh(a x))sinh(a x) + 2cosh(a x)  + 4cosh(a x)  + 2
+--R      *
+--R         atan(sinh(a x) + cosh(a x))
+--R     + 
+--R                      4                      3                2              2
+--R           - sinh(a x)  - 4cosh(a x)sinh(a x)  + (- 6cosh(a x)  - 2)sinh(a x)
+--R         + 
+--R                        3                                   4             2
+--R           (- 4cosh(a x)  - 4cosh(a x))sinh(a x) - cosh(a x)  - 2cosh(a x)  - 1
+--R      *
+--R         atan(sinh(a x))
+--R     + 
+--R                               4                               3
+--R           - sech(a x)sinh(a x)  - 4cosh(a x)sech(a x)sinh(a x)
+--R         + 
+--R                        2                       2
+--R           (- 6cosh(a x)  - 2)sech(a x)sinh(a x)
+--R         + 
+--R                        3
+--R           (- 4cosh(a x)  - 4cosh(a x))sech(a x)sinh(a x)
+--R         + 
+--R                       4             2
+--R           (- cosh(a x)  - 2cosh(a x)  - 1)sech(a x)
+--R      *
+--R         tanh(a x)
+--R     + 
+--R                 3                      2              2
+--R       2sinh(a x)  + 6cosh(a x)sinh(a x)  + (6cosh(a x)  - 2)sinh(a x)
+--R     + 
+--R                 3
+--R       2cosh(a x)  - 2cosh(a x)
+--R  /
+--R                   4                        3                 2               2
+--R       2a sinh(a x)  + 8a cosh(a x)sinh(a x)  + (12a cosh(a x)  + 4a)sinh(a x)
+--R     + 
+--R                    3                                        4               2
+--R       (8a cosh(a x)  + 8a cosh(a x))sinh(a x) + 2a cosh(a x)  + 4a cosh(a x)
+--R     + 
+--R       2a
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.629~~~~~$\displaystyle
@@ -93,7 +301,7 @@ $$
 <<*>>=
 )clear all
 
---S 4 of 10
+--S 21
 aa:=integrate(sech(a*x)^n*tanh(a*x),x)
 --R 
 --R
@@ -111,6 +319,100 @@ aa:=integrate(sech(a*x)^n*tanh(a*x),x)
 --R     a n
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 22
+bb:=-sech(a*x)^n/(n*a)
+--R
+--R                   n
+--R          sech(a x)
+--R   (2)  - ----------
+--R              a n
+--R                                                     Type: Expression Integer
+--E
+
+--S 23
+cc:=aa-bb
+--R
+--R   (3)
+--R                                 2sinh(a x) + 2cosh(a x)
+--R       - sinh(n log(-------------------------------------------------))
+--R                             2                                  2
+--R                    sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  + 1
+--R     + 
+--R                                 2sinh(a x) + 2cosh(a x)
+--R       - cosh(n log(-------------------------------------------------))
+--R                             2                                  2
+--R                    sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  + 1
+--R     + 
+--R                n
+--R       sech(a x)
+--R  /
+--R     a n
+--R                                                     Type: Expression Integer
+--E
+
+--S 24
+sechrule:=rule(sech(x) == 1/cosh(x))
+--R
+--R                      1
+--R   (4)  sech(x) == -------
+--R                   cosh(x)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 25
+dd:=sechrule cc
+--R
+--R   (5)
+--R                                 2sinh(a x) + 2cosh(a x)
+--R       - sinh(n log(-------------------------------------------------))
+--R                             2                                  2
+--R                    sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  + 1
+--R     + 
+--R                                 2sinh(a x) + 2cosh(a x)
+--R       - cosh(n log(-------------------------------------------------))
+--R                             2                                  2
+--R                    sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  + 1
+--R     + 
+--R            1     n
+--R       (---------)
+--R        cosh(a x)
+--R  /
+--R     a n
+--R                                                     Type: Expression Integer
+--E
+
+--S 26
+ee:=expandLog dd
+--R
+--R   (6)
+--R       sinh
+--R                           2                                  2
+--R            n log(sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  + 1)
+--R          + 
+--R            - n log(sinh(a x) + cosh(a x)) - n log(2)
+--R     + 
+--R       -
+--R          cosh
+--R                              2                                  2
+--R               n log(sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  + 1)
+--R             + 
+--R               - n log(sinh(a x) + cosh(a x)) - n log(2)
+--R     + 
+--R            1     n
+--R       (---------)
+--R        cosh(a x)
+--R  /
+--R     a n
+--R                                                     Type: Expression Integer
+--E
+
+--S 27     14:629 Schaums and Axiom agree
+ff:=complexNormalize ee
+--R
+--R   (7)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.630~~~~~$\displaystyle
@@ -121,7 +423,7 @@ $$
 <<*>>=
 )clear all
 
---S 5 of 10
+--S 28
 aa:=integrate(1/sech(a*x),x)
 --R 
 --R
@@ -130,6 +432,22 @@ aa:=integrate(1/sech(a*x),x)
 --R            a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 29
+bb:=sinh(a*x)/a
+--R
+--R        sinh(a x)
+--R   (2)  ---------
+--R            a
+--R                                                     Type: Expression Integer
+--E
+
+--S 30     14:630 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.631~~~~~$\displaystyle
@@ -142,7 +460,7 @@ $$
 <<*>>=
 )clear all
 
---S 6 of 10
+--S 31     14:631 Axiom cannot compute this integral
 aa:=integrate(x*sech(a*x),x)
 --R 
 --R
@@ -162,7 +480,7 @@ $$
 <<*>>=
 )clear all
 
---S 7 of 10
+--S 32
 aa:=integrate(x*sech(a*x)^2,x)
 --R 
 --R
@@ -181,6 +499,161 @@ aa:=integrate(x*sech(a*x)^2,x)
 --R     a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  + a
 --R                                          Type: Union(Expression Integer,...)
 --E
+
+--S 33
+bb:=(x*tanh(a*x))/a-1/a^2*log(cosh(a*x))
+--R
+--R        - log(cosh(a x)) + a x tanh(a x)
+--R   (2)  --------------------------------
+--R                        2
+--R                       a
+--R                                                     Type: Expression Integer
+--E
+
+--S 34
+cc:=aa-bb
+--R
+--R   (3)
+--R                 2                                  2
+--R       (sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  + 1)log(cosh(a x))
+--R     + 
+--R                     2                                  2
+--R         (- sinh(a x)  - 2cosh(a x)sinh(a x) - cosh(a x)  - 1)
+--R      *
+--R                     2cosh(a x)
+--R         log(- ---------------------)
+--R               sinh(a x) - cosh(a x)
+--R     + 
+--R                         2                                          2
+--R         (- a x sinh(a x)  - 2a x cosh(a x)sinh(a x) - a x cosh(a x)  - a x)
+--R      *
+--R         tanh(a x)
+--R     + 
+--R                     2                                           2
+--R       2a x sinh(a x)  + 4a x cosh(a x)sinh(a x) + 2a x cosh(a x)
+--R  /
+--R      2         2     2                      2         2    2
+--R     a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 35
+dd:=expandLog cc
+--R
+--R   (4)
+--R                   2                                  2
+--R         (sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  + 1)
+--R      *
+--R         log(sinh(a x) - cosh(a x))
+--R     + 
+--R                         2                                          2
+--R         (- a x sinh(a x)  - 2a x cosh(a x)sinh(a x) - a x cosh(a x)  - a x)
+--R      *
+--R         tanh(a x)
+--R     + 
+--R                                   2
+--R       (- log(- 2) + 2a x)sinh(a x)  + (- 2log(- 2) + 4a x)cosh(a x)sinh(a x)
+--R     + 
+--R                                   2
+--R       (- log(- 2) + 2a x)cosh(a x)  - log(- 2)
+--R  /
+--R      2         2     2                      2         2    2
+--R     a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 36
+sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2)
+--R
+--R               2    cosh(2x) - 1
+--R   (5)  sinh(x)  == ------------
+--R                          2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 37
+ee:=sinhsqrrule dd
+--R
+--R   (6)
+--R                                                       2
+--R         (4cosh(a x)sinh(a x) + cosh(2a x) + 2cosh(a x)  + 1)
+--R      *
+--R         log(sinh(a x) - cosh(a x))
+--R     + 
+--R                                                                     2
+--R         (- 4a x cosh(a x)sinh(a x) - a x cosh(2a x) - 2a x cosh(a x)  - a x)
+--R      *
+--R         tanh(a x)
+--R     + 
+--R       (- 4log(- 2) + 8a x)cosh(a x)sinh(a x) + (- log(- 2) + 2a x)cosh(2a x)
+--R     + 
+--R                                    2
+--R       (- 2log(- 2) + 4a x)cosh(a x)  - log(- 2) - 2a x
+--R  /
+--R       2                      2               2         2    2
+--R     4a cosh(a x)sinh(a x) + a cosh(2a x) + 2a cosh(a x)  + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 38
+coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2)
+--R
+--R               2    cosh(2x) + 1
+--R   (7)  cosh(x)  == ------------
+--R                          2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 39
+ff:=coshsqrrule ee
+--R
+--R   (8)
+--R       (2cosh(a x)sinh(a x) + cosh(2a x) + 1)log(sinh(a x) - cosh(a x))
+--R     + 
+--R       (- 2a x cosh(a x)sinh(a x) - a x cosh(2a x) - a x)tanh(a x)
+--R     + 
+--R       (- 2log(- 2) + 4a x)cosh(a x)sinh(a x) + (- log(- 2) + 2a x)cosh(2a x)
+--R     + 
+--R       - log(- 2)
+--R  /
+--R       2                      2              2
+--R     2a cosh(a x)sinh(a x) + a cosh(2a x) + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 40
+sinhcoshrule:=rule(sinh(x)*cosh(y) == 1/2*(sinh(x+y)+sinh(x-y)))
+--R
+--I                             %P sinh(y + x) - %P sinh(y - x)
+--I   (9)  %P cosh(y)sinh(x) == -------------------------------
+--R                                            2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 41
+gg:=sinhcoshrule ff
+--R
+--R   (10)
+--R       (sinh(2a x) + cosh(2a x) + 1)log(sinh(a x) - cosh(a x))
+--R     + 
+--R       (- a x sinh(2a x) - a x cosh(2a x) - a x)tanh(a x)
+--R     + 
+--R       (- log(- 2) + 2a x)sinh(2a x) + (- log(- 2) + 2a x)cosh(2a x) - log(- 2)
+--R  /
+--R      2              2              2
+--R     a sinh(2a x) + a cosh(2a x) + a
+--R                                                     Type: Expression Integer
+--E
+
+--S 42     14:632 Schaums and Axiom differ by a constant
+hh:=complexNormalize gg
+--R
+--R         log(- 1) - log(- 2)
+--R   (11)  -------------------
+--R                   2
+--R                  a
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.633~~~~~$\displaystyle
@@ -192,7 +665,7 @@ $$
 <<*>>=
 )clear all
 
---S 8 of 10
+--S 43     14:633 Axiom cannot compute this integral
 aa:=integrate(sech(a*x)/x,x)
 --R 
 --R
@@ -212,7 +685,7 @@ $$
 <<*>>=
 )clear all
 
---S 9 of 10
+--S 44
 aa:=integrate(1/(q+p*sech(a*x)),x)
 --R 
 --R
@@ -259,6 +732,238 @@ aa:=integrate(1/(q+p*sech(a*x)),x)
 --R                                a q\|q  - p
 --R                                     Type: Union(List Expression Integer,...)
 --E 
+
+--S 45
+t1:=integrate(1/(p+q*cosh(a*x)),x)
+--R
+--R   (2)
+--R   [
+--R       log
+--R                   2         2      2                              2         2
+--R                  q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
+--R                + 
+--R                                    2     2
+--R                  2p q cosh(a x) - q  + 2p
+--R             *
+--R                 +---------+
+--R                 |   2    2
+--R                \|- q  + p
+--R            + 
+--R                 3     2                 3     2                  2     3
+--R              (2q  - 2p q)sinh(a x) + (2q  - 2p q)cosh(a x) + 2p q  - 2p
+--R         /
+--R                         2                                             2
+--R              q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
+--R            + 
+--R              2p cosh(a x) + q
+--R    /
+--R         +---------+
+--R         |   2    2
+--R       a\|- q  + p
+--R     ,
+--R                                          +-------+
+--R                                          | 2    2
+--R          (q sinh(a x) + q cosh(a x) + p)\|q  - p
+--R    2atan(-----------------------------------------)
+--R                            2    2
+--R                           q  - p
+--R    ------------------------------------------------]
+--R                         +-------+
+--R                         | 2    2
+--R                       a\|q  - p
+--R                                     Type: Union(List Expression Integer,...)
+--E
+
+--S 46
+bb1:=x/q-p/q*t1.1
+--R
+--R   (3)
+--R       -
+--R            p
+--R         *
+--R            log
+--R                        2         2      2
+--R                       q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x)
+--R                     + 
+--R                        2         2                     2     2
+--R                       q cosh(a x)  + 2p q cosh(a x) - q  + 2p
+--R                  *
+--R                      +---------+
+--R                      |   2    2
+--R                     \|- q  + p
+--R                 + 
+--R                      3     2                 3     2                  2     3
+--R                   (2q  - 2p q)sinh(a x) + (2q  - 2p q)cosh(a x) + 2p q  - 2p
+--R              /
+--R                              2                                             2
+--R                   q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
+--R                 + 
+--R                   2p cosh(a x) + q
+--R     + 
+--R           +---------+
+--R           |   2    2
+--R       a x\|- q  + p
+--R  /
+--R         +---------+
+--R         |   2    2
+--R     a q\|- q  + p
+--R                                                     Type: Expression Integer
+--E
+
+--S 47
+bb2:=x/q-p/q*t1.2
+--R
+--R                                                  +-------+
+--R                                                  | 2    2         +-------+
+--R                  (q sinh(a x) + q cosh(a x) + p)\|q  - p          | 2    2
+--R        - 2p atan(-----------------------------------------) + a x\|q  - p
+--R                                    2    2
+--R                                   q  - p
+--R   (4)  --------------------------------------------------------------------
+--R                                        +-------+
+--R                                        | 2    2
+--R                                    a q\|q  - p
+--R                                                     Type: Expression Integer
+--E
+
+--S 48
+cc1:=aa.1-bb1
+--R
+--R   (5)
+--R         p
+--R      *
+--R         log
+--R                     2         2      2                              2         2
+--R                    q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
+--R                  + 
+--R                                      2     2
+--R                    2p q cosh(a x) - q  + 2p
+--R               *
+--R                   +---------+
+--R                   |   2    2
+--R                  \|- q  + p
+--R              + 
+--R                   3     2                 3     2                  2     3
+--R                (2q  - 2p q)sinh(a x) + (2q  - 2p q)cosh(a x) + 2p q  - 2p
+--R           /
+--R                           2                                             2
+--R                q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
+--R              + 
+--R                2p cosh(a x) + q
+--R     + 
+--R         p
+--R      *
+--R         log
+--R                     2         2      2                              2         2
+--R                    q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
+--R                  + 
+--R                                      2     2
+--R                    2p q cosh(a x) - q  + 2p
+--R               *
+--R                   +---------+
+--R                   |   2    2
+--R                  \|- q  + p
+--R              + 
+--R                     3     2                   3     2                  2     3
+--R                (- 2q  + 2p q)sinh(a x) + (- 2q  + 2p q)cosh(a x) - 2p q  + 2p
+--R           /
+--R                           2                                             2
+--R                q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
+--R              + 
+--R                2p cosh(a x) + q
+--R  /
+--R         +---------+
+--R         |   2    2
+--R     a q\|- q  + p
+--R                                                     Type: Expression Integer
+--E
+
+--S 49
+cc2:=aa.2-bb1
+--R
+--R   (6)
+--R           +-------+
+--R           | 2    2
+--R         p\|q  - p
+--R      *
+--R         log
+--R                     2         2      2                              2         2
+--R                    q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
+--R                  + 
+--R                                      2     2
+--R                    2p q cosh(a x) - q  + 2p
+--R               *
+--R                   +---------+
+--R                   |   2    2
+--R                  \|- q  + p
+--R              + 
+--R                   3     2                 3     2                  2     3
+--R                (2q  - 2p q)sinh(a x) + (2q  - 2p q)cosh(a x) + 2p q  - 2p
+--R           /
+--R                           2                                             2
+--R                q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
+--R              + 
+--R                2p cosh(a x) + q
+--R     + 
+--R                                                            +-------+
+--R            +---------+                                     | 2    2
+--R            |   2    2      (q sinh(a x) + q cosh(a x) + p)\|q  - p
+--R       - 2p\|- q  + p  atan(-----------------------------------------)
+--R                                              2    2
+--R                                             q  - p
+--R  /
+--R         +---------+ +-------+
+--R         |   2    2  | 2    2
+--R     a q\|- q  + p  \|q  - p
+--R                                                     Type: Expression Integer
+--E
+
+--S 50
+cc3:=aa.1-bb2
+--R
+--R   (7)
+--R           +-------+
+--R           | 2    2
+--R         p\|q  - p
+--R      *
+--R         log
+--R                     2         2      2                              2         2
+--R                    q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
+--R                  + 
+--R                                      2     2
+--R                    2p q cosh(a x) - q  + 2p
+--R               *
+--R                   +---------+
+--R                   |   2    2
+--R                  \|- q  + p
+--R              + 
+--R                     3     2                   3     2                  2     3
+--R                (- 2q  + 2p q)sinh(a x) + (- 2q  + 2p q)cosh(a x) - 2p q  + 2p
+--R           /
+--R                           2                                             2
+--R                q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
+--R              + 
+--R                2p cosh(a x) + q
+--R     + 
+--R                                                          +-------+
+--R          +---------+                                     | 2    2
+--R          |   2    2      (q sinh(a x) + q cosh(a x) + p)\|q  - p
+--R       2p\|- q  + p  atan(-----------------------------------------)
+--R                                            2    2
+--R                                           q  - p
+--R  /
+--R         +---------+ +-------+
+--R         |   2    2  | 2    2
+--R     a q\|- q  + p  \|q  - p
+--R                                                     Type: Expression Integer
+--E
+
+--S 51     14:634 Schaums and Axiom agree
+cc4:=aa.2-bb2
+--R
+--R   (8)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.635~~~~~$\displaystyle
@@ -270,7 +975,7 @@ $$
 <<*>>=
 )clear all
 
---S 10 of 10
+--S 52     14:635 Axiom cannot compute this integral
 aa:=integrate(sech(a*x)^n,x)
 --R 
 --R
diff --git a/src/input/schaum33.input.pamphlet b/src/input/schaum33.input.pamphlet
index c5ee6a2..74e0c8b 100644
--- a/src/input/schaum33.input.pamphlet
+++ b/src/input/schaum33.input.pamphlet
@@ -18,7 +18,7 @@ $$
 )set message auto off
 )clear all
 
---S 1 of 10
+--S 1
 aa:=integrate(csch(a*x),x)
 --R 
 --R
@@ -27,6 +27,38 @@ aa:=integrate(csch(a*x),x)
 --R                                        a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 2
+bb:=1/a*log(tanh((a*x)/2))
+--R
+--R                 a x
+--R        log(tanh(---))
+--R                  2
+--R   (2)  --------------
+--R               a
+--R                                                     Type: Expression Integer
+--E
+
+--S 3
+cc:=aa-bb
+--R
+--R   (3)
+--R                  a x
+--R       - log(tanh(---)) - log(sinh(a x) + cosh(a x) + 1)
+--R                   2
+--R     + 
+--R       log(sinh(a x) + cosh(a x) - 1)
+--R  /
+--R     a
+--R                                                     Type: Expression Integer
+--E
+
+--S 4      14:636 Schaums and Axiom agree
+dd:=complexNormalize cc
+--R
+--R   (4)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.637~~~~~$\displaystyle
@@ -37,7 +69,7 @@ $$
 <<*>>=
 )clear all
 
---S 2 of 10
+--S 5
 aa:=integrate(csch(a*x)^2,x)
 --R 
 --R
@@ -47,6 +79,30 @@ aa:=integrate(csch(a*x)^2,x)
 --R          a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  - a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 6
+bb:=-coth(a*x)/a
+--R
+--R          coth(a x)
+--R   (2)  - ---------
+--R              a
+--R                                                     Type: Expression Integer
+--E
+
+--S 7      14:637 Axiom cannot simplify this expression
+cc:=aa-bb
+--R
+--R   (3)
+--R                         2
+--R       coth(a x)sinh(a x)  + 2cosh(a x)coth(a x)sinh(a x)
+--R     + 
+--R                 2
+--R       (cosh(a x)  - 1)coth(a x) - 2
+--R  /
+--R                2                                      2
+--R     a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  - a
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.638~~~~~$\displaystyle
@@ -57,7 +113,7 @@ $$
 <<*>>=
 )clear all
 
---S 3 of 10
+--S 8
 aa:=integrate(csch(a*x)^3,x)
 --R 
 --R
@@ -93,6 +149,72 @@ aa:=integrate(csch(a*x)^3,x)
 --R       2a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 9
+bb:=-(csch(a*x)*coth(a*x))/(2*a)-1/(2*a)*log(tanh((a*x)/2))
+--R
+--R                   a x
+--R        - log(tanh(---)) - coth(a x)csch(a x)
+--R                    2
+--R   (2)  -------------------------------------
+--R                          2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 10     14:638 Axiom cannot simplify this expression
+cc:=aa-bb
+--R
+--R   (3)
+--R                    4                      3              2              2
+--R           sinh(a x)  + 4cosh(a x)sinh(a x)  + (6cosh(a x)  - 2)sinh(a x)
+--R         + 
+--R                      3                                   4             2
+--R           (4cosh(a x)  - 4cosh(a x))sinh(a x) + cosh(a x)  - 2cosh(a x)  + 1
+--R      *
+--R                  a x
+--R         log(tanh(---))
+--R                   2
+--R     + 
+--R                    4                      3              2              2
+--R           sinh(a x)  + 4cosh(a x)sinh(a x)  + (6cosh(a x)  - 2)sinh(a x)
+--R         + 
+--R                      3                                   4             2
+--R           (4cosh(a x)  - 4cosh(a x))sinh(a x) + cosh(a x)  - 2cosh(a x)  + 1
+--R      *
+--R         log(sinh(a x) + cosh(a x) + 1)
+--R     + 
+--R                      4                      3                2              2
+--R           - sinh(a x)  - 4cosh(a x)sinh(a x)  + (- 6cosh(a x)  + 2)sinh(a x)
+--R         + 
+--R                        3                                   4             2
+--R           (- 4cosh(a x)  + 4cosh(a x))sinh(a x) - cosh(a x)  + 2cosh(a x)  - 1
+--R      *
+--R         log(sinh(a x) + cosh(a x) - 1)
+--R     + 
+--R                                  4
+--R       coth(a x)csch(a x)sinh(a x)
+--R     + 
+--R                                                  3
+--R       (4cosh(a x)coth(a x)csch(a x) - 2)sinh(a x)
+--R     + 
+--R                   2                                              2
+--R       ((6cosh(a x)  - 2)coth(a x)csch(a x) - 6cosh(a x))sinh(a x)
+--R     + 
+--R                   3                                             2
+--R       ((4cosh(a x)  - 4cosh(a x))coth(a x)csch(a x) - 6cosh(a x)  - 2)sinh(a x)
+--R     + 
+--R               4             2                                    3
+--R     (cosh(a x)  - 2cosh(a x)  + 1)coth(a x)csch(a x) - 2cosh(a x)  - 2cosh(a x)
+--R  /
+--R                   4                        3                 2               2
+--R       2a sinh(a x)  + 8a cosh(a x)sinh(a x)  + (12a cosh(a x)  - 4a)sinh(a x)
+--R     + 
+--R                    3                                        4               2
+--R       (8a cosh(a x)  - 8a cosh(a x))sinh(a x) + 2a cosh(a x)  - 4a cosh(a x)
+--R     + 
+--R       2a
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.639~~~~~$\displaystyle
@@ -103,7 +225,7 @@ $$
 <<*>>=
 )clear all
 
---S 4 of 10
+--S 11
 aa:=integrate(csch(a*x)^n*coth(a*x),x)
 --R 
 --R
@@ -121,6 +243,202 @@ aa:=integrate(csch(a*x)^n*coth(a*x),x)
 --R     a n
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 12
+bb:=-csch(a*x)^n/(n*a)
+--R
+--R                   n
+--R          csch(a x)
+--R   (2)  - ----------
+--R              a n
+--R                                                     Type: Expression Integer
+--E
+
+--S 13
+cc:=aa-bb
+--R
+--R   (3)
+--R                                 2sinh(a x) + 2cosh(a x)
+--R       - sinh(n log(-------------------------------------------------))
+--R                             2                                  2
+--R                    sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  - 1
+--R     + 
+--R                                 2sinh(a x) + 2cosh(a x)
+--R       - cosh(n log(-------------------------------------------------))
+--R                             2                                  2
+--R                    sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  - 1
+--R     + 
+--R                n
+--R       csch(a x)
+--R  /
+--R     a n
+--R                                                     Type: Expression Integer
+--E
+
+--S 14
+cschrule:=rule(csch(x) == 1/sinh(x))
+--R
+--R                      1
+--R   (4)  csch(x) == -------
+--R                   sinh(x)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 15
+dd:=cschrule cc
+--R
+--R   (5)
+--R                                 2sinh(a x) + 2cosh(a x)
+--R       - sinh(n log(-------------------------------------------------))
+--R                             2                                  2
+--R                    sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  - 1
+--R     + 
+--R                                 2sinh(a x) + 2cosh(a x)
+--R       - cosh(n log(-------------------------------------------------))
+--R                             2                                  2
+--R                    sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  - 1
+--R     + 
+--R            1     n
+--R       (---------)
+--R        sinh(a x)
+--R  /
+--R     a n
+--R                                                     Type: Expression Integer
+--E
+
+--S 16
+ee:=expandLog dd
+--R
+--R   (6)
+--R       sinh
+--R                           2                                  2
+--R            n log(sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  - 1)
+--R          + 
+--R            - n log(sinh(a x) + cosh(a x)) - n log(2)
+--R     + 
+--R       -
+--R          cosh
+--R                              2                                  2
+--R               n log(sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  - 1)
+--R             + 
+--R               - n log(sinh(a x) + cosh(a x)) - n log(2)
+--R     + 
+--R            1     n
+--R       (---------)
+--R        sinh(a x)
+--R  /
+--R     a n
+--R                                                     Type: Expression Integer
+--E
+
+--S 17
+sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2)
+--R
+--R               2    cosh(2x) - 1
+--R   (7)  sinh(x)  == ------------
+--R                          2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 18
+ff:=sinhsqrrule ee
+--R
+--R   (8)
+--R       sinh
+--R                                                               2
+--R                  4cosh(a x)sinh(a x) + cosh(2a x) + 2cosh(a x)  - 3
+--R            n log(--------------------------------------------------)
+--R                                           2
+--R          + 
+--R            - n log(sinh(a x) + cosh(a x)) - n log(2)
+--R     + 
+--R       -
+--R          cosh
+--R                                                                  2
+--R                     4cosh(a x)sinh(a x) + cosh(2a x) + 2cosh(a x)  - 3
+--R               n log(--------------------------------------------------)
+--R                                              2
+--R             + 
+--R               - n log(sinh(a x) + cosh(a x)) - n log(2)
+--R     + 
+--R            1     n
+--R       (---------)
+--R        sinh(a x)
+--R  /
+--R     a n
+--R                                                     Type: Expression Integer
+--E
+
+--S 19
+coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2)
+--R
+--R               2    cosh(2x) + 1
+--R   (9)  cosh(x)  == ------------
+--R                          2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 20
+gg:=coshsqrrule ff
+--R
+--R   (10)
+--R       sinh
+--R            n log(2cosh(a x)sinh(a x) + cosh(2a x) - 1)
+--R          + 
+--R            - n log(sinh(a x) + cosh(a x)) - n log(2)
+--R     + 
+--R       -
+--R          cosh
+--R               n log(2cosh(a x)sinh(a x) + cosh(2a x) - 1)
+--R             + 
+--R               - n log(sinh(a x) + cosh(a x)) - n log(2)
+--R     + 
+--R            1     n
+--R       (---------)
+--R        sinh(a x)
+--R  /
+--R     a n
+--R                                                     Type: Expression Integer
+--E
+
+--S 21
+sinhcoshrule:=rule(sinh(x)*cosh(y) == 1/2*(sinh(x+y)+sinh(x-y)))
+--R
+--I                              %O sinh(y + x) - %O sinh(y - x)
+--I   (11)  %O cosh(y)sinh(x) == -------------------------------
+--R                                             2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 22
+hh:=sinhcoshrule gg
+--R
+--R   (12)
+--R       sinh
+--R            n log(sinh(2a x) + cosh(2a x) - 1) - n log(sinh(a x) + cosh(a x))
+--R          + 
+--R            - n log(2)
+--R     + 
+--R       -
+--R          cosh
+--R               n log(sinh(2a x) + cosh(2a x) - 1) - n log(sinh(a x) + cosh(a x))
+--R             + 
+--R               - n log(2)
+--R     + 
+--R            1     n
+--R       (---------)
+--R        sinh(a x)
+--R  /
+--R     a n
+--R                                                     Type: Expression Integer
+--E
+
+--S 23     14:639 Schaums and Axiom agree
+ii:=complexNormalize hh
+--R
+--R   (13)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.640~~~~~$\displaystyle
@@ -131,7 +449,7 @@ $$
 <<*>>=
 )clear all
 
---S 5 of 10
+--S 24
 aa:=integrate(1/csch(a*x),x)
 --R 
 --R
@@ -140,6 +458,22 @@ aa:=integrate(1/csch(a*x),x)
 --R            a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 25
+bb:=1/a*cosh(a*x)
+--R
+--R        cosh(a x)
+--R   (2)  ---------
+--R            a
+--R                                                     Type: Expression Integer
+--E
+
+--S 26     14:640 Schaums and Axiom agree
+cc:=aa-bb
+--R
+--R   (3)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.641~~~~~$\displaystyle
@@ -152,7 +486,7 @@ $$
 <<*>>=
 )clear all
 
---S 6 of 10
+--S 27     14:641 Axiom cannot compute this integral
 aa:=integrate(x*csch(a*x),x)
 --R 
 --R
@@ -172,7 +506,7 @@ $$
 <<*>>=
 )clear all
 
---S 7 of 10
+--S 28
 aa:=integrate(x*csch(a*x)^2,x)
 --R 
 --R
@@ -191,6 +525,156 @@ aa:=integrate(x*csch(a*x)^2,x)
 --R     a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  - a
 --R                                          Type: Union(Expression Integer,...)
 --E
+
+--S 29
+bb:=-(x*coth(a*x))/a+1/a^2*log(sinh(a*x))
+--R
+--R        log(sinh(a x)) - a x coth(a x)
+--R   (2)  ------------------------------
+--R                       2
+--R                      a
+--R                                                     Type: Expression Integer
+--E
+
+--S 30
+cc:=aa-bb
+--R
+--R   (3)
+--R                   2                                  2
+--R       (- sinh(a x)  - 2cosh(a x)sinh(a x) - cosh(a x)  + 1)log(sinh(a x))
+--R     + 
+--R                   2                                  2
+--R         (sinh(a x)  + 2cosh(a x)sinh(a x) + cosh(a x)  - 1)
+--R      *
+--R                     2sinh(a x)
+--R         log(- ---------------------)
+--R               sinh(a x) - cosh(a x)
+--R     + 
+--R                                      2
+--R       (a x coth(a x) - 2a x)sinh(a x)
+--R     + 
+--R       (2a x cosh(a x)coth(a x) - 4a x cosh(a x))sinh(a x)
+--R     + 
+--R                     2                                 2
+--R       (a x cosh(a x)  - a x)coth(a x) - 2a x cosh(a x)
+--R  /
+--R      2         2     2                      2         2    2
+--R     a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  - a
+--R                                                     Type: Expression Integer
+--E
+
+--S 31
+dd:=expandLog cc
+--R
+--R   (4)
+--R                     2                                  2
+--R         (- sinh(a x)  - 2cosh(a x)sinh(a x) - cosh(a x)  + 1)
+--R      *
+--R         log(sinh(a x) - cosh(a x))
+--R     + 
+--R                                                 2
+--R       (a x coth(a x) + log(- 2) - 2a x)sinh(a x)
+--R     + 
+--R       (2a x cosh(a x)coth(a x) + (2log(- 2) - 4a x)cosh(a x))sinh(a x)
+--R     + 
+--R                     2                                             2
+--R       (a x cosh(a x)  - a x)coth(a x) + (log(- 2) - 2a x)cosh(a x)  - log(- 2)
+--R  /
+--R      2         2     2                      2         2    2
+--R     a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  - a
+--R                                                     Type: Expression Integer
+--E
+
+--S 32
+sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2)
+--R
+--R               2    cosh(2x) - 1
+--R   (5)  sinh(x)  == ------------
+--R                          2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 33
+ee:=sinhsqrrule dd
+--R
+--R   (6)
+--R                                                         2
+--R         (- 4cosh(a x)sinh(a x) - cosh(2a x) - 2cosh(a x)  + 3)
+--R      *
+--R         log(sinh(a x) - cosh(a x))
+--R     + 
+--R       (4a x cosh(a x)coth(a x) + (4log(- 2) - 8a x)cosh(a x))sinh(a x)
+--R     + 
+--R                                       2
+--R       (a x cosh(2a x) + 2a x cosh(a x)  - 3a x)coth(a x)
+--R     + 
+--R                                                                2
+--R       (log(- 2) - 2a x)cosh(2a x) + (2log(- 2) - 4a x)cosh(a x)  - 3log(- 2)
+--R     + 
+--R       2a x
+--R  /
+--R       2                      2               2         2     2
+--R     4a cosh(a x)sinh(a x) + a cosh(2a x) + 2a cosh(a x)  - 3a
+--R                                                     Type: Expression Integer
+--E
+
+--S 34
+coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2)
+--R
+--R               2    cosh(2x) + 1
+--R   (7)  cosh(x)  == ------------
+--R                          2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 35
+ff:=coshsqrrule ee
+--R
+--R   (8)
+--R       (- 2cosh(a x)sinh(a x) - cosh(2a x) + 1)log(sinh(a x) - cosh(a x))
+--R     + 
+--R       (2a x cosh(a x)coth(a x) + (2log(- 2) - 4a x)cosh(a x))sinh(a x)
+--R     + 
+--R       (a x cosh(2a x) - a x)coth(a x) + (log(- 2) - 2a x)cosh(2a x) - log(- 2)
+--R  /
+--R       2                      2              2
+--R     2a cosh(a x)sinh(a x) + a cosh(2a x) - a
+--R                                                     Type: Expression Integer
+--E
+
+--S 36
+sinhcoshrule:=rule(sinh(x)*cosh(y) == 1/2*(sinh(x+y)+sinh(x-y)))
+--R
+--I                             %P sinh(y + x) - %P sinh(y - x)
+--I   (9)  %P cosh(y)sinh(x) == -------------------------------
+--R                                            2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 37
+gg:=sinhcoshrule ff
+--R
+--R   (10)
+--R       (- sinh(2a x) - cosh(2a x) + 1)log(sinh(a x) - cosh(a x))
+--R     + 
+--R       (a x coth(a x) + log(- 2) - 2a x)sinh(2a x)
+--R     + 
+--R       (a x cosh(2a x) - a x)coth(a x) + (log(- 2) - 2a x)cosh(2a x) - log(- 2)
+--R  /
+--R      2              2              2
+--R     a sinh(2a x) + a cosh(2a x) - a
+--R                                                     Type: Expression Integer
+--E
+
+--S 38     14:642 Axiom cannot simplify this expression
+hh:=complexNormalize gg
+--R
+--R         - log(- 1) + log(- 2)
+--R   (11)  ---------------------
+--R                    2
+--R                   a
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.643~~~~~$\displaystyle
@@ -202,7 +686,7 @@ $$
 <<*>>=
 )clear all
 
---S 8 of 10
+--S 39     14:643 Axiom cannot compute this integral
 aa:=integrate(csch(a*x)/x,x)
 --R 
 --R
@@ -222,7 +706,7 @@ $$
 <<*>>=
 )clear all
 
---S 9 of 10
+--S 40
 aa:=integrate(1/(q+p*csch(a*x)),x)
 --R 
 --R
@@ -257,6 +741,251 @@ aa:=integrate(1/(q+p*csch(a*x)),x)
 --R     a q\|q  + p
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 41
+t1:=integrate(1/(p+q*sinh(a*x)),x)
+--R
+--R   (2)
+--R     log
+--R                 2         2      2                              2         2
+--R                q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
+--R              + 
+--R                                  2     2
+--R                2p q cosh(a x) + q  + 2p
+--R           *
+--R               +-------+
+--R               | 2    2
+--R              \|q  + p
+--R          + 
+--R                 3     2                   3     2                  2     3
+--R            (- 2q  - 2p q)sinh(a x) + (- 2q  - 2p q)cosh(a x) - 2p q  - 2p
+--R       /
+--R                       2                                             2
+--R            q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
+--R          + 
+--R            2p cosh(a x) - q
+--R  /
+--R       +-------+
+--R       | 2    2
+--R     a\|q  + p
+--R                                          Type: Union(Expression Integer,...)
+--E
+
+--S 42
+bb:=x/q-p/q*t1
+--R
+--R   (3)
+--R       -
+--R            p
+--R         *
+--R            log
+--R                        2         2      2
+--R                       q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x)
+--R                     + 
+--R                        2         2                     2     2
+--R                       q cosh(a x)  + 2p q cosh(a x) + q  + 2p
+--R                  *
+--R                      +-------+
+--R                      | 2    2
+--R                     \|q  + p
+--R                 + 
+--R                      3     2                   3     2                  2     3
+--R                 (- 2q  - 2p q)sinh(a x) + (- 2q  - 2p q)cosh(a x) - 2p q  - 2p
+--R              /
+--R                              2                                             2
+--R                   q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
+--R                 + 
+--R                   2p cosh(a x) - q
+--R     + 
+--R           +-------+
+--R           | 2    2
+--R       a x\|q  + p
+--R  /
+--R         +-------+
+--R         | 2    2
+--R     a q\|q  + p
+--R                                                     Type: Expression Integer
+--E
+
+--S 43
+cc:=aa-bb
+--R
+--R   (4)
+--R         p
+--R      *
+--R         log
+--R                     2         2      2                              2         2
+--R                    q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
+--R                  + 
+--R                                      2     2
+--R                    2p q cosh(a x) + q  + 2p
+--R               *
+--R                   +-------+
+--R                   | 2    2
+--R                  \|q  + p
+--R              + 
+--R                   3     2                 3     2                  2     3
+--R                (2q  + 2p q)sinh(a x) + (2q  + 2p q)cosh(a x) + 2p q  + 2p
+--R           /
+--R                           2                                             2
+--R                q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
+--R              + 
+--R                2p cosh(a x) - q
+--R     + 
+--R         p
+--R      *
+--R         log
+--R                     2         2      2                              2         2
+--R                    q sinh(a x)  + (2q cosh(a x) + 2p q)sinh(a x) + q cosh(a x)
+--R                  + 
+--R                                      2     2
+--R                    2p q cosh(a x) + q  + 2p
+--R               *
+--R                   +-------+
+--R                   | 2    2
+--R                  \|q  + p
+--R              + 
+--R                     3     2                   3     2                  2     3
+--R                (- 2q  - 2p q)sinh(a x) + (- 2q  - 2p q)cosh(a x) - 2p q  - 2p
+--R           /
+--R                           2                                             2
+--R                q sinh(a x)  + (2q cosh(a x) + 2p)sinh(a x) + q cosh(a x)
+--R              + 
+--R                2p cosh(a x) - q
+--R  /
+--R         +-------+
+--R         | 2    2
+--R     a q\|q  + p
+--R                                                     Type: Expression Integer
+--E
+
+--S 44
+sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2)
+--R
+--R               2    cosh(2x) - 1
+--R   (5)  sinh(x)  == ------------
+--R                          2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 45
+dd:=sinhsqrrule cc
+--R
+--R   (6)
+--R         p
+--R      *
+--R         log
+--R                       2                              2
+--R                    (4q cosh(a x) + 4p q)sinh(a x) + q cosh(2a x)
+--R                  + 
+--R                      2         2                     2     2
+--R                    2q cosh(a x)  + 4p q cosh(a x) + q  + 4p
+--R               *
+--R                   +-------+
+--R                   | 2    2
+--R                  \|q  + p
+--R              + 
+--R                   3     2                 3     2                  2     3
+--R                (4q  + 4p q)sinh(a x) + (4q  + 4p q)cosh(a x) + 4p q  + 4p
+--R           /
+--R                                                                          2
+--R                (4q cosh(a x) + 4p)sinh(a x) + q cosh(2a x) + 2q cosh(a x)
+--R              + 
+--R                4p cosh(a x) - 3q
+--R     + 
+--R         p
+--R      *
+--R         log
+--R                       2                              2
+--R                    (4q cosh(a x) + 4p q)sinh(a x) + q cosh(2a x)
+--R                  + 
+--R                      2         2                     2     2
+--R                    2q cosh(a x)  + 4p q cosh(a x) + q  + 4p
+--R               *
+--R                   +-------+
+--R                   | 2    2
+--R                  \|q  + p
+--R              + 
+--R                     3     2                   3     2                  2     3
+--R                (- 4q  - 4p q)sinh(a x) + (- 4q  - 4p q)cosh(a x) - 4p q  - 4p
+--R           /
+--R                                                                          2
+--R                (4q cosh(a x) + 4p)sinh(a x) + q cosh(2a x) + 2q cosh(a x)
+--R              + 
+--R                4p cosh(a x) - 3q
+--R  /
+--R         +-------+
+--R         | 2    2
+--R     a q\|q  + p
+--R                                                     Type: Expression Integer
+--E
+
+--S 46
+coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2)
+--R
+--R               2    cosh(2x) + 1
+--R   (7)  cosh(x)  == ------------
+--R                          2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 47
+ee:=coshsqrrule dd
+--R
+--R   (8)
+--R         p
+--R      *
+--R         log
+--R                       2                              2
+--R                    (2q cosh(a x) + 2p q)sinh(a x) + q cosh(2a x)
+--R                  + 
+--R                                      2     2
+--R                    2p q cosh(a x) + q  + 2p
+--R               *
+--R                   +-------+
+--R                   | 2    2
+--R                  \|q  + p
+--R              + 
+--R                   3     2                 3     2                  2     3
+--R                (2q  + 2p q)sinh(a x) + (2q  + 2p q)cosh(a x) + 2p q  + 2p
+--R           /
+--R              (2q cosh(a x) + 2p)sinh(a x) + q cosh(2a x) + 2p cosh(a x) - q
+--R     + 
+--R         p
+--R      *
+--R         log
+--R                       2                              2
+--R                    (2q cosh(a x) + 2p q)sinh(a x) + q cosh(2a x)
+--R                  + 
+--R                                      2     2
+--R                    2p q cosh(a x) + q  + 2p
+--R               *
+--R                   +-------+
+--R                   | 2    2
+--R                  \|q  + p
+--R              + 
+--R                     3     2                   3     2                  2     3
+--R                (- 2q  - 2p q)sinh(a x) + (- 2q  - 2p q)cosh(a x) - 2p q  - 2p
+--R           /
+--R              (2q cosh(a x) + 2p)sinh(a x) + q cosh(2a x) + 2p cosh(a x) - q
+--R  /
+--R         +-------+
+--R         | 2    2
+--R     a q\|q  + p
+--R                                                     Type: Expression Integer
+--E
+
+--S 48     14:644 Schaums and Axiom differ by a constant
+ff:=complexNormalize ee
+--R
+--R               4    2 2
+--R        p log(q  + p q )
+--R   (9)  ----------------
+--R              +-------+
+--R              | 2    2
+--R          a q\|q  + p
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.645~~~~~$\displaystyle
@@ -268,7 +997,7 @@ $$
 <<*>>=
 )clear all
 
---S 10 of 10
+--S 49     14:645 Axiom cannot compute this integral
 aa:=integrate(csch(a*x)^n,x)
 --R 
 --R
diff --git a/src/input/schaum34.input.pamphlet b/src/input/schaum34.input.pamphlet
index 1a5c359..83d7061 100644
--- a/src/input/schaum34.input.pamphlet
+++ b/src/input/schaum34.input.pamphlet
@@ -18,7 +18,7 @@ $$
 )set message auto off
 )clear all
 
---S 1 of 32
+--S 1
 aa:=integrate(asinh(x/a),x)
 --R 
 --R
@@ -33,6 +33,69 @@ aa:=integrate(asinh(x/a),x)
 --R                                \|x  + a   - x
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 2
+bb:=x*asinh(x/a)-sqrt(x^2+a^2)
+--R
+--R           +-------+
+--R           | 2    2            x
+--R   (2)  - \|x  + a   + x asinh(-)
+--R                               a
+--R                                                     Type: Expression Integer
+--E
+
+--S 3
+cc:=aa-bb
+--R
+--R               +-------+
+--R               | 2    2
+--R              \|x  + a   + x            x
+--R   (3)  x log(--------------) - x asinh(-)
+--R                     a                  a
+--R                                                     Type: Expression Integer
+--E
+
+--S 4
+asinhlogrule:=rule(asinh(x) == log(x+sqrt(x^2+1)))
+--R
+--R                         +------+
+--R                         | 2
+--R   (4)  asinh(x) == log(\|x  + 1  + x)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 5
+dd:=asinhlogrule cc
+--R
+--R                                        +-------+
+--R                                        | 2    2
+--R                                        |x  + a
+--R               +-------+              a |-------  + x
+--R               | 2    2                 |    2
+--R              \|x  + a   + x           \|   a
+--R   (5)  x log(--------------) - x log(---------------)
+--R                     a                       a
+--R                                                     Type: Expression Integer
+--E
+
+--S 6
+ee:=expandLog dd
+--R
+--R                                        +-------+
+--R               +-------+                | 2    2
+--R               | 2    2                 |x  + a
+--R   (6)  x log(\|x  + a   + x) - x log(a |-------  + x)
+--R                                        |    2
+--R                                       \|   a
+--R                                                     Type: Expression Integer
+--E
+
+--S 7      14:646 Schaums and Axiom agree
+ff:=rootSimp ee
+--R
+--R   (7)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.647~~~~~$\displaystyle
@@ -44,7 +107,7 @@ $$
 <<*>>=
 )clear all
 
---S 2 of 32
+--S 8
 aa:=integrate(x*asinh(x/a),x)
 --R 
 --R
@@ -64,6 +127,77 @@ aa:=integrate(x*asinh(x/a),x)
 --R     8x\|x  + a   - 8x  - 4a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 9
+bb:=(x^2/2+a^2/4)*asinh(x/a)-(x*sqrt(x^2+a^2))/4
+--R
+--R            +-------+
+--R            | 2    2       2    2       x
+--R        - x\|x  + a   + (2x  + a )asinh(-)
+--R                                        a
+--R   (2)  ----------------------------------
+--R                         4
+--R                                                     Type: Expression Integer
+--E
+
+--S 10
+cc:=aa-bb
+--R
+--R                       +-------+
+--R                       | 2    2
+--R           2    2     \|x  + a   + x         2    2       x
+--R        (2x  + a )log(--------------) + (- 2x  - a )asinh(-)
+--R                             a                            a
+--R   (3)  ----------------------------------------------------
+--R                                  4
+--R                                                     Type: Expression Integer
+--E
+
+--S 11
+asinhlogrule:=rule(asinh(x) == log(x+sqrt(x^2+1)))
+--R
+--R                         +------+
+--R                         | 2
+--R   (4)  asinh(x) == log(\|x  + 1  + x)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 12
+dd:=asinhlogrule cc
+--R
+--R                                                          +-------+
+--R                                                          | 2    2
+--R                                                          |x  + a
+--R                       +-------+                        a |-------  + x
+--R                       | 2    2                           |    2
+--R           2    2     \|x  + a   + x         2    2      \|   a
+--R        (2x  + a )log(--------------) + (- 2x  - a )log(---------------)
+--R                             a                                 a
+--R   (5)  ----------------------------------------------------------------
+--R                                        4
+--R                                                     Type: Expression Integer
+--E
+
+--S 13
+ee:=expandLog dd
+--R
+--R                                                          +-------+
+--R                       +-------+                          | 2    2
+--R           2    2      | 2    2              2    2       |x  + a
+--R        (2x  + a )log(\|x  + a   + x) + (- 2x  - a )log(a |-------  + x)
+--R                                                          |    2
+--R                                                         \|   a
+--R   (6)  ----------------------------------------------------------------
+--R                                        4
+--R                                                     Type: Expression Integer
+--E
+
+--S 14     14:647 Schaums and Axiom agree
+ff:=rootSimp ee
+--R
+--R   (7)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.648~~~~~$\displaystyle
@@ -74,7 +208,7 @@ $$
 <<*>>=
 )clear all
 
---S 3 of 32
+--S 15
 aa:=integrate(x^2*asinh(x/a),x)
 --R 
 --R
@@ -94,6 +228,77 @@ aa:=integrate(x^2*asinh(x/a),x)
 --R     (36x  + 9a )\|x  + a   - 36x  - 27a x
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 16
+bb:=x^3/3*asinh(x/a)+((2*a^2-x^2)*sqrt(x^2+a^2))/9
+--R
+--R                     +-------+
+--R            2     2  | 2    2      3      x
+--R        (- x  + 2a )\|x  + a   + 3x asinh(-)
+--R                                          a
+--R   (2)  ------------------------------------
+--R                          9
+--R                                                     Type: Expression Integer
+--E
+
+--S 17
+cc:=aa-bb
+--R
+--R               +-------+
+--R               | 2    2
+--R         3    \|x  + a   + x     3      x
+--R        x log(--------------) - x asinh(-)
+--R                     a                  a
+--R   (3)  ----------------------------------
+--R                         3
+--R                                                     Type: Expression Integer
+--E
+
+--S 18
+asinhlogrule:=rule(asinh(x) == log(x+sqrt(x^2+1)))
+--R
+--R                         +------+
+--R                         | 2
+--R   (4)  asinh(x) == log(\|x  + 1  + x)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 19
+dd:=asinhlogrule cc
+--R
+--R                                        +-------+
+--R                                        | 2    2
+--R                                        |x  + a
+--R               +-------+              a |-------  + x
+--R               | 2    2                 |    2
+--R         3    \|x  + a   + x     3     \|   a
+--R        x log(--------------) - x log(---------------)
+--R                     a                       a
+--R   (5)  ----------------------------------------------
+--R                               3
+--R                                                     Type: Expression Integer
+--E
+
+--S 20
+ee:=expandLog dd
+--R
+--R                                        +-------+
+--R               +-------+                | 2    2
+--R         3     | 2    2          3      |x  + a
+--R        x log(\|x  + a   + x) - x log(a |-------  + x)
+--R                                        |    2
+--R                                       \|   a
+--R   (6)  ----------------------------------------------
+--R                               3
+--R                                                     Type: Expression Integer
+--E
+
+--S 21     14:648 Schaums and Axiom agree
+ff:=rootSimp ee
+--R
+--R   (7)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.649~~~~~$\displaystyle
@@ -124,7 +329,7 @@ $$
 <<*>>=
 )clear all
 
---S 4 of 32
+--S 22     14:649 Axiom cannot compute this integral
 aa:=integrate(asinh(x/a)/x,x)
 --R 
 --R
@@ -146,7 +351,7 @@ $$
 <<*>>=
 )clear all
 
---S 5 of 32
+--S 23
 aa:=integrate(asinh(x/a)/x^2,x)
 --R 
 --R
@@ -164,6 +369,113 @@ aa:=integrate(asinh(x/a)/x^2,x)
 --R     a x
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 24
+bb:=-asinh(x/a)/x-1/a*log((a+sqrt(x^2+a^2))/x)
+--R
+--R                 +-------+
+--R                 | 2    2
+--R                \|x  + a   + a            x
+--R        - x log(--------------) - a asinh(-)
+--R                       x                  a
+--R   (2)  ------------------------------------
+--R                         a x
+--R                                                     Type: Expression Integer
+--E
+
+--S 25
+cc:=aa-bb
+--R
+--R   (3)
+--R                +-------+                   +-------+
+--R                | 2    2                    | 2    2
+--R       - x log(\|x  + a   - x + a) + x log(\|x  + a   - x - a)
+--R     + 
+--R                +-------+               +-------+
+--R                | 2    2                | 2    2
+--R               \|x  + a   + x          \|x  + a   + a            x
+--R       - a log(--------------) + x log(--------------) + a asinh(-)
+--R                      a                       x                  a
+--R  /
+--R     a x
+--R                                                     Type: Expression Integer
+--E
+
+--S 26
+asinhlogrule:=rule(asinh(x) == log(x+sqrt(x^2+1)))
+--R
+--R                         +------+
+--R                         | 2
+--R   (4)  asinh(x) == log(\|x  + 1  + x)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 27
+dd:=asinhlogrule cc
+--R
+--R   (5)
+--R                +-------+                   +-------+
+--R                | 2    2                    | 2    2
+--R       - x log(\|x  + a   - x + a) + x log(\|x  + a   - x - a)
+--R     + 
+--R                                                                 +-------+
+--R                                                                 | 2    2
+--R                                                                 |x  + a
+--R                +-------+               +-------+              a |-------  + x
+--R                | 2    2                | 2    2                 |    2
+--R               \|x  + a   + x          \|x  + a   + a           \|   a
+--R       - a log(--------------) + x log(--------------) + a log(---------------)
+--R                      a                       x                       a
+--R  /
+--R     a x
+--R                                                     Type: Expression Integer
+--E
+
+--S 28
+ee:=expandLog dd
+--R
+--R   (6)
+--R                +-------+               +-------+
+--R                | 2    2                | 2    2
+--R       - a log(\|x  + a   + x) + x log(\|x  + a   + a)
+--R     + 
+--R                +-------+                   +-------+
+--R                | 2    2                    | 2    2
+--R       - x log(\|x  + a   - x + a) + x log(\|x  + a   - x - a)
+--R     + 
+--R               +-------+
+--R               | 2    2
+--R               |x  + a
+--R       a log(a |-------  + x) - x log(x)
+--R               |    2
+--R              \|   a
+--R  /
+--R     a x
+--R                                                     Type: Expression Integer
+--E
+
+--S 29
+ff:=rootSimp ee
+--R
+--R   (7)
+--R            +-------+             +-------+                 +-------+
+--R            | 2    2              | 2    2                  | 2    2
+--R       log(\|x  + a   + a) - log(\|x  + a   - x + a) + log(\|x  + a   - x - a)
+--R     + 
+--R       - log(x)
+--R  /
+--R     a
+--R                                                     Type: Expression Integer
+--E
+
+--S 30     14:650 Schaums and Axiom differ by a constant
+gg:=complexNormalize ff
+--R
+--R          log(- 1)
+--R   (8)  - --------
+--R              a
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.651~~~~~$\displaystyle
@@ -182,7 +494,7 @@ $$
 <<*>>=
 )clear all
 
---S 6 of 32
+--S 31
 aa:=integrate(acosh(x/a),x)
 --R 
 --R
@@ -197,6 +509,100 @@ aa:=integrate(acosh(x/a),x)
 --R                                \|x  - a   - x
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 32
+bb1:=x*acosh(x/a)-sqrt(x^2-a^2)
+--R
+--R           +-------+
+--R           | 2    2            x
+--R   (2)  - \|x  - a   + x acosh(-)
+--R                               a
+--R                                                     Type: Expression Integer
+--E
+
+--S 33
+bb2:=x*acosh(x/a)+sqrt(x^2-a^2)
+--R
+--R         +-------+
+--R         | 2    2            x
+--R   (3)  \|x  - a   + x acosh(-)
+--R                             a
+--R                                                     Type: Expression Integer
+--E
+
+--S 34
+cc1:=aa-bb1
+--R
+--R               +-------+
+--R               | 2    2
+--R              \|x  - a   + x            x
+--R   (4)  x log(--------------) - x acosh(-)
+--R                     a                  a
+--R                                                     Type: Expression Integer
+--E
+
+--S 35
+cc2:=aa-bb2
+--R
+--R   (5)
+--R                              +-------+
+--R          +-------+           | 2    2                             +-------+
+--R          | 2    2     2     \|x  - a   + x               x        | 2    2
+--R       (x\|x  - a   - x )log(--------------) + (- x acosh(-) + 2x)\|x  - a
+--R                                    a                     a
+--R     + 
+--R        2      x      2     2
+--R       x acosh(-) - 2x  + 2a
+--R               a
+--R  /
+--R      +-------+
+--R      | 2    2
+--R     \|x  - a   - x
+--R                                                     Type: Expression Integer
+--E
+
+--S 36
+acoshlogrule:=rule(acosh(x) == log(x+sqrt(x^2-1)))
+--R
+--R                         +------+
+--R                         | 2
+--R   (6)  acosh(x) == log(\|x  - 1  + x)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 37
+dd1:=acoshlogrule cc1
+--R
+--R                                        +-------+
+--R                                        | 2    2
+--R                                        |x  - a
+--R               +-------+              a |-------  + x
+--R               | 2    2                 |    2
+--R              \|x  - a   + x           \|   a
+--R   (7)  x log(--------------) - x log(---------------)
+--R                     a                       a
+--R                                                     Type: Expression Integer
+--E
+
+--S 38
+ee1:=expandLog dd1
+--R
+--R                                        +-------+
+--R               +-------+                | 2    2
+--R               | 2    2                 |x  - a
+--R   (8)  x log(\|x  - a   + x) - x log(a |-------  + x)
+--R                                        |    2
+--R                                       \|   a
+--R                                                     Type: Expression Integer
+--E
+
+--S 39     14:651 Schaums and Axiom agree
+ff1:=rootSimp ee1
+--R
+--R   (9)  0
+--R                                                     Type: Expression Integer
+--E
+
 @
 
 \section{\cite{1}:14.652~~~~~$\displaystyle
@@ -217,7 +623,7 @@ $$
 <<*>>=
 )clear all
 
---S 7 of 32
+--S 40
 aa:=integrate(x*acosh(x/a),x)
 --R 
 --R
@@ -237,6 +643,114 @@ aa:=integrate(x*acosh(x/a),x)
 --R     8x\|x  - a   - 8x  + 4a
 --R                                          Type: Union(Expression Integer,...)
 --E
+
+--S 41
+bb1:=1/4*(2*x^2-a^2)*acosh(x/a)-1/4*x*sqrt(x^2-a^2)
+--R
+--R            +-------+
+--R            | 2    2       2    2       x
+--R        - x\|x  - a   + (2x  - a )acosh(-)
+--R                                        a
+--R   (2)  ----------------------------------
+--R                         4
+--R                                                     Type: Expression Integer
+--E
+
+--S 42
+bb2:=1/4*(2*x^2-a^2)*acosh(x/a)+1/4*x*sqrt(x^2-a^2)
+--R
+--R          +-------+
+--R          | 2    2       2    2       x
+--R        x\|x  - a   + (2x  - a )acosh(-)
+--R                                      a
+--R   (3)  --------------------------------
+--R                        4
+--R                                                     Type: Expression Integer
+--E
+
+--S 43
+cc1:=aa-bb1
+--R
+--R                       +-------+
+--R                       | 2    2
+--R           2    2     \|x  - a   + x         2    2       x
+--R        (2x  - a )log(--------------) + (- 2x  + a )acosh(-)
+--R                             a                            a
+--R   (4)  ----------------------------------------------------
+--R                                  4
+--R                                                     Type: Expression Integer
+--E
+
+--S 44
+cc2:=aa-bb2
+--R
+--R   (5)
+--R                                                       +-------+
+--R                     +-------+                         | 2    2
+--R           3     2   | 2    2      4     2 2    4     \|x  - a   + x
+--R       ((4x  - 2a x)\|x  - a   - 4x  + 4a x  - a )log(--------------)
+--R                                                             a
+--R     + 
+--R                                             +-------+
+--R             3     2        x      3     2   | 2    2
+--R       ((- 4x  + 2a x)acosh(-) + 4x  - 2a x)\|x  - a
+--R                            a
+--R     + 
+--R          4     2 2    4       x      4     2 2
+--R       (4x  - 4a x  + a )acosh(-) - 4x  + 4a x
+--R                               a
+--R  /
+--R        +-------+
+--R        | 2    2      2     2
+--R     8x\|x  - a   - 8x  + 4a
+--R                                                     Type: Expression Integer
+--E
+
+--S 45
+acoshlogrule:=rule(acosh(x) == log(x+sqrt(x^2-1)))
+--R
+--R                         +------+
+--R                         | 2
+--R   (6)  acosh(x) == log(\|x  - 1  + x)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 46
+dd1:=acoshlogrule cc1
+--R
+--R                                                          +-------+
+--R                                                          | 2    2
+--R                                                          |x  - a
+--R                       +-------+                        a |-------  + x
+--R                       | 2    2                           |    2
+--R           2    2     \|x  - a   + x         2    2      \|   a
+--R        (2x  - a )log(--------------) + (- 2x  + a )log(---------------)
+--R                             a                                 a
+--R   (7)  ----------------------------------------------------------------
+--R                                        4
+--R                                                     Type: Expression Integer
+--E
+
+--S 47
+ee1:=expandLog dd1
+--R
+--R                                                          +-------+
+--R                       +-------+                          | 2    2
+--R           2    2      | 2    2              2    2       |x  - a
+--R        (2x  - a )log(\|x  - a   + x) + (- 2x  + a )log(a |-------  + x)
+--R                                                          |    2
+--R                                                         \|   a
+--R   (8)  ----------------------------------------------------------------
+--R                                        4
+--R                                                     Type: Expression Integer
+--E
+
+--S 48     14:652 Schaums and Axiom agree
+ff1:=rootSimp ee1
+--R
+--R   (9)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.653~~~~~$\displaystyle
@@ -257,7 +771,7 @@ $$
 <<*>>=
 )clear all
 
---S 8 of 32
+--S 49
 aa:=integrate(x^2*acosh(x/a),x)
 --R 
 --R
@@ -277,6 +791,114 @@ aa:=integrate(x^2*acosh(x/a),x)
 --R     (36x  - 9a )\|x  - a   - 36x  + 27a x
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 50
+bb1:=1/3*x^3*acosh(x/a)-1/9*(x^2+2*a^2)*sqrt(x^2-a^2)
+--R
+--R                     +-------+
+--R            2     2  | 2    2      3      x
+--R        (- x  - 2a )\|x  - a   + 3x acosh(-)
+--R                                          a
+--R   (2)  ------------------------------------
+--R                          9
+--R                                                     Type: Expression Integer
+--E
+
+--S 51
+bb2:=1/3*x^3*acosh(x/a)+1/9*(x^2+2*a^2)*sqrt(x^2-a^2)
+--R
+--R                   +-------+
+--R          2     2  | 2    2      3      x
+--R        (x  + 2a )\|x  - a   + 3x acosh(-)
+--R                                        a
+--R   (3)  ----------------------------------
+--R                         9
+--R                                                     Type: Expression Integer
+--E
+
+--S 52
+cc1:=aa-bb1
+--R
+--R               +-------+
+--R               | 2    2
+--R         3    \|x  - a   + x     3      x
+--R        x log(--------------) - x acosh(-)
+--R                     a                  a
+--R   (4)  ----------------------------------
+--R                         3
+--R                                                     Type: Expression Integer
+--E
+
+--S 53
+cc2:=aa-bb2
+--R
+--R   (5)
+--R                                                     +-------+
+--R                       +-------+                     | 2    2
+--R            5     2 3  | 2    2       6     2 4     \|x  - a   + x
+--R       ((12x  - 3a x )\|x  - a   - 12x  + 9a x )log(--------------)
+--R                                                           a
+--R     + 
+--R                                                         +-------+
+--R              5     2 3       x      5      2 3      4   | 2    2
+--R       ((- 12x  + 3a x )acosh(-) + 8x  + 10a x  - 12a x)\|x  - a
+--R                              a
+--R     + 
+--R           6     2 4       x      6     2 4      4 2     6
+--R       (12x  - 9a x )acosh(-) - 8x  - 6a x  + 18a x  - 4a
+--R                           a
+--R  /
+--R                  +-------+
+--R         2     2  | 2    2       3      2
+--R     (36x  - 9a )\|x  - a   - 36x  + 27a x
+--R                                                     Type: Expression Integer
+--E
+
+--S 54
+acoshlogrule:=rule(acosh(x) == log(x+sqrt(x^2-1)))
+--R
+--R                         +------+
+--R                         | 2
+--R   (6)  acosh(x) == log(\|x  - 1  + x)
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 55
+dd1:=acoshlogrule cc1
+--R
+--R                                        +-------+
+--R                                        | 2    2
+--R                                        |x  - a
+--R               +-------+              a |-------  + x
+--R               | 2    2                 |    2
+--R         3    \|x  - a   + x     3     \|   a
+--R        x log(--------------) - x log(---------------)
+--R                     a                       a
+--R   (7)  ----------------------------------------------
+--R                               3
+--R                                                     Type: Expression Integer
+--E
+
+--S 56
+ee1:=expandLog dd1
+--R
+--R                                        +-------+
+--R               +-------+                | 2    2
+--R         3     | 2    2          3      |x  - a
+--R        x log(\|x  - a   + x) - x log(a |-------  + x)
+--R                                        |    2
+--R                                       \|   a
+--R   (8)  ----------------------------------------------
+--R                               3
+--R                                                     Type: Expression Integer
+--E
+
+--S 57     14:653 Schaums and Axiom agree
+ff1:=rootSimp ee1
+--R
+--R   (9)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.654~~~~~$\displaystyle
@@ -296,7 +918,7 @@ $$
 <<*>>=
 )clear all
 
---S 9 of 32
+--S 58     14:654 Axiom cannot compute this integral
 aa:=integrate(acosh(x/a)/x,x)
 --R 
 --R
@@ -325,7 +947,7 @@ $$
 <<*>>=
 )clear all
 
---S 10 of 32
+--S 59
 aa:=integrate(acosh(x/a)/x^2,x)
 --R 
 --R
@@ -338,6 +960,68 @@ aa:=integrate(acosh(x/a)/x^2,x)
 --R                               a x
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 60
+bb1:=-acosh(x/a)/x-1/a*log((a+sqrt(x^2+a^2))/x)
+--R
+--R                 +-------+
+--R                 | 2    2
+--R                \|x  + a   + a            x
+--R        - x log(--------------) - a acosh(-)
+--R                       x                  a
+--R   (2)  ------------------------------------
+--R                         a x
+--R                                                     Type: Expression Integer
+--E
+
+--S 61
+bb2:=-acosh(x/a)/x+1/a*log((a+sqrt(x^2+a^2))/x)
+--R
+--R               +-------+
+--R               | 2    2
+--R              \|x  + a   + a            x
+--R        x log(--------------) - a acosh(-)
+--R                     x                  a
+--R   (3)  ----------------------------------
+--R                        a x
+--R                                                     Type: Expression Integer
+--E
+
+--S 62
+cc1:=aa-bb1
+--R
+--R   (4)
+--R              +-------+               +-------+                 +-------+
+--R              | 2    2                | 2    2                  | 2    2
+--R             \|x  + a   + a          \|x  - a   + x            \|x  - a   - x
+--R       x log(--------------) - a log(--------------) + 2x atan(--------------)
+--R                    x                       a                         a
+--R     + 
+--R               x
+--R       a acosh(-)
+--R               a
+--R  /
+--R     a x
+--R                                                     Type: Expression Integer
+--E
+
+--S 63     14:655 Axiom cannot simplify these expressions
+cc2:=aa-bb2
+--R
+--R   (5)
+--R                +-------+               +-------+                 +-------+
+--R                | 2    2                | 2    2                  | 2    2
+--R               \|x  + a   + a          \|x  - a   + x            \|x  - a   - x
+--R       - x log(--------------) - a log(--------------) + 2x atan(--------------)
+--R                      x                       a                         a
+--R     + 
+--R               x
+--R       a acosh(-)
+--R               a
+--R  /
+--R     a x
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.656~~~~~$\displaystyle
@@ -348,7 +1032,7 @@ $$
 <<*>>=
 )clear all
 
---S 11 of 32
+--S 64
 aa:=integrate(atanh(x/a),x)
 --R 
 --R
@@ -359,6 +1043,58 @@ aa:=integrate(atanh(x/a),x)
 --R                       2
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 65
+bb:=x*atanh(x/a)+a/2*log(a^2-x^2)
+--R
+--R                 2    2             x
+--R        a log(- x  + a ) + 2x atanh(-)
+--R                                    a
+--R   (2)  ------------------------------
+--R                       2
+--R                                                     Type: Expression Integer
+--E
+
+--S 66
+cc:=aa-bb
+--R
+--R               2    2          - x - a             2    2             x
+--R        a log(x  - a ) + x log(-------) - a log(- x  + a ) - 2x atanh(-)
+--R                                x - a                                 a
+--R   (3)  ----------------------------------------------------------------
+--R                                        2
+--R                                                     Type: Expression Integer
+--E
+
+--S 67
+atanhrule:=rule(atanh(x) == 1/2*log((1+x)/(1-x)))
+--R
+--R                        - x - 1
+--R                    log(-------)
+--R                         x - 1
+--R   (4)  atanh(x) == ------------
+--R                          2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 68
+dd:=atanhrule cc
+--R
+--R               2    2             2    2
+--R        a log(x  - a ) - a log(- x  + a )
+--R   (5)  ---------------------------------
+--R                        2
+--R                                                     Type: Expression Integer
+--E
+
+--S 69     14:656 Schaums and Axiom differ by a constant
+ee:=complexNormalize dd
+--R
+--R        a log(- 1)
+--R   (6)  ----------
+--R             2
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.657~~~~~$\displaystyle
@@ -369,7 +1105,7 @@ $$
 <<*>>=
 )clear all
 
---S 12 of 32
+--S 70
 aa:=integrate(x*atanh(x/a),x)
 --R 
 --R
@@ -380,6 +1116,46 @@ aa:=integrate(x*atanh(x/a),x)
 --R                      4
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 71
+bb:=(a*x)/2+1/2*(x^2-a^2)*atanh(x/a)
+--R
+--R          2    2       x
+--R        (x  - a )atanh(-) + a x
+--R                       a
+--R   (2)  -----------------------
+--R                   2
+--R                                                     Type: Expression Integer
+--E
+
+--S 72
+cc:=aa-bb
+--R
+--R          2    2     - x - a         2     2       x
+--R        (x  - a )log(-------) + (- 2x  + 2a )atanh(-)
+--R                      x - a                        a
+--R   (3)  ---------------------------------------------
+--R                              4
+--R                                                     Type: Expression Integer
+--E
+
+--S 73
+atanhrule:=rule(atanh(x) == 1/2*log((1+x)/(1-x)))
+--R
+--R                        - x - 1
+--R                    log(-------)
+--R                         x - 1
+--R   (4)  atanh(x) == ------------
+--R                          2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 74     14:657 Schaums and Axiom agree
+dd:=atanhrule cc
+--R
+--R   (5)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.658~~~~~$\displaystyle
@@ -391,7 +1167,7 @@ $$
 <<*>>=
 )clear all
 
---S 13 of 32
+--S 75
 aa:=integrate(x^2*atanh(x/a),x)
 --R 
 --R
@@ -402,6 +1178,59 @@ aa:=integrate(x^2*atanh(x/a),x)
 --R                           6
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 76
+bb:=(a*x^2)/6+x^3/3*atanh(x/a)+a^3/6*log(a^2-x^2)
+--R
+--R         3       2    2      3      x       2
+--R        a log(- x  + a ) + 2x atanh(-) + a x
+--R                                    a
+--R   (2)  -------------------------------------
+--R                          6
+--R                                                     Type: Expression Integer
+--E
+
+--S 77
+cc:=aa-bb
+--R
+--R         3     2    2     3    - x - a     3       2    2      3      x
+--R        a log(x  - a ) + x log(-------) - a log(- x  + a ) - 2x atanh(-)
+--R                                x - a                                 a
+--R   (3)  ----------------------------------------------------------------
+--R                                        6
+--R                                                     Type: Expression Integer
+--E
+
+--S 78
+atanhrule:=rule(atanh(x) == 1/2*log((1+x)/(1-x)))
+--R
+--R                        - x - 1
+--R                    log(-------)
+--R                         x - 1
+--R   (4)  atanh(x) == ------------
+--R                          2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 79
+dd:=atanhrule cc
+--R
+--R         3     2    2     3       2    2
+--R        a log(x  - a ) - a log(- x  + a )
+--R   (5)  ---------------------------------
+--R                        6
+--R                                                     Type: Expression Integer
+--E
+
+--S 80     14:658 Schaums and Axiom differ by a constant
+ee:=complexNormalize dd
+--R
+--R         3
+--R        a log(- 1)
+--R   (6)  ----------
+--R             6
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.659~~~~~$\displaystyle
@@ -412,7 +1241,7 @@ $$
 <<*>>=
 )clear all
 
---S 14 of 32
+--S 81     14:659 Axiom cannot compute this integral
 aa:=integrate(atanh(x/a)/x,x)
 --R 
 --R
@@ -433,7 +1262,7 @@ $$
 <<*>>=
 )clear all
 
---S 15 of 32
+--S 82
 aa:=integrate(atanh(x/a)/x^2,x)
 --R 
 --R
@@ -444,6 +1273,70 @@ aa:=integrate(atanh(x/a)/x^2,x)
 --R                             2a x
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 83
+bb:=-atanh(x/a)/x+1/(2*a)*log(x^2/(a^2-x^2))
+--R
+--R                    2
+--R                   x                x
+--R        x log(- -------) - 2a atanh(-)
+--R                 2    2             a
+--R                x  - a
+--R   (2)  ------------------------------
+--R                     2a x
+--R                                                     Type: Expression Integer
+--E
+
+--S 84
+cc:=aa-bb
+--R
+--R   (3)
+--R                                                  2
+--R                2    2                           x             - x - a
+--R       - x log(x  - a ) + 2x log(x) - x log(- -------) - a log(-------)
+--R                                               2    2           x - a
+--R                                              x  - a
+--R     + 
+--R                x
+--R       2a atanh(-)
+--R                a
+--R  /
+--R     2a x
+--R                                                     Type: Expression Integer
+--E
+
+--S 85
+atanhrule:=rule(atanh(x) == 1/2*log((1+x)/(1-x)))
+--R
+--R                        - x - 1
+--R                    log(-------)
+--R                         x - 1
+--R   (4)  atanh(x) == ------------
+--R                          2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 86
+dd:=atanhrule cc
+--R
+--R                                             2
+--R               2    2                       x
+--R        - log(x  - a ) + 2log(x) - log(- -------)
+--R                                          2    2
+--R                                         x  - a
+--R   (5)  -----------------------------------------
+--R                            2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 87     14:660 Schaums and Axiom agree
+ee:=expandLog dd
+--R
+--R          log(- 1)
+--R   (6)  - --------
+--R             2a
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.661~~~~~$\displaystyle
@@ -451,10 +1344,15 @@ aa:=integrate(atanh(x/a)/x^2,x)
 $$\int{\coth^{-1}\frac{x}{a}}=
 x\coth^{-1}{x}+\frac{a}{2}\ln(x^2-a^2)
 $$
+
+Note that it appears there is a typo in Schaums (1968 printing 4). 
+$$\int{\coth^{-1}\frac{x}{a}}=
+x\coth^{-1}{x/a}+\frac{a}{2}\ln(x^2-a^2)
+$$
 <<*>>=
 )clear all
 
---S 16 of 32
+--S 88
 aa:=integrate(acoth(x/a),x)
 --R 
 --R
@@ -465,6 +1363,46 @@ aa:=integrate(acoth(x/a),x)
 --R                      2
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 89
+bb:=x*acoth(x/a)+a/2*log(x^2-a^2)
+--R
+--R               2    2             x
+--R        a log(x  - a ) + 2x acoth(-)
+--R                                  a
+--R   (2)  ----------------------------
+--R                      2
+--R                                                     Type: Expression Integer
+--E
+
+--S 90
+cc:=aa-bb
+--R
+--R              x + a             x
+--R        x log(-----) - 2x acoth(-)
+--R              x - a             a
+--R   (3)  --------------------------
+--R                     2
+--R                                                     Type: Expression Integer
+--E
+
+--S 91
+acothrule:=rule(acoth(x) == 1/2*log((x+1)/(x-1)))
+--R
+--R                        x + 1
+--R                    log(-----)
+--R                        x - 1
+--R   (4)  acoth(x) == ----------
+--R                         2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 92     14:661 Schaums and Axiom agree
+dd:=acothrule cc
+--R
+--R   (5)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.662~~~~~$\displaystyle
@@ -475,7 +1413,7 @@ $$
 <<*>>=
 )clear all
 
---S 17 of 32
+--S 93
 aa:=integrate(x*acoth(x/a),x)
 --R 
 --R
@@ -486,6 +1424,46 @@ aa:=integrate(x*acoth(x/a),x)
 --R                     4
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 94
+bb:=(a*x)/2+1/2*(x^2-a^2)*acoth(x/a)
+--R
+--R          2    2       x
+--R        (x  - a )acoth(-) + a x
+--R                       a
+--R   (2)  -----------------------
+--R                   2
+--R                                                     Type: Expression Integer
+--E
+
+--S 95
+cc:=aa-bb
+--R
+--R          2    2     x + a         2     2       x
+--R        (x  - a )log(-----) + (- 2x  + 2a )acoth(-)
+--R                     x - a                       a
+--R   (3)  -------------------------------------------
+--R                             4
+--R                                                     Type: Expression Integer
+--E
+
+--S 96
+acothrule:=rule(acoth(x) == 1/2*log((x+1)/(x-1)))
+--R
+--R                        x + 1
+--R                    log(-----)
+--R                        x - 1
+--R   (4)  acoth(x) == ----------
+--R                         2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 97     14:662 Schaums and Axiom agree
+dd:=acothrule cc
+--R
+--R   (5)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.663~~~~~$\displaystyle
@@ -497,7 +1475,7 @@ $$
 <<*>>=
 )clear all
 
---S 18 of 32
+--S 98
 aa:=integrate(x^2*acoth(x/a),x)
 --R 
 --R
@@ -508,6 +1486,46 @@ aa:=integrate(x^2*acoth(x/a),x)
 --R                          6
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 99
+bb:=(a*x^2)/6+x^3/3*acoth(x/a)+a^3/6*log(x^2-a^2)
+--R
+--R         3     2    2      3      x       2
+--R        a log(x  - a ) + 2x acoth(-) + a x
+--R                                  a
+--R   (2)  -----------------------------------
+--R                         6
+--R                                                     Type: Expression Integer
+--E
+
+--S 100
+cc:=aa-bb
+--R
+--R         3    x + a      3      x
+--R        x log(-----) - 2x acoth(-)
+--R              x - a             a
+--R   (3)  --------------------------
+--R                     6
+--R                                                     Type: Expression Integer
+--E
+
+--S 101
+acothrule:=rule(acoth(x) == 1/2*log((x+1)/(x-1)))
+--R
+--R                        x + 1
+--R                    log(-----)
+--R                        x - 1
+--R   (4)  acoth(x) == ----------
+--R                         2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 102    14:663 Schaums and Axiom agree
+dd:=acothrule cc
+--R
+--R   (5)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.664~~~~~$\displaystyle
@@ -518,7 +1536,7 @@ $$
 <<*>>=
 )clear all
 
---S 19 of 32
+--S 103    14:664 Axiom cannot compute this integral
 aa:=integrate(acoth(x/a)/x,x)
 --R 
 --R
@@ -539,7 +1557,7 @@ $$
 <<*>>=
 )clear all
 
---S 20 of 32
+--S 104
 aa:=integrate(acoth(x/a)/x^2,x)
 --R 
 --R
@@ -550,6 +1568,64 @@ aa:=integrate(acoth(x/a)/x^2,x)
 --R                            2a x
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 105
+bb:=-acoth(x/a)/x+1/(2*a)*log(x^2/(x^2-a^2))
+--R
+--R                  2
+--R                 x                x
+--R        x log(-------) - 2a acoth(-)
+--R               2    2             a
+--R              x  - a
+--R   (2)  ----------------------------
+--R                    2a x
+--R                                                     Type: Expression Integer
+--E
+
+--S 106
+cc:=aa-bb
+--R
+--R   (3)
+--R                                                           2
+--R            2    2                      x + a             x                x
+--R   - x log(x  - a ) + 2x log(x) - a log(-----) - x log(-------) + 2a acoth(-)
+--R                                        x - a           2    2             a
+--R                                                       x  - a
+--R   --------------------------------------------------------------------------
+--R                                      2a x
+--R                                                     Type: Expression Integer
+--E
+
+--S 107
+acothrule:=rule(acoth(x) == 1/2*log((x+1)/(x-1)))
+--R
+--R                        x + 1
+--R                    log(-----)
+--R                        x - 1
+--R   (4)  acoth(x) == ----------
+--R                         2
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 108
+dd:=acothrule cc
+--R
+--R                                           2
+--R               2    2                     x
+--R        - log(x  - a ) + 2log(x) - log(-------)
+--R                                        2    2
+--R                                       x  - a
+--R   (5)  ---------------------------------------
+--R                           2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 109    14:665 Schaums and Axiom agree
+ee:=expandLog dd
+--R
+--R   (6)  0
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.666~~~~~$\displaystyle
@@ -568,7 +1644,7 @@ $$
 <<*>>=
 )clear all
 
---S 21 of 32
+--S 110
 aa:=integrate(asech(x/a),x)
 --R 
 --R
@@ -579,7 +1655,308 @@ aa:=integrate(asech(x/a),x)
 --R                      x                           x
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 111
+bb1:=x*asech(x/a)+a*asin(x/a)
+--R
+--R               x            x
+--R   (2)  a asin(-) + x asech(-)
+--R               a            a
+--R                                                     Type: Expression Integer
+--E
+
+--S 112
+bb2:=x*asech(x/a)-a*asin(x/a)
+--R
+--R                 x            x
+--R   (3)  - a asin(-) + x asech(-)
+--R                 a            a
+--R                                                     Type: Expression Integer
+--E
+
+--S 113
+cc1:=aa-bb1
+--R
+--R   (4)
+--R          +---------+                 +---------+
+--R          |   2    2                  |   2    2
+--R         \|- x  + a   + a            \|- x  + a   - a           x            x
+--R   x log(----------------) - 2a atan(----------------) - a asin(-) - x asech(-)
+--R                 x                           x                  a            a
+--R                                                     Type: Expression Integer
+--E
+
+--S 114
+cc2:=aa-bb2
+--R
+--R   (5)
+--R          +---------+                 +---------+
+--R          |   2    2                  |   2    2
+--R         \|- x  + a   + a            \|- x  + a   - a           x            x
+--R   x log(----------------) - 2a atan(----------------) + a asin(-) - x asech(-)
+--R                 x                           x                  a            a
+--R                                                     Type: Expression Integer
+--E
+
+--S 115
+asechrule:=rule(asech(x) == log(1/x+sqrt(1/x^2-1)))
+--R
+--R                          +--------+
+--R                          |   2
+--R                          |- x  + 1
+--R                        x |--------  + 1
+--R                          |    2
+--R                         \|   x
+--R   (6)  asech(x) == log(----------------)
+--R                                x
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 116
+dd1:=asechrule cc1
+--R
+--R   (7)
+--R               +---------+
+--R               |   2    2
+--R               |- x  + a
+--R             x |---------  + a           +---------+
+--R               |     2                   |   2    2
+--R              \|    x                   \|- x  + a   + a
+--R     - x log(-----------------) + x log(----------------)
+--R                     x                          x
+--R   + 
+--R                +---------+
+--R                |   2    2
+--R               \|- x  + a   - a           x
+--R     - 2a atan(----------------) - a asin(-)
+--R                       x                  a
+--R                                                     Type: Expression Integer
+--E
+
+--S 117
+asinrule:=rule(asin(x) == %i*log(-%i*x+sqrt(1-x^2)))
+--R
+--R                           +--------+
+--R                           |   2
+--R   (8)  asin(x) == %i log(\|- x  + 1  - %i x)
+--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
+--E
+
+--S 118
+ee1:=asinrule dd1
+--R
+--R   (9)
+--R               +---------+                   +---------+
+--R               |   2    2                    |   2    2
+--R               |- x  + a                     |- x  + a
+--R             x |---------  + a             a |---------  - %i x
+--R               |     2                       |     2
+--R              \|    x                       \|    a
+--R     - x log(-----------------) - %i a log(--------------------)
+--R                     x                               a
+--R   + 
+--R            +---------+                 +---------+
+--R            |   2    2                  |   2    2
+--R           \|- x  + a   + a            \|- x  + a   - a
+--R     x log(----------------) - 2a atan(----------------)
+--R                   x                           x
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 119
+atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x)))
+--R
+--R                             - x + %i
+--R                      %i log(--------)
+--R                              x + %i
+--R   (10)  atan(x) == - ----------------
+--R                              2
+--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
+--E
+
+--S 120
+ff1:=atanrule ee1
+--R
+--R   (11)
+--R               +---------+                   +---------+
+--R               |   2    2                    |   2    2
+--R               |- x  + a                     |- x  + a
+--R             x |---------  + a             a |---------  - %i x
+--R               |     2                       |     2
+--R              \|    x                       \|    a
+--R     - x log(-----------------) - %i a log(--------------------)
+--R                     x                               a
+--R   + 
+--R            +---------+                    +---------+
+--R            |   2    2                     |   2    2
+--R           \|- x  + a   + a             - \|- x  + a   + %i x + a
+--R     x log(----------------) + %i a log(-------------------------)
+--R                   x                      +---------+
+--R                                          |   2    2
+--R                                         \|- x  + a   + %i x - a
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 121
+gg1:=expandLog ff1
+--R
+--R   (12)
+--R               +---------+                   +---------+
+--R               |   2    2                    |   2    2
+--R               |- x  + a                     |- x  + a
+--R     - x log(x |---------  + a) - %i a log(a |---------  - %i x)
+--R               |     2                       |     2
+--R              \|    x                       \|    a
+--R   + 
+--R                 +---------+                      +---------+
+--R                 |   2    2                       |   2    2
+--R     - %i a log(\|- x  + a   + %i x - a) + x log(\|- x  + a   + a)
+--R   + 
+--R               +---------+
+--R               |   2    2
+--R     %i a log(\|- x  + a   - %i x - a) + %i a log(a) + %i a log(- 1)
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 122
+hh1:=rootSimp gg1
+--R
+--R   (13)
+--R                   +-------+                           +-------+
+--R                   | 2    2                            | 2    2
+--R     - %i a log(%i\|x  - a   + %i x - a) - %i a log(%i\|x  - a   - %i x)
+--R   + 
+--R                 +-------+
+--R                 | 2    2
+--R     %i a log(%i\|x  - a   - %i x - a) + %i a log(a) + %i a log(- 1)
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 123    14:666 Schaums and Axiom agree
+ii1:=complexNormalize hh1
+--R
+--R   (14)  0
+--R                                             Type: Expression Complex Integer
+--E
+
+@
+Note that Axiom has a built-in assumption about the sign of asech(x/a).
+We can see this if we simplify the cc2 value and show that it differs
+by a complex value of x.
+<<*>>=
+--S 124
+dd2:=asechrule cc2
+--R
+--R   (15)
+--R               +---------+
+--R               |   2    2
+--R               |- x  + a
+--R             x |---------  + a           +---------+
+--R               |     2                   |   2    2
+--R              \|    x                   \|- x  + a   + a
+--R     - x log(-----------------) + x log(----------------)
+--R                     x                          x
+--R   + 
+--R                +---------+
+--R                |   2    2
+--R               \|- x  + a   - a           x
+--R     - 2a atan(----------------) + a asin(-)
+--R                       x                  a
+--R                                                     Type: Expression Integer
+--E
+
+--S 125
+ee2:=asinrule dd2
+--R
+--R   (16)
+--R               +---------+                   +---------+
+--R               |   2    2                    |   2    2
+--R               |- x  + a                     |- x  + a
+--R             x |---------  + a             a |---------  - %i x
+--R               |     2                       |     2
+--R              \|    x                       \|    a
+--R     - x log(-----------------) + %i a log(--------------------)
+--R                     x                               a
+--R   + 
+--R            +---------+                 +---------+
+--R            |   2    2                  |   2    2
+--R           \|- x  + a   + a            \|- x  + a   - a
+--R     x log(----------------) - 2a atan(----------------)
+--R                   x                           x
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 126
+ff2:=atanrule ee2
+--R
+--R   (17)
+--R               +---------+                   +---------+
+--R               |   2    2                    |   2    2
+--R               |- x  + a                     |- x  + a
+--R             x |---------  + a             a |---------  - %i x
+--R               |     2                       |     2
+--R              \|    x                       \|    a
+--R     - x log(-----------------) + %i a log(--------------------)
+--R                     x                               a
+--R   + 
+--R            +---------+                    +---------+
+--R            |   2    2                     |   2    2
+--R           \|- x  + a   + a             - \|- x  + a   + %i x + a
+--R     x log(----------------) + %i a log(-------------------------)
+--R                   x                      +---------+
+--R                                          |   2    2
+--R                                         \|- x  + a   + %i x - a
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 127
+gg2:=expandLog ff2
+--R
+--R   (18)
+--R               +---------+                   +---------+
+--R               |   2    2                    |   2    2
+--R               |- x  + a                     |- x  + a
+--R     - x log(x |---------  + a) + %i a log(a |---------  - %i x)
+--R               |     2                       |     2
+--R              \|    x                       \|    a
+--R   + 
+--R                 +---------+                      +---------+
+--R                 |   2    2                       |   2    2
+--R     - %i a log(\|- x  + a   + %i x - a) + x log(\|- x  + a   + a)
+--R   + 
+--R               +---------+
+--R               |   2    2
+--R     %i a log(\|- x  + a   - %i x - a) - %i a log(a) + %i a log(- 1)
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 128
+hh2:=rootSimp gg2
+--R
+--R   (19)
+--R                   +-------+                           +-------+
+--R                   | 2    2                            | 2    2
+--R     - %i a log(%i\|x  - a   + %i x - a) + %i a log(%i\|x  - a   - %i x)
+--R   + 
+--R                 +-------+
+--R                 | 2    2
+--R     %i a log(%i\|x  - a   - %i x - a) - %i a log(a) + %i a log(- 1)
+--R                                             Type: Expression Complex Integer
+--E
+
+--S 129
+ii2:=complexNormalize hh2
+--R
+--R                      +-------+
+--R                      | 2    2
+--R   (20)  2%i a log(%i\|x  - a   - %i x) - 2%i a log(a)
+--R                                             Type: Expression Complex Integer
+--E
+
 @
+Thus we can conjecture that solutions that show up with x in only the
+imaginary part do so when the assumption of the sign of an inverse
+function differs.
 
 \section{\cite{1}:14.667~~~~~$\displaystyle
 \int{x{\rm ~sech}^{-1}\frac{x}{a}}~dx$}
@@ -599,7 +1976,7 @@ $$
 <<*>>=
 )clear all
 
---S 22 of 32
+--S 130
 aa:=integrate(x*asech(x/a),x)
 --R 
 --R
@@ -614,6 +1991,118 @@ aa:=integrate(x*asech(x/a),x)
 --R                         2\|- x  + a   - 2a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 131
+bb1:=1/2*x^2*asech(x/a)-1/2*a*sqrt(a^2-x^2)
+--R
+--R            +---------+
+--R            |   2    2     2      x
+--R        - a\|- x  + a   + x asech(-)
+--R                                  a
+--R   (2)  ----------------------------
+--R                      2
+--R                                                     Type: Expression Integer
+--E
+
+--S 132
+bb2:=1/2*x^2*asech(x/a)+1/2*a*sqrt(a^2-x^2)
+--R
+--R          +---------+
+--R          |   2    2     2      x
+--R        a\|- x  + a   + x asech(-)
+--R                                a
+--R   (3)  --------------------------
+--R                     2
+--R                                                     Type: Expression Integer
+--E
+
+--S 133
+cc1:=aa-bb1
+--R
+--R               +---------+
+--R               |   2    2
+--R         2    \|- x  + a   + a     2      x     2
+--R        x log(----------------) - x asech(-) - a
+--R                      x                   a
+--R   (4)  -----------------------------------------
+--R                            2
+--R                                                     Type: Expression Integer
+--E
+
+--S 134
+cc2:=aa-bb2
+--R
+--R   (5)
+--R                                   +---------+
+--R           +---------+             |   2    2
+--R         2 |   2    2       2     \|- x  + a   + a
+--R       (x \|- x  + a   - a x )log(----------------)
+--R                                          x
+--R     + 
+--R                           +---------+
+--R           2      x     2  |   2    2       2      x        2    3
+--R       (- x asech(-) + a )\|- x  + a   + a x asech(-) + 2a x  - a
+--R                  a                                a
+--R  /
+--R       +---------+
+--R       |   2    2
+--R     2\|- x  + a   - 2a
+--R                                                     Type: Expression Integer
+--E
+
+--S 135
+asechrule:=rule(asech(x) == log(1/x+sqrt(1/x^2-1)))
+--R
+--R                          +--------+
+--R                          |   2
+--R                          |- x  + 1
+--R                        x |--------  + 1
+--R                          |    2
+--R                         \|   x
+--R   (6)  asech(x) == log(----------------)
+--R                                x
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E
+
+--S 136
+dd1:=asechrule cc1
+--R
+--R                  +---------+
+--R                  |   2    2
+--R                  |- x  + a
+--R                x |---------  + a           +---------+
+--R                  |     2                   |   2    2
+--R           2     \|    x              2    \|- x  + a   + a     2
+--R        - x log(-----------------) + x log(----------------) - a
+--R                        x                          x
+--R   (7)  ---------------------------------------------------------
+--R                                    2
+--R                                                     Type: Expression Integer
+--E
+
+--S 137
+ee1:=expandLog dd1
+--R
+--R                  +---------+
+--R                  |   2    2                +---------+
+--R           2      |- x  + a           2     |   2    2          2
+--R        - x log(x |---------  + a) + x log(\|- x  + a   + a) - a
+--R                  |     2
+--R                 \|    x
+--R   (8)  ---------------------------------------------------------
+--R                                    2
+--R                                                     Type: Expression Integer
+--E
+
+--S 138    14:667 Schaums and Axiom differ by a constant
+ff1:=rootSimp ee1
+--R
+--R           2
+--R          a
+--R   (9)  - --
+--R           2
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.668~~~~~$\displaystyle
@@ -633,10 +2122,13 @@ $$\int{\frac{{\rm sech}^{-1}(x/a)}{x}}=
 \end{array}
 \right.
 $$
+
+This is a interesting result since Axiom gives a closed form 
+solution to the problem but Schaums gives a series solution.
 <<*>>=
 )clear all
 
---S 23 of 32
+--S 139    14:668 SCHAUMS AND AXIOM DIFFER (Axiom has closed form)
 aa:=integrate(asech(x/a)/x,x)
 --R 
 --R
@@ -660,7 +2152,7 @@ $$
 <<*>>=
 )clear all
 
---S 24 of 32
+--S 140
 aa:=integrate(acsch(x/a),x)
 --R 
 --R
@@ -671,6 +2163,48 @@ aa:=integrate(acsch(x/a),x)
 --R                                               x
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 141
+bb1:=x*acsch(x/a)+a*asinh(x/a)
+--R
+--R                x            x
+--R   (2)  a asinh(-) + x acsch(-)
+--R                a            a
+--R                                                     Type: Expression Integer
+--E
+
+--S 142
+bb2:=x*acsch(x/a)-a*asinh(x/a)
+--R
+--R                  x            x
+--R   (3)  - a asinh(-) + x acsch(-)
+--R                  a            a
+--R                                                     Type: Expression Integer
+--E
+
+--S 143
+cc1:=aa-bb1
+--R
+--R   (4)
+--R                                    +-------+
+--R            +-------+               | 2    2
+--R            | 2    2               \|x  + a   + a            x            x
+--R   - a log(\|x  + a   - x) + x log(--------------) - a asinh(-) - x acsch(-)
+--R                                          x                  a            a
+--R                                                     Type: Expression Integer
+--E
+
+--S 144    14:669 Axiom cannot simplify these expressions
+cc2:=aa-bb2
+--R
+--R   (5)
+--R                                    +-------+
+--R            +-------+               | 2    2
+--R            | 2    2               \|x  + a   + a            x            x
+--R   - a log(\|x  + a   - x) + x log(--------------) + a asinh(-) - x acsch(-)
+--R                                          x                  a            a
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.670~~~~~$\displaystyle
@@ -682,7 +2216,7 @@ $$
 <<*>>=
 )clear all
 
---S 25 of 32
+--S 145
 aa:=integrate(x*acsch(x/a),x)
 --R 
 --R
@@ -697,6 +2231,63 @@ aa:=integrate(x*acsch(x/a),x)
 --R                                 2\|x  + a   - 2x
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
+--S 146
+bb1:=x^2/2*acsch(x/a)+(a*sqrt(x^2+a^2))/2
+--R
+--R          +-------+
+--R          | 2    2     2      x
+--R        a\|x  + a   + x acsch(-)
+--R                              a
+--R   (2)  ------------------------
+--R                    2
+--R                                                     Type: Expression Integer
+--E
+
+--S 147
+bb2:=x^2/2*acsch(x/a)-(a*sqrt(x^2+a^2))/2
+--R
+--R            +-------+
+--R            | 2    2     2      x
+--R        - a\|x  + a   + x acsch(-)
+--R                                a
+--R   (3)  --------------------------
+--R                     2
+--R                                                     Type: Expression Integer
+--E
+
+--S 148
+cc1:=aa-bb1
+--R
+--R               +-------+
+--R               | 2    2
+--R         2    \|x  + a   + a     2      x
+--R        x log(--------------) - x acsch(-)
+--R                     x                  a
+--R   (4)  ----------------------------------
+--R                         2
+--R                                                     Type: Expression Integer
+--E
+
+--S 149    14:670 Axiom cannot simplify these expressions
+cc2:=aa-bb2
+--R
+--R   (5)
+--R                               +-------+
+--R           +-------+           | 2    2                               +-------+
+--R         2 | 2    2     3     \|x  + a   + a        2      x          | 2    2
+--R       (x \|x  + a   - x )log(--------------) + (- x acsch(-) - 2a x)\|x  + a
+--R                                     x                     a
+--R     + 
+--R        3      x        2     3
+--R       x acsch(-) + 2a x  + 2a
+--R               a
+--R  /
+--R       +-------+
+--R       | 2    2
+--R     2\|x  + a   - 2x
+--R                                                     Type: Expression Integer
+--E
 @
 
 \section{\cite{1}:14.671~~~~~$\displaystyle
@@ -721,10 +2312,13 @@ $$\int{\frac{{\rm csch}^{-1}(x/a)}{x}}=
 \end{array}
 \right.
 $$
+
+Schaums gives 3 different series expansions for this integral
+but Axiom has computed a closed form.
 <<*>>=
 )clear all
 
---S 26 of 32
+--S 150    14:671 SCHAUMS AND AXIOM DIFFER (Axiom has closed form)
 aa:=integrate(acsch(x/a)/x,x)
 --R 
 --R
@@ -737,6 +2331,7 @@ aa:=integrate(acsch(x/a)/x,x)
 --R                        2a
 --R                                          Type: Union(Expression Integer,...)
 --E 
+
 @
 
 \section{\cite{1}:14.672~~~~~$\displaystyle
@@ -748,7 +2343,7 @@ $$
 <<*>>=
 )clear all
 
---S 27 of 32
+--S 151    14:672 Axiom cannot compute this integral
 aa:=integrate(x^m*asinh(x/a),x)
 --R 
 --R
@@ -780,7 +2375,7 @@ $$
 <<*>>=
 )clear all
 
---S 28 of 32
+--S 152    14:673 Axiom cannot compute this integral
 aa:=integrate(x^m*acosh(x/a),x)
 --R 
 --R
@@ -801,7 +2396,7 @@ $$
 <<*>>=
 )clear all
 
---S 29 of 32
+--S 153    14:674 Axiom cannot compute this integral
 aa:=integrate(x^m*atanh(x/a),x)
 --R 
 --R
@@ -822,7 +2417,7 @@ $$
 <<*>>=
 )clear all
 
---S 30 of 32
+--S 154    14:675 Axiom cannot compute this integral
 aa:=integrate(x^m*acoth(x/a),x)
 --R 
 --R
@@ -854,7 +2449,7 @@ $$
 <<*>>=
 )clear all
 
---S 31 of 32
+--S 155    14:676 Axiom cannot compute this integral
 aa:=integrate(x^m*asech(x/a),x)
 --R 
 --R
@@ -877,7 +2472,7 @@ $$
 <<*>>=
 )clear all
 
---S 32 of 32
+--S 156    14:677 Axiom cannot compute this integral
 aa:=integrate(x^m*acsch(x/a),x)
 --R 
 --R



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To: axiom-developer@nongnu.org
Subject: Re: [Axiom-developer] please check your Schaums
Date: Mon, 28 Apr 2008 11:23:07 +0400
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Just a question.
What is a book which you mansion as Schaum?
Does you have any references?

Anatoly
On Monday 28 April 2008 09:08:30 daly@axiom-developer.org wrote:
> In 14.661 Schaums claims:
>
> integral acoth(x/a) = x*acoth(x)+a/2*log(x^2-a^2)
>                         ^^^^^^^^
>
> Axiom claims
>
> integral acoth(x/a) = x*acoth(x/a)+a/2*log(x^2-a^2)
>                         ^^^^^^^^^^
>
> Is this a Schaums typo?
>
> Tim
>
>
>
> _______________________________________________
> Axiom-developer mailing list
> Axiom-developer@nongnu.org
> http://lists.nongnu.org/mailman/listinfo/axiom-developer





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daly@axiom-developer.org writes:

>   14:668 SCHAUMS AND AXIOM DIFFER (Axiom has closed form)

But I'm not so sure that it is correct, at least not for a=1 and x in 0..1.

draw(D(integrate(asech(x)/x,x),x)-asech(x)/x, x=0..1)

I'm an absolute nobody on this stuff, so I may well be missing something.  On
the other hand, the power series for (asech x)/x + (log x - log 2)/x is
Dfinite:

(76) -> guessPRec [coefficient(series normalize((asech x + log x - log 2) / x)::GSERIES(EXPR INT, x, 0), i) for i in 0..30]

   (76)
   [
     [
       function =
         BRACKET
            f(n):
                2                         2                                  1
              (n  + 6n + 9)f(n + 2) + (- n  - 3n - 2)f(n)= 0,f(0)= 0,f(1)= - -
                                                                             4
       ,
      order= 0]
     ]
    Type: List Record(function: Expression Integer,order: NonNegativeInteger)

and this doesn't agree at all with the power series you get from
D(integrate(asech(x)/x,x),x).

Should be investigated,

Martin





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daly@axiom-developer.org wrote:
> In 14.661 Schaums claims:
>
> integral acoth(x/a) = x*acoth(x)+a/2*log(x^2-a^2)
>                         ^^^^^^^^
>
> Axiom claims
>
> integral acoth(x/a) = x*acoth(x/a)+a/2*log(x^2-a^2)
>                         ^^^^^^^^^^
>
> Is this a Schaums typo?
>
> Tim
>
>
>
> _______________________________________________
> Axiom-developer mailing list
> Axiom-developer@nongnu.org
> http://lists.nongnu.org/mailman/listinfo/axiom-developer
>
>   
My schaums is the same as your Schaums but it is old (not as old as 
yours) I have a New Schaums at work But I will not Be in to work today  :-)


My Maxima agrees with Axium.

integrate(acoth(x/a),x);
(%o8) (a*log(x^2/a^2-1))/2+x*acoth(x/a)
 



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A.M.Raportirenko wrote:
> Just a question.
> What is a book which you mansion as Schaum?
> Does you have any references?
>
> Anatoly
> On Monday 28 April 2008 09:08:30 daly@axiom-developer.org wrote:
>   
>> In 14.661 Schaums claims:
>>
>> integral acoth(x/a) = x*acoth(x)+a/2*log(x^2-a^2)
>>                         ^^^^^^^^
>>
>> Axiom claims
>>
>> integral acoth(x/a) = x*acoth(x/a)+a/2*log(x^2-a^2)
>>                         ^^^^^^^^^^
>>
>> Is this a Schaums typo?
>>
>> Tim
>>
>>
>>     

http://www.mhprofessional.com/product.php?cat=145&isbn=0070382034&cat=145




http://www.mhprofessional.com/category/?cat=145




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Doug Stewart wrote:
> daly@axiom-developer.org wrote:
>> In 14.661 Schaums claims:
>>
>> integral acoth(x/a) = x*acoth(x)+a/2*log(x^2-a^2)
>>                         ^^^^^^^^
>>
>> Axiom claims
>>
>> integral acoth(x/a) = x*acoth(x/a)+a/2*log(x^2-a^2)
>>                         ^^^^^^^^^^
>>
>> Is this a Schaums typo?
>>
>> Tim
>>
>>
>>
>> _______________________________________________
>> Axiom-developer mailing list
>> Axiom-developer@nongnu.org
>> http://lists.nongnu.org/mailman/listinfo/axiom-developer
>>
>>   
> My schaums is the same as your Schaums but it is old (not as old as 
> yours) I have a New Schaums at work But I will not Be in to work 
> today  :-)
>
>
> My Maxima agrees with Axium.
>
> integrate(acoth(x/a),x);
> (%o8) (a*log(x^2/a^2-1))/2+x*acoth(x/a)
>
According to "Table of Integrals, Series, and Products" I.S. 
Gradshteyn/I.M. Ryzhik;
Axiom is right.  In fact a dimensional analysis says that Schaums must 
be wrong.  My personal integration says that Axiom/"Table.."  are off by 
a constant, but it's hard to argue about a constant of integration.  The 
meaning of that statement is: set y=x/a  and evaluate, then back 
substitute and multiply by a to get F(x/a); having done that you would 
get log((x/a)^2+1) as the trailing terms.  But this is the same with a 
constant difference.


RayR



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Bertfried Fauser wrote:
> Hi,
>
> am I stupid, why not just differentiating to see which expression is correct?
>
>   
>>>> In 14.661 Schaums claims:
>>>>
>>>> integral acoth(x/a) = x*acoth(x)+a/2*log(x^2-a^2)
>>>>                        ^^^^^^^^
>>>>
>>>> Axiom claims
>>>>
>>>> integral acoth(x/a) = x*acoth(x/a)+a/2*log(x^2-a^2)
>>>>                        ^^^^^^^^^^
>>>>
>>>> Is this a Schaums typo?
>>>>         
>
> I used maple to differentiate the second option, which loos correct:
>
>   
>> diff(x*arccoth(x/a)+a/2*log(x^2-a^2),x);
>> simplify(%);
>>     
> --> arccoth(x/a)
>
> with axiom its even simpler, if you type
>
>   
>>  x*acoth(x/a)+a/2*log(x^2-a^2)
>>  differentiate(%,x)
>>     
> --> acoth(x/a)
>
> So this is the correct expression and Schaum (as given above, I don't
> ow a copy)
> has a typo.
>
>
> Ciao
> BF.
>   



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I'd be very grateful if somebody could look at the input file below. (Don't be
afraid, most of the definitions are not needed)

I would have thought that bug() would yield twice the same thing.  It may be a
mistake on my side, of course, but note that

* axiom does not compute 

  map(c +-> sqrtrule c, series(first Phi Psi Phi [x,y,Z.2], t=0)::ULS(EXPR INT, t, 0))

* neither axiom nor fricas can compute

  map(c +-> sqrtrule c, series(first Phi Psi Phi [x,y,Z.2], t=0)::ULS(EXPR INT, t, 0))-first Phi Psi Phi [x,y,Z2]


since this is actual work, I'd be extremely grateful for help!

Martin

-------------------------------------------------------------------------------
K := ((t*y+t*x)*z*z+(t*y*y+(-x*y)+t*x*x)*z+t*x*y*y+t*x*x*y)
Z := zerosOf(K, z)

sqrtrule := rule sqrt(a^2*?b) == a*sqrt b
Z1 := map(c +-> sqrtrule c, series(Z.1, t=0)::ULS(EXPR INT, t, 0))::ULS(FRAC POLY INT, t, 0)
Z2 := map(c +-> sqrtrule c, series(Z.2, t=0)::ULS(EXPR INT, t, 0))::ULS(FRAC POLY INT, t, 0)

Phi l == [l.2 * l.3/ l.1, l.2, l.3]

Psi l == [l.1, l.1 * l.3/l.2, l.3]

-- I guess the following is a bug:
-- I cannot even subtract the two!
bug() == 
    output map(c +-> sqrtrule c, series(first Phi Psi Phi [x,y,Z.2], t=0)::ULS(EXPR INT, t, 0))
    output first Phi Psi Phi [x,y,Z2]




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From: "William Sit" <wyscc@sci.ccny.cuny.edu>
Subject: Re: [Axiom-developer] possible bug
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Dear Martin:

I don't know what you are computing, but it appears that 
f1:=first Phi Psi Phi [x,y,Z.2] when expanded in series at 
t=0 has denominators (in coefficients of t^3, t^7 for 
example) which would be transformed to zero by sqrtrule. 
(The expansion sf1:=series(f1,t=0) gives UPS instead of 
ULS, but it can be coerced to ULS.)

See output below.

William
--

(14) -> f1:=first Phi Psi Phi [x,y,Z.2]

    (14)
            2 4       2         3    2 2       2       3 
    2 4
          (t y  + (- t  - 2t)x y  + x y  + (- t  - 2t)x y 
+ t x )
       *
           +------------------------------------------------------------------+
           | 2 4        2         3        2      2 2 
       2       3     2 4
          \|t y  + (- 4t  - 2t)x y  + (- 6t  + 1)x y  + (- 
4t  - 2t)x y + t x
      +
         3 6        3     2    5        3     2       2 4 
       3      3 3
        t y  + (- 3t  - 3t )x y  + (- 3t  + 3t  + 3t)x y 
 + (- 6t  - 1)x y
      +
             3     2       4 2        3     2  5     3 6
        (- 3t  + 3t  + 3t)x y  + (- 3t  - 3t )x y + t x
   /
            2 3     2   2    2 2
          (t y  + 2t x y  + t x y)
       *
           +------------------------------------------------------------------+
           | 2 4        2         3        2      2 2 
       2       3     2 4
          \|t y  + (- 4t  - 2t)x y  + (- 6t  + 1)x y  + (- 
4t  - 2t)x y + t x
      +
         3 5      3    2    4      3     2  2 3      3 
   2  3 2    3 4
        t y  + (2t  - t )x y  + (2t  - 2t )x y  + (2t  - t 
)x y  + t x y
                                                      Type: 
Expression Integer
(15) -> sf1:=series(f1,t=0)

    (15)
             2                     2     3
            x y       - 2    - 2x y  - 2x   - 1
      -------------- t    + -------------- t
       2           2         2           2
      y  + 2x y + x         y  + 2x y + x
    +
                                             +----+
              4       3     2 2     3     4  | 2 2       5 
    2 4      3 3
          (- y  - 2x y  - 6x y  - 2x y - x )\|x y   + x y 
 - 6x y  - 10x y
        +
              4 2    5
          - 6x y  + x y
     /
            4     2 3     3 2
        2x y  + 4x y  + 2x y
    +
                                                            
 +----+
               6      5     2 4     3 3     4 2    5 
     6  | 2 2        7
            (2y  + x y  + 8x y  + 2x y  + 8x y  + x y + 2x 
)\|x y   + 2x y
          +
             2 6     3 5     4 4     5 3    6 2     7
            x y  + 8x y  + 2x y  + 8x y  + x y  + 2x y
       /
            2 5     3 4     4 3
          2x y  + 4x y  + 2x y
     *
        t
    +
                     8       7     2 6      3 5      4 4 
     5 3     6 2     7
                  - y  + 4x y  + 8x y  + 28x y  + 34x y  + 
28x y  + 8x y  + 4x y
                +
                     8
                  - x
           *
               +----+
               | 2 2
              \|x y
          +
               9     2 8     3 7      4 6      5 5      6 
4     7 3     8 2    9
          - x y  + 4x y  + 6x y  + 20x y  + 22x y  + 20x y 
 + 6x y  + 4x y  - x y

       /
            3 6     4 5     5 4
          2x y  + 4x y  + 2x y
     *
         2
        t
    +
                                                            
   +----+
                6       5     2 4     3 3     4 2     5 
    6  | 2 2       7
            (- y  + 4x y  + 5x y  + 8x y  + 5x y  + 4x y - 
x )\|x y   - x y
          +
                3 5     5 3    7
            - 3x y  - 3x y  - x y
       /
            3 4
          2x y
     *
         3
        t
    +
                                                            
        +----+
                 6       5      2 4      3 3      4 2 
    5      6  | 2 2
            (- 3y  - 9x y  - 21x y  - 30x y  - 21x y  - 9x 
y - 3x )\|x y
          +
                7     2 6      3 5      4 4      5 3     6 
2     7
            3x y  + 7x y  + 13x y  + 18x y  + 13x y  + 7x 
y  + 3x y
       /
               +----+
           2 3 | 2 2     3 4
          x y \|x y   - x y
     *
         4
        t
    +
                    8        7      2 6       3 5       4 
4       5 3      6 2
                - 4y  - 20x y  - 64x y  - 108x y  - 120x y 
 - 108x y  - 64x y
              +
                     7      8
                - 20x y - 4x
           *
               +----+
               | 2 2
              \|x y
          +
                9      2 8      3 7      4 6      5 5 
     6 4      7 3      8 2
            4x y  + 12x y  + 32x y  + 52x y  + 56x y  + 
52x y  + 32x y  + 12x y
          +
              9
            4x y
       /
               +----+
           3 4 | 2 2     4 5
          x y \|x y   - x y
     *
         5
        t
    +
                    10        9       2 8       3 7 
      4 6       5 5       6 4

                - 5y   - 39x y  - 148x y  - 314x y  - 503x 
y  - 606x y  - 503x y
              +
                      7 3       8 2      9      10
                - 314x y  - 148x y  - 39x y - 5x
           *
               +----+
               | 2 2
              \|x y
          +
                11      2 10      3 9       4 8       5 7 
      6 6       7 5
            5x y   + 21x y   + 72x y  + 146x y  + 227x y 
 + 274x y  + 227x y
          +
                8 4      9 3      10 2     11
            146x y  + 72x y  + 21x  y  + 5x  y
       /
               +----+
           4 5 | 2 2     5 6
          x y \|x y   - x y
     *
         6
        t
    +
                    12        11       2 10       3 9 
       4 8        5 7
                - 6y   - 68x y   - 303x y   - 822x y  - 
1674x y  - 2470x y
              +
                       6 6        7 5        8 4       9 3 
      10 2      11
                - 2754x y  - 2470x y  - 1674x y  - 822x y 
 - 303x  y  - 68x  y
              +
                    12
                - 6x
           *
               +----+
               | 2 2
              \|x y
          +
                13      2 12       3 11       4 10       5 
9        6 8
            6x y   + 36x y   + 149x y   + 378x y   + 746x 
y  + 1090x y
          +
               7 7        8 6       9 5       10 4 
      11 3      12 2     13
          1206x y  + 1090x y  + 746x y  + 378x  y  + 149x 
 y  + 36x  y  + 6x  y
       /
               +----+
           5 6 | 2 2     6 7
          x y \|x y   - x y
     *
         7
        t
    +
                    14         13       2 12        3 11 
       4 10        5 9
                - 7y   - 109x y   - 580x y   - 1960x y   - 
4774x y   - 8547x y
              +
                        6 8         7 7         8 6 
       9 5        10 4
                - 12111x y  - 13712x y  - 12111x y  - 
8547x y  - 4774x  y
              +
                       11 3       12 2       13      14
                - 1960x  y  - 580x  y  - 109x  y - 7x
           *
               +----+
               | 2 2
              \|x y
          +
                15      2 14       3 13       4 12 
       5 11        6 10
            7x y   + 59x y   + 288x y   + 896x y   + 2114x 
y   + 3717x y
          +
                 7 9        8 8        9 7        10 6 
       11 5       12 4
            5207x y  + 5888x y  + 5207x y  + 3717x  y  + 
2114x  y  + 896x  y
          +
                13 3      14 2     15
            288x  y  + 59x  y  + 7x  y
       /
               +----+
           6 7 | 2 2     7 8
          x y \|x y   - x y
     *
         8
        t
    +
         9
      O(t )
                         Type: 
UnivariatePuiseuxSeries(Expression Integer,t,0)




On 29 Apr 2008 18:00:25 +0200
  Martin Rubey <martin.rubey@univie.ac.at> wrote:
>I'd be very grateful if somebody could look at the input 
>file below. (Don't be
>afraid, most of the definitions are not needed)
>
>I would have thought that bug() would yield twice the 
>same thing.  It may be a
>mistake on my side, of course, but note that
>
>* axiom does not compute 
>
>   map(c +-> sqrtrule c, series(first Phi Psi Phi 
>[x,y,Z.2], t=0)::ULS(EXPR INT, t, 0))
>
>* neither axiom nor fricas can compute
>
>   map(c +-> sqrtrule c, series(first Phi Psi Phi 
>[x,y,Z.2], t=0)::ULS(EXPR INT, t, 0))-first Phi Psi Phi 
>[x,y,Z2]
>
>
>since this is actual work, I'd be extremely grateful for 
>help!
>
>Martin
>
>-------------------------------------------------------------------------------
>K := 
>((t*y+t*x)*z*z+(t*y*y+(-x*y)+t*x*x)*z+t*x*y*y+t*x*x*y)
>Z := zerosOf(K, z)
>
>sqrtrule := rule sqrt(a^2*?b) == a*sqrt b
>Z1 := map(c +-> sqrtrule c, series(Z.1, t=0)::ULS(EXPR 
>INT, t, 0))::ULS(FRAC POLY INT, t, 0)
>Z2 := map(c +-> sqrtrule c, series(Z.2, t=0)::ULS(EXPR 
>INT, t, 0))::ULS(FRAC POLY INT, t, 0)
>
>Phi l == [l.2 * l.3/ l.1, l.2, l.3]
>
>Psi l == [l.1, l.1 * l.3/l.2, l.3]
>
>-- I guess the following is a bug:
>-- I cannot even subtract the two!
>bug() == 
>     output map(c +-> sqrtrule c, series(first Phi Psi 
>Phi [x,y,Z.2], t=0)::ULS(EXPR INT, t, 0))
>     output first Phi Psi Phi [x,y,Z2]
>
>
>
>_______________________________________________
>Axiom-developer mailing list
>Axiom-developer@nongnu.org
>http://lists.nongnu.org/mailman/listinfo/axiom-developer

William Sit, 
Professor of Mathematics, City College of New York 
                 
Office: R6/202C Tel: 212-650-5179, Fax: 212-862-0004
Home Page: http://scisun.sci.ccny.cuny.edu/~wyscc/



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Subject: [Axiom-developer] Re: [fricas-devel] possible bug
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Martin Rubey wrote:
> 
> I'd be very grateful if somebody could look at the input file below. (Don't be
> afraid, most of the definitions are not needed)
> 
> I would have thought that bug() would yield twice the same thing.  It may be a
> mistake on my side, of course, but note that
> 
> * axiom does not compute 
> 
>   map(c +-> sqrtrule c, series(first Phi Psi Phi [x,y,Z.2], t=0)::ULS(EXPR INT, t, 0))
> 

Using FriCAS I get errors.  I would prefer clearer error message, but
as William Sit noted, this can not really work due to zero denominators.

> * neither axiom nor fricas can compute
> 
>   map(c +-> sqrtrule c, series(first Phi Psi Phi [x,y,Z.2], t=0)::ULS(EXPR INT, t, 0))-first Phi Psi Phi [x,y,Z2]
> 
> 
> since this is actual work, I'd be extremely grateful for help!
> 
> Martin
> 
> -------------------------------------------------------------------------------
> K := ((t*y+t*x)*z*z+(t*y*y+(-x*y)+t*x*x)*z+t*x*y*y+t*x*x*y)
> Z := zerosOf(K, z)
> 
> sqrtrule := rule sqrt(a^2*?b) == a*sqrt b
> Z1 := map(c +-> sqrtrule c, series(Z.1, t=0)::ULS(EXPR INT, t, 0))::ULS(FRAC POLY INT, t, 0)
> Z2 := map(c +-> sqrtrule c, series(Z.2, t=0)::ULS(EXPR INT, t, 0))::ULS(FRAC POLY INT, t, 0)
> 
> Phi l == [l.2 * l.3/ l.1, l.2, l.3]
> 
> Psi l == [l.1, l.1 * l.3/l.2, l.3]
> 
> -- I guess the following is a bug:
> -- I cannot even subtract the two!
> bug() == 
>     output map(c +-> sqrtrule c, series(first Phi Psi Phi [x,y,Z.2], t=0)::ULS(EXPR INT, t, 0))
>     output first Phi Psi Phi [x,y,Z2]
> 

You may consider alternative way of doing computation:

sd := x*y*sqrt(argument (kernels(numer(Z.1)::Expression Integer + t*y^2_
-x*y + t*x^2).1).1/(x^2*y^2))
ZZ1 := (sd - (t*y^2 -x*y + t*x^2))/(2*t*(x+y))
ZZ2 := (-sd - (t*y^2 -x*y + t*x^2))/(2*t*(x+y))

then

series(first Phi Psi Phi [x,y,ZZ2], t=0)::ULS(EXPR INT, t, 0)_
 - first Phi Psi Phi [x,y,Z2]

gives me 0.

-- 
                              Waldek Hebisch
hebisch@math.uni.wroc.pl 



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	post-mortem fixes)
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This is a collection of post-mortem fixes for the CATS tests files.
Due to my personal non-zero error rate I reviewed the files once more,
with feeling, to try to catch further mistakes. Unfortunately, but
predictably, there were a few.

Tim

=======================================================================
diff --git a/changelog b/changelog
index c94aa65..6e74f31 100644
--- a/changelog
+++ b/changelog
@@ -1,3 +1,20 @@
+20080428 tpd src/input/schaum19.input post-mortem fixes
+20080428 tpd src/input/schaum23.input post-mortem fixes
+20080428 tpd src/input/schaum24.input post-mortem fixes
+20080428 tpd src/input/schaum27.input post-mortem fixes
+20080428 tpd src/input/schaum28.input post-mortem fixes
+20080428 tpd src/input/schaum29.input post-mortem fixes
+20080428 tpd src/input/schaum33.input post-mortem fixes
+20080428 tpd src/input/schaum6.input post-mortem fixes
+20080428 tpd src/input/schaum7.input post-mortem fixes
+20080428 tpd src/input/schaum9.input post-mortem fixes
+20080427 tpd src/input/schaum34.input show Schaums-Axiom equivalence
+20080427 tpd src/input/schaum33.input show Schaums-Axiom equivalence
+20080427 tpd src/input/schaum32.input show Schaums-Axiom equivalence
+20080427 tpd src/input/schaum31.input show Schaums-Axiom equivalence
+20080427 tpd src/input/schaum30.input show Schaums-Axiom equivalence
+20080427 tpd src/input/schaum29.input show Schaums-Axiom equivalence
+20080427 tpd src/input/schaum28.input fix Schaums-Axiom equivalence
 20080426 tpd src/input/schaum28.input show Schaums-Axiom equivalence
 20080426 tpd src/input/schaum27.input show Schaums-Axiom equivalence
 20080426 tpd src/input/schaum26.input show Schaums-Axiom equivalence
diff --git a/src/input/schaum19.input.pamphlet b/src/input/schaum19.input.pamphlet
index bf580f0..343ab8a 100644
--- a/src/input/schaum19.input.pamphlet
+++ b/src/input/schaum19.input.pamphlet
@@ -1569,7 +1569,7 @@ cc:=aa-bb
 --R                                                     Type: Expression Integer
 --E
 
---S 125    14:416 Schaums and Axiom differ by a constant
+--S 125    14:416 Schaums and Axiom agree
 dd:=expandLog cc
 --R
 --R   (4)  0
diff --git a/src/input/schaum23.input.pamphlet b/src/input/schaum23.input.pamphlet
index c24ef73..d285a80 100644
--- a/src/input/schaum23.input.pamphlet
+++ b/src/input/schaum23.input.pamphlet
@@ -658,6 +658,34 @@ aa:=integrate(1/(q+p*csc(a*x)),x)
 
 --S 47
 t1:=integrate(1/(p+q*sin(a*x)),x)
+--R
+--R   (2)
+--R   [
+--R       log
+--R                                                      +-------+
+--R                                2    2             2  | 2    2
+--R              (p q sin(a x) + (q  - p )cos(a x) + q )\|q  - p
+--R            + 
+--R                    2    3                3    2              3    2
+--R              (- p q  + p )sin(a x) + (- q  + p q)cos(a x) - q  + p q
+--R         /
+--R            q sin(a x) + p
+--R    /
+--R         +-------+
+--R         | 2    2
+--R       a\|q  - p
+--R     ,
+--R                                          +---------+
+--R                                          |   2    2
+--R            (p sin(a x) + q cos(a x) + q)\|- q  + p
+--R      2atan(-----------------------------------------)
+--R                     2    2             2    2
+--R                   (q  - p )cos(a x) + q  - p
+--R    - ------------------------------------------------]
+--R                          +---------+
+--R                          |   2    2
+--R                        a\|- q  + p
+--R                                     Type: Union(List Expression Integer,...)
 --E
 
 --S 48
diff --git a/src/input/schaum24.input.pamphlet b/src/input/schaum24.input.pamphlet
index 9c034da..24b4527 100644
--- a/src/input/schaum24.input.pamphlet
+++ b/src/input/schaum24.input.pamphlet
@@ -2318,10 +2318,10 @@ ff:=expandLog ee
 --R                 2
 --R                                             Type: Expression Complex Integer
 --E
+@
 And we get the surprising result that they are not equal.
 In fact, they differ by a complex value depending on x.
 Likely there is a branch-cut issue lurking somewhere.
-@
 
 \section{\cite{1}:14.506~~~~~$\displaystyle
 \int{x^m\cot^{-1}\frac{x}{a}}~dx$}
diff --git a/src/input/schaum27.input.pamphlet b/src/input/schaum27.input.pamphlet
index cc233e4..68d33a3 100644
--- a/src/input/schaum27.input.pamphlet
+++ b/src/input/schaum27.input.pamphlet
@@ -355,7 +355,7 @@ sinhcoshrule:=rule(sinh(x)*cosh(y) == 1/2*(sinh(x+y)+sinh(x-y)))
 --R                        Type: RewriteRule(Integer,Integer,Expression Integer)
 --E
 
---S 27     14:548 Axiom cannot simplify this expression
+--S 27     14:548 Schaums and Axiom agree
 ff:=sinhcoshrule ee
 --R
 --R   (9)  0
diff --git a/src/input/schaum28.input.pamphlet b/src/input/schaum28.input.pamphlet
index 3ba0bfc..49efb0e 100644
--- a/src/input/schaum28.input.pamphlet
+++ b/src/input/schaum28.input.pamphlet
@@ -410,7 +410,9 @@ cc:=aa-bb
 --R                         2                                      2
 --R              a sinh(a x)  + 2a cosh(a x)sinh(a x) + a cosh(a x)  + a
 --R                                                     Type: Expression Integer
---S 32
+--E
+
+--S 32     14:571 Schaums and Axiom differ by a constant
 dd:=complexNormalize cc
 --R
 --R          1
@@ -526,7 +528,7 @@ sinhcoshrule:=rule(sinh(x)*cosh(y) == 1/2*(sinh(x+y)+sinh(x-y)))
 --R                        Type: RewriteRule(Integer,Integer,Expression Integer)
 --E
 
---S 41     14:572 Schaums and Axiom agree
+--S 41     14:572 Axiom cannot simplify this expression
 ff:=sinhcoshrule ee
 --R
 --R   (9)
@@ -787,9 +789,9 @@ dd:=tanhrule cc
 --S 61
 sinhcoshrule:=rule(sinh(x)*cosh(y) == 1/2*(sinh(x+y)+sinh(x-y)))
 --R
---I                             %B sinh(y + x) - %B sinh(y - x)
---I   (6)  %B cosh(y)sinh(x) == -------------------------------
---R                                            2
+--I                              %BC sinh(y + x) - %BC sinh(y - x)
+--I   (6)  %BC cosh(y)sinh(x) == -------------------------------
+--R                                              2
 --R                        Type: RewriteRule(Integer,Integer,Expression Integer)
 --E
 
@@ -809,9 +811,9 @@ ee:=sinhcoshrule dd
 --S 63
 sinhsinhrule:=rule(sinh(x)*sinh(y)==1/2*(cosh(x+y)-cosh(x-y)))
 --R
---I                             %B cosh(y + x) - %B cosh(y - x)
---I   (8)  %B sinh(x)sinh(y) == -------------------------------
---R                                            2
+--I                              %BD sinh(y + x) - %BD sinh(y - x)
+--I   (8)  %BD cosh(y)sinh(x) == -------------------------------
+--R                                              2
 --R                        Type: RewriteRule(Integer,Integer,Expression Integer)
 --E
 
@@ -1485,7 +1487,7 @@ bb:=1/(2*a)*coth((a*x)/2)-1/(6*a)*coth((a*x)/2)^3
 --R                                                     Type: Expression Integer
 --E
 
---S 107    14:580 Axiom cannot compute this integral
+--S 107    14:580 Axiom cannot simplify this expression
 cc:=aa-bb
 --R
 --R   (3)
@@ -2681,7 +2683,7 @@ cc1:=aa-bb1
 --R                                                     Type: Expression Integer
 --E
 
---S 134    14:584 Axiom cannot compute this integral
+--S 134    14:584 Axiom cannot simplify this expression
 cc2:=aa-bb2
 --R
 --R   (5)
diff --git a/src/input/schaum29.input.pamphlet b/src/input/schaum29.input.pamphlet
index 1aff49f..9c79630 100644
--- a/src/input/schaum29.input.pamphlet
+++ b/src/input/schaum29.input.pamphlet
@@ -77,7 +77,7 @@ coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2)
 --R                        Type: RewriteRule(Integer,Integer,Expression Integer)
 --E
 
---S 7      14:590 Schaums and Axiom agree
+--S 7      14:590 Schaums and Axiom differ by a constant
 ee:=coshsqrrule dd
 --R
 --R         1
@@ -209,6 +209,7 @@ bb:=cosh(a*x)^(n+1)/((n+1)*a)
 --E
 
 --S 16     14:593 Axiom cannot simplify this expression
+cc:=aa-bb
 --R
 --R   (3)
 --R       - cosh(a x)sinh(n log(cosh(a x))) - cosh(a x)cosh(n log(cosh(a x)))
@@ -727,6 +728,7 @@ bb:=-(2*coth(2*a*x))/a
 --E
 
 --S 47     14:598 Axiom cannot simplify this expression
+cc:=aa-bb
 --R
 --R   (3)
 --R                           4                                3
diff --git a/src/input/schaum33.input.pamphlet b/src/input/schaum33.input.pamphlet
index 74e0c8b..61506d7 100644
--- a/src/input/schaum33.input.pamphlet
+++ b/src/input/schaum33.input.pamphlet
@@ -666,7 +666,7 @@ gg:=sinhcoshrule ff
 --R                                                     Type: Expression Integer
 --E
 
---S 38     14:642 Axiom cannot simplify this expression
+--S 38     14:642 Schaums and Axiom differ by a constant
 hh:=complexNormalize gg
 --R
 --R         - log(- 1) + log(- 2)
diff --git a/src/input/schaum6.input.pamphlet b/src/input/schaum6.input.pamphlet
index 854e780..ca2c6aa 100644
--- a/src/input/schaum6.input.pamphlet
+++ b/src/input/schaum6.input.pamphlet
@@ -467,7 +467,7 @@ bb:=-x/(2*(x^2+a^2))+1/(2*a)*atan(x/a)
 --R                                                     Type: Expression Integer
 --E
 
---S 38     14:134 Schaums and Axiom differ by a constant
+--S 38     14:134 Schaums and Axiom agree
 cc:=aa-bb
 --R
 --R   (3)  0
diff --git a/src/input/schaum7.input.pamphlet b/src/input/schaum7.input.pamphlet
index fcdd71c..52e0b97 100644
--- a/src/input/schaum7.input.pamphlet
+++ b/src/input/schaum7.input.pamphlet
@@ -410,9 +410,9 @@ t2:=logpow t1
 
 --S 35     14:150 Schaums and Axiom agree
 cc:=aa-t2
-
-   (7)  0
-                                                     Type: Expression Integer
+--R
+--R   (7)  0
+--R                                                     Type: Expression Integer
 --E
 @
 
diff --git a/src/input/schaum9.input.pamphlet b/src/input/schaum9.input.pamphlet
index d632de7..fa7d4f2 100644
--- a/src/input/schaum9.input.pamphlet
+++ b/src/input/schaum9.input.pamphlet
@@ -392,12 +392,12 @@ dd:=expandLog cc
 
 --S 28     14:188 Schaums and Axiom differ by a constant
 ee:=complexNormalize dd
-
-        log(- 1)
-   (5)  --------
-             3
-           2a
-                                                     Type: Expression Integer
+--R
+--R        log(- 1)
+--R   (5)  --------
+--R             3
+--R           2a
+--R                                                     Type: Expression Integer
 --E
 
 @



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Dear William, Dear Waldek,

many thanks for your help!

I guess, the real problem is that

(71) -> ex := ((-2*t*x*y)+(-2*t*x^2))/(y*(t^2*y^4+((-4*t^2)+(-2*t))*x*y^3+((-6*t^2)+1)*x^2*y^2+((-4*t^2)+(-2*t))*x^3*y+t^2*x^4)^(1/2)+t*y^3+(-x*y^2)+t*x^2*y)

                                                              2
                                               - 2t x y - 2t x
   (71)  --------------------------------------------------------------------------------------------
           +------------------------------------------------------------------+
           | 2 4        2         3        2      2 2        2       3     2 4       3      2      2
         y\|t y  + (- 4t  - 2t)x y  + (- 6t  + 1)x y  + (- 4t  - 2t)x y + t x   + t y  - x y  + t x y
                                                                                                Type: Expression Integer
(72) -> series(ex, t=0)

                      2          3       2     2      3
           - 2x y - 2x       - 2y  - 2x y  - 2x y - 2x   2      3
   (72)  --------------- t + -------------------------- t  + O(t )
           +----+                    +----+
           | 2 2       2           2 | 2 2       3
         y\|x y   - x y           y \|x y   - x y
                                                                   Type: UnivariatePuiseuxSeries(Expression Integer,t,0)

is not correct in general, eg., when x*y > 0.  In my case, I consider x and y
in fact as formal power series in t themselves, and I think I also want that
sqrt(x^2)=x.


Martin




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On 04/30/2008 02:10 PM, Martin Rubey wrote:
> In my case, I consider x and y in fact as formal power series in t
> themselves, and I think I also want that sqrt(x^2)=x.

Replace x by the formal power series in t having only the constant term -1.

Ralf



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Ralf Hemmecke <ralf@hemmecke.de> writes:

> On 04/30/2008 02:10 PM, Martin Rubey wrote:
> > In my case, I consider x and y in fact as formal power series in t
> > themselves, and I think I also want that sqrt(x^2)=x.
> 
> Replace x by the formal power series in t having only the constant term -1.

I know, but (I believe that) my formal power series has positive leading
coefficient.

Martin




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Hello,

Next week I'll make a short description of Axioms to some mathematic 
French teachers.

I'll be happy to cite the conclusion of your test about the Schaum book.

How many integrals is there in the book ?
How many do you test ? (all ?!)
How many are immediately the same ?
How many are false ? (no one I expect !)
How many differs ?
Do you have any idea about the result of others CAS ?

Might you give me some tips for one or two slides...

Many thanks.

Francois in France.



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Date: Wed, 30 Apr 2008 14:58:05 -0400
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Subject: [Axiom-developer] Re: About Schaums.
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How many integrals is there in the book ? ... 619 
How many do you test ? (all ?!) .... all
How many are immediately the same ? 
How many are false ? (no one I expect !) 
How many differs ?
Do you have any idea about the result of others CAS ? 
  .... no but this effort is called CATS (Computer Algebra Test Suite)
  and is intended to be tested against, and used as a standard for test
  against, other systems. I plan to test other systems as time permits.

All of these results can be found in the axiom distribution under
  src/input/schaum*.input.pamphlet

===============================================================
619 integrals
   237 agreements (differ by 0) (38%)
   134 differ by a constant (22%)
 371 total (60%)
   108 simplification failures (17.5%)
   135 integrals not in closed form (21.5%)
 243 total (39%)

There were a few "other" answers which were not part of the above. 
Of interest was:

  Axiom found 2 typos in Schaums (1968 printing 4)

  Differing by a constant seems to be related to the choice of 
  signs and branch cuts. There is much of interest to be learned
  by these values which I hope to explore later.

  Axiom has a closed form for 2 integrals where Schaums has series.

    Axiom claims to be a "decision procedure" for elementary integrals.
    If there is a closed form for the result, Axiom will return it.
    If Axiom returns the original integral, then no closed form exists.

  It is undecided if the values that did not simplify agree with Schaums.
  These simplifications will be checked in more detail using Axiom and
  other computer algebra systems. In particular, this has caused me to 
  work on a more general purpose simplification procedure for Axiom.

(Spiegel, Murray R.; Schaums Mathematical Handbook, 1968, printing 4)
(Axiom March 2008 release)

  14:59 Schaums and Axiom agree
  14:60 Schaums and Axiom agree
  14:61 Schaums and Axiom differ by a constant
  14:62 Schaums and Axiom differ by a constant
  14:63 Schaums and Axiom agree
  14:64 Schaums and Axiom agree
  14:65 Schaums and Axiom agree
  14:66 Schaums and Axiom agree
  14:67 Schaums and Axiom agree
  14:68 Schaums and Axiom differ by a constant
  14:69 Schaums and Axiom differ by a constant
  14:70 Schaums and Axiom agree
  14:71 Schaums and Axiom agree
  14:72 Schaums and Axiom differ by a constant
  14:73 Schaums and Axiom differ by a constant
  14:74 Schaums and Axiom agree
  14:75 Schaums and Axiom agree
  14:76 Schaums and Axiom agree
  14:77 Schaums and Axiom differ by a constant
  14:78 Schaums and Axiom agree
  14:79 Schaums and Axiom agree
  14:80 Schaums and Axiom agree
  14:82 Schaums and Axiom agree
  14:83 Axiom cannot do this integration
  14:84 Schaums and Axiom agree
  14:85 Schaums and Axiom agree
  14:86 Schaums and Axiom agree
  14:87a Schaums and Axiom differ by a constant
  14:87b Schaums and Axiom differ by a constant
  14:88 Schaums and Axiom differ by a constant
  14:89 Schaums and Axiom differ by a constant
  14:90 Schaums and Axiom agree
  14:91 Axiom cannot simplify this expression. Schaums typo?
  14:92 Axiom cannot simplify this expression
  14:93 Schaums and Axiom agree
  14:94 Axiom cannot do this integral
  14:95 Axiom cannot do this integral
  14:96 Axiom cannot do this integral
  14:97 Axiom cannot do this integral
  14:98 Axiom cannot do this integral
  14:99 Schaums and Axiom agree
  14:xxx Schaums and Axiom agree
  14:100 Schaums and Axiom agree
  14:101 Schaums and Axiom agree
  14:102 Axiom cannot do this integral
  14:103 Axiom cannot do this integral
  14:104 Axiom cannot do this integral
  14:105 Schaums and Axiom agree
  14:106 Schaums and Axiom agree
  14:107 Schaums and Axiom agree
  14:108 Schaums and Axiom agree
  14:109 Schaums and Axiom agree
  14:110 Axiom cannot do this integral
  14:111 Schaums and Axiom agree
  14:112 Axiom cannot do this integral
  14:113 Schaums and Axiom agree
  14:114 Axiom cannot simplify these answers
  14:115 Axiom cannot simplify these answers
  14:116 Axiom cannot compute this integral
  14:117 Axiom cannot compute this integral
  14:118 Axiom cannot compute this integral
  14:119 Axiom cannot compute this integral
  14:120 Axiom cannot simplify these answers
  14:121 Axiom cannot simplify this answer
  14:122 Axiom cannot simplify this answer
  14:123 Axiom cannot simplify these results
  14:124 Axiom cannot simplify this result
  14:125 Schaums and Axiom agree
  14:126 Schaums and Axiom agree
  14:127 Schaums and Axiom agree
  14:128 Schaums and Axiom agree
  14:129 Schaums and Axiom agree
  14:130 Schaums and Axiom agree
  14:131 Schaums and Axiom agree
  14:132 Schaums and Axiom agree
  14:133 Schaums and Axiom agree
  14:134 Schaums and Axiom agree
  14:135 Schaums and Axiom agree
  14:136 Schaums and Axiom agree
  14:137 Schaums and Axiom agree
  14:138 Schaums and Axiom agree
  14:139 Axiom cannot do this integral
  14:140 Schaums and Axiom agree
  14:141 Axiom cannot do this integral
  14:142 Axiom cannot do this integral
  14:143 Axiom cannot do this integral
  14:144 Schaums and Axiom agree
  14:145 Schaums and Axiom agree
  14:146 Schaums and Axiom agree
  14:147 Schaums and Axiom agree
  14:148 Schaums and Axiom agree
  14:149 Schaums and Axiom agree
  14:150 Schaums and Axiom agree
  14:151 Schaums and Axiom agree
  14:152 Schaums and Axiom agree
  14:153 Schaums and Axiom agree
  14:154 Schaums and Axiom agree
  14:155 Schaums and Axiom agree
  14:156 Schaums and Axiom agree
  14:157 Schaums and Axiom agree
  14:158 Axiom cannot do this integral
  14:159 Schaums and Axiom agree
  14:160 Axiom cannot compute this integral
  14:161 Axiom cannot compute this integral
  14:162 Axiom cannot compute this integral
  14:163 Schaums and Axiom differ by a constant
  14:164 Schaums and Axiom differ by a constant
  14:165 Schaums and Axiom differ by a constant
  14:166 Schaums and Axiom differ by a constant
  14:167 Schaums and Axiom differ by a constant
  14:168 Schaums and Axiom differ by a constant
  14:169 Schaums and Axiom differ by a constant
  14:170 Schaums and Axiom differ by a constant
  14:171 Schaums and Axiom agree
  14:172 Schaums and Axiom differ by a constant
  14:173 Schaums and Axiom differ by a constant
  14:174 Schaums and Axiom differ by a constant
  14:175 Schaums and Axiom differ by a constant
  14:176 Schaums and Axiom differ by a constant
  14:177 Axiom cannot do this integration
  14:178 Schaums and Axiom agree
  14:179 Axiom cannot integrate this expression
  14:180 Axiom cannot integrate this expression
  14:181 Axiom cannot integrate this expression
  14:182 Schaums and Axiom differ by a constant
  14:183 Schaums and Axiom agree
  14:184 Schaums and Axiom differ by a constant
  14:185 Schaums and Axiom agree
  14:186 Schaums and Axiom differ by a constant
  14:187 Schaums and Axiom differ by a constant
  14:188 Schaums and Axiom differ by a constant
  14:189 Schaums and Axiom differ by a constant
  14:190 Schaums and Axiom agree
  14:191 Schaums and Axiom differ by a constant
  14:192 Schaums and Axiom agree
  14:193 Schaums and Axiom differ by a constant
  14:194 Schaums and Axiom differ by a constant
  14:195 Schaums and Axiom differ by a constant
  14:196 Schaums and Axiom differ by a constant
  14:197 Schaums and Axiom agree
  14:198 Schaums and Axiom differ by a constant
  14:199 Schaums and Axiom agree
  14:200 Schaums and Axiom differ by a constant
  14:201 Schaums and Axiom differ by a constant
  14:202 Schaums and Axiom differ by a constant
  14:203 Schaums and Axiom differ by a constant
  14:204 Schaums and Axiom agree
  14:205 Schaums and Axiom differ by a constant
  14:206 Schaums and Axiom agree
  14:207 Schaums and Axiom differ by a constant
  14:208 Schaums and Axiom differ by a constant
  14:209 Schaums and Axiom differ by a constant
  14:210 Schaums and Axiom differ by a constant
  14:211 Schaums and Axiom differ by a constant
  14:212 Schaums and Axiom agree
  14:213 Schaums and Axiom differ by a constant
  14:214 Schaums and Axiom differ by a constant
  14:215 Schaums and Axiom differ by a constant
  14:216 Schaums and Axiom differ by a constant 
  14:217 Schaums and Axiom agree
  14:218 Schaums and Axiom differ by a constant
  14:219 Schaums and Axiom agree
  14:220 Schaums and Axiom differ by a constant
  14:221 Schaums and Axiom differ by a constant
  14:222 Schaums and Axiom differ by a constant
  14:223 Schaums and Axiom differ by a constant
  14:224 Schaums and Axiom agree
  14:225 Schaums and Axiom differ by a constant
  14:226 Schaums and Axiom agree
  14:227 Schaums and Axiom differ by a constant
  14:228 Schaums and Axiom differ by a constant
  14:229 Schaums and Axiom differ by a constant
  14:230 Schaums and Axiom differ by a constant
  14:231 Schaums and Axiom agree
  14:232 Schaums and Axiom differ by a constant
  14:233 Schaums and Axiom agree
  14:234 Schaums and Axiom differ by a constant
  14:235 Schaums and Axiom differ by a constant
  14:236 Schaums and Axiom differ by a constant
  14:238 Schaums and Axiom agree
  14:238 Schaums and Axiom differ by a constant
  14:239 Schaums and Axiom agree
  14:240 Schaums and Axiom differ by a constant
  14:241 Schaums and Axiom differ by a constant
  14:242 Schaums and Axiom agree
  14:243 Schaums and Axiom differ by a constant
  14:244 Schaums and Axiom agree
  14:245 Schaums and Axiom differ by a constant
  14:246 Schaums and Axiom agree
  14:247 Schaums and Axiom differ by a constant
  14:248 Schaums and Axiom differ by a constant
  14:249 Schaums and Axiom agree
  14:250 Schaums and Axiom differ by a constant
  14:251 Schaums and Axiom agree
  14:252 Schaums and Axiom differ by a constant
  14:253 Schaums and Axiom agree
  14:254 Schaums and Axiom differ by a constant
  14:255 Schaums and Axiom differ by a constant
  14:256 Schaums and Axiom agree
  14:257 Schaums and Axiom differ by a constant
  14:258 Schaums and Axiom agree
  14:259 Schaums and Axiom differ by a constant
  14:260 Schaums and Axiom agree
  14:261 Schaums and Axiom differ by a constant
  14:262 Schaums and Axiom differ by a constant
  14:263 Schaums and Axiom agree
  14:264 Schaums and Axiom differ by a constant
  14:265 Axiom cannot simplify these expressions
  14:266 Axiom cannot simplify these expressions
  14:267 Schaums and Axiom differ by a constant
  14:268 Axiom cannot compute this integral
  14:269 Schaums and Axiom differ by a constant
  14:270 Schaums and Axiom differ by a constant
  14:271 Axiom cannot compute this integral
  14:272 Axiom cannot simplify these expressions
  14:273 Schaums and Axiom differ by a constant
  14:274 Schaums and Axiom agree
  14:275 Axiom cannot compute this integral
  14:276 Axiom cannot compute this integral
  14:277 Schaums and Axiom differ by a constant
  14:278 Schaums and Axiom differ by a constant
  14:279 Axiom cannot compute this integral
  14:280 Axiom cannot simplify these expressions
  14:281 Axiom cannot simplify these expressions
  14:282 Axiom cannot simplify these expressions
  14:283 Axiom cannot simplify these expressions
  14:284 Axiom cannot simplify these expressions
  14:284 Axiom cannot simplify these expressions
  14:285 Axiom cannot simplify these expressions
  14:286 Axiom cannot simplify these expressions
  14:287 Axiom cannot simplify these expressions
  14:288 Axiom cannot simplify these expressions
  14:289 Axiom cannot simplify these expressions
  14:290 Axiom cannot simplify these expressions
  14:291 Axiom cannot simplify these expressions
  14:292 Axiom cannot simplify these expressions
  14:293 Axiom cannot simplify these expressions
  14:295 Axiom cannot compute this integral
  14:296 Axiom cannot compute this integral
  14:297 Axiom cannot compute this integral
  14:298 Axiom cannot compute this integral
  14:299 Schaums and Axiom agree
  14:300 Schaums and Axiom agree
  14:301 Schaums and Axiom agree
  14:302 Schaums and Axiom agree
  14:303 Schaums and Axiom agree
  14:304 Schaums and Axiom agree
  14:305 Schaums and Axiom agree
  14:306 Schaums and Axiom agree
  14:307 Schaums and Axiom agree
  14:308 Schaums and Axiom agree
  14:309 Axiom cannot compute this integral
  14:310 Axiom cannot compute this integral
  14:311 Schaums and Axiom differ by a constant
  14:312 Schaums and Axiom agree
  14:313 Schaums and Axiom differ by a constant
  14:314 Schaums and Axiom agree
  14:315 Schaums and Axiom agree
  14:316 Schaums and Axiom differ by a constant
  14:317 Schaums and Axiom agree
  14:318 Schaums and Axiom agree
  14:319 Schaums and Axiom agree
  14:320 Schaums and Axiom agree
  14:321 Schaums and Axiom agree
  14:322 Schaums and Axiom agree
  14:323 Schaums and Axiom agree
  14:324 Schaums and Axiom agree
  14:325 Axiom cannot simplify this expression
  14:326 Schaums and Axiom agree
  14:327 Axiom cannot compute this integral
  14:328 Axiom cannot compute this integral
  14:329 Schaums and Axiom differ by a constant
  14:330 Schaums and Axiom agree
  14:331 Schaums and Axiom agree
  14:332 Axiom cannot compute this integral
  14:333 Axiom cannot compute this integral
  14:334 Axiom cannot simplify this expression
  14:335 Axiom cannot compute this integral
  14:336 Axiom cannot compute this integral
  14:337 Axiom cannot compute this integral
  14:338 Axiom cannot compute this integral
  14:339 Schaums and Axiom agree
  14:340 Schaums and Axiom agree
  14:341 Schaums and Axiom agree
  14:342 Schaums and Axiom agree
  14:343 Schaums and Axiom agree by definition
  14:344 Axiom cannot compute this integral
  14:345 Schaums and Axiom agree
  14:346 Axiom cannot compute this integral
  14:347 Schaums and Axiom agreee
  14:348 Schaums and Axiom differ by a constant
  14:349 Schaums and Axiom agree
  14:350 Schaums and Axiom agree
  14:351 Schaums and Axiom agree
  14:352 Schaums and Axiom agree
  14:353 Axiom cannot simplify this expression
  14:354 Schaums and Axiom differ by a constant
  14:355 Axiom cannot simplify this expression
  14:356 Axiom cannot simplify this expression
  14:357 Axiom cannot simplify this expression
  14:358 Axiom cannot simplify this expression
  14:359 Axiom cannot simplify this expression
  14:360 Axiom cannot simplify these equations
  14:361 Schaums and Axiom differ by a constant
  14:362 Axiom cannot simplify this expression
  14:363 Axiom cannot simplify this expression
  14:364 Axiom cannot compute this integral
  14:365 Axiom cannot compute this integral
  14:366 Axiom cannot compute this integral
  14:367 Axiom cannot compute this integral
  14:368 Axiom cannot compute this integral
  14:369 Schaums and Axiom agree
  14:370 Schaums and Axiom agree
  14:371 Schaums and Axiom agree
  14:372 Schaums and Axiom agree
  14:373 Schaums and Axiom agree by definition
  14:374 Axiom cannot compute this integral
  14:375 Axiom cannot simplify these expressions
  14:376 Axiom cannot compute this integral
  14:377 Schaums and Axiom agree
  14:378 Schaums and Axiom differ by a constant
  14:379 Schaums and Axiom agree
  14:380 Axiom cannot simplify this expression
  14:381 Schaums and Axiom agree
  14:382 Axiom cannot simplify this expression
  14:383 Axiom cannot simplify this expression
  14:384 Axiom cannot simplify this expression
  14:385 Axiom cannot simplify this expression
  14:386 Axiom cannot simplify this expression
  14:387 Axiom cannot simplify this expression
  14:388 Axiom cannot simplify this expression
  14:389 Axiom cannot simplify this expression
  14:390 Axiom cannot simplify these expressions
  14:391 Schaums and Axiom agree
  14:392 Axiom cannot simplify these expressions
  14:393 Axiom cannot simplify these expressions
  14:394 Axiom cannot compute this integral
  14:395 Axiom cannot compute this integral
  14:396 Axiom cannot compute this integral
  14:397 Axiom cannot compute this integral
  14:398 Axiom cannot compute this integral
  14:399 Schaums and Axiom differ by a constant
  14:400 Axiom is unable to simplify this expression
  14:401 Schaums and Axiom agree
  14:402 Schaums and Axiom agree
  14:403 Schaums and Axiom agree
  14:404 Schaums and Axiom differ by a constant
  14:405 Schaums and Axiom differ by a constant
  14:406 Schaums and Axiom differ by a constant
  14:407 Schaums and Axiom agree
  14:408 Schaums and Axiom differ by a constant
  14:409 Schaums and Axiom agree
  14:410 Schaums and Axiom differ by a constant
  14:411 Schaums and Axiom differ by a constant
  14:412 Axiom cannot simplify this expression
  14:413 Schaums and Axiom agree
  14:414 Schaums and Axiom agree
  14:415 Schaums and Axiom differ by a constant
  14:416 Schaums and Axiom agree
  14:417 Schaums and Axiom agree
  14:418 Schaums and Axiom agree
  14:419 Axiom cannot simplify this expression
  14:420 Axiom cannot simplify these expressions
  14:421 Schaums and Axiom agree
  14:422 Axiom cannot simplify this expression
  14:423 Axiom cannot simplify this expressions
  14:424 Schaums and Axiom differ by a constant
  14:425 Axiom cannot compute this integral
  14:426 Axiom cannot compute this integral
  14:427 Axiom cannot compute this integral
  14:428 Axiom cannot compute this integral
  14:429 Schaums and Axiom agree
  14:430 Schaums and Axiom agree
  14:431 Schaums and Axiom agree
  14:432 Schaums and Axiom agree
  14:433 Schaums and Axiom differ by a constant
  14:435 Axiom cannot compute this integral
  14:436 Axiom cannot compute this integral
  14:437 Schaums and Axiom agree
  14:438 Schaums and Axiom agree
  14:439 Axiom cannot compute this integral
  14:440 Schaums and Axiom agree
  14:441 Schaums and Axiom agree
  14:442 Schaums and Axiom agree
  14:443 Schaums and Axiom agree
  14:444 Schaums and Axiom differ by a constant
  14:445 Schaums and Axiom agree
  14:446 Axiom cannot compute this integral
  14:447 Axiom cannot compute this integral
  14:448 Schaums and Axiom agree
  14:449 Axiom cannot simplify this expression
  14:450 Axiom cannot compute this integral
  14:451 Schaums and Axiom differ by a constant
  14:452 Schaums and Axiom agree
  14:453 Schaums and Axiom differ by a constant
  14:454 Axiom cannot simplify this expression
  14:455 Schaums and Axiom agree
  14:456 Axiom cannot compute this integral
  14:457 Axiom cannot compute this integral
  14:458 Schaums and Axiom differ by a constant
  14:459 Schaums and Axiom agree
  14:460 Axiom cannot compute this integral
  14:461 Schaums and Axiom agree
  14:462 Schaums and Axiom agree
  14:463 Schaums and Axiom agree
  14:464 Axiom cannot simplify this expression
  14:465 Schaums and Axiom agree
  14:466 Axiom cannot compute this integral
  14:467 Axiom cannot compute this integral
  14:468 Schaums and Axiom differ by a constant
  14:469 Schaums and Axiom agree
  14:470 Axiom cannot compute this integral
  14:471 Axiom cannot simplify this expression
  14:472 Axiom cannot simplify this expression
  14:473 Axiom cannot simplify this expression
  14:474 Axiom cannot compute this integral
  14:475 Axiom cannot simplify this expression
  14:476 Axiom cannot simplify this expression
  14:477 Axiom cannot simplify this expression
  14:478 Axiom cannot simplify this expression
  14:479 Axiom cannot simplify this expression
  14:480 Axiom cannot compute this integral
  14:481 Axiom cannot simplify this expression
  14:482 Axiom cannot simplify this expression
  14:483 SCHAUMS AND AXIOM DIFFER? (BRANCH CUTS?)
  14:484 Axiom cannot compute this integral
  14:485 Axiom cannot simplify this expression
  14:486 Axiom cannot compute this integral
  14:487 SCHAUMS AND AXIOM DIFFER? (branch cuts?)
  14:488 Axiom and Schaums agree
  14:489 Axiom and Schaums agree
  14:490 Axiom and Schaums agree
  14:491 Axiom cannot compute this integral
  14:492 Schaums and Axiom agree
  14:493 Axiom cannot simplify these expressions
  14:494 Axiom cannot simplify these expressions
  14:495 Axiom cannot simplify these expressions
  14:496 Axiom cannot compute this integral
  14:497 Axiom cannot simplify these expressions
  14:498 Axiom cannot simplify these expressions
  14:499 Axiom cannot simplify these expressions
  14:500 Axiom cannot simplify this expression
  14:501 Axiom cannot compute this integral
  14:502 Axiom cannot simplify this expression
  14:503 Axiom cannot compute this integral
  14:504 Axiom cannot compute this integral
  14:505 SCHAUMS AND AXIOM DISAGREE? (branch cuts?)
  14:506 Axiom cannot compute this integral
  14:507 Axiom cannot compute this integral
  14:508 Axiom cannot compute this integral
  14:509 Schaums and Axiom agree
  14:510 Schaums and Axiom agree
  14:511 Schaums and Axiom agree
  14:512 Axiom cannot compute this integral
  14:513 Schaums and Axiom agree by definition
  14:514 Axiom cannot compute this integral
  14:515 Schaums and Axiom agree
  14:516 Schaums and Axiom agree
  14:517 Axiom cannot simplify these expressions
  14:518 Schaums and Axiom agree
  14:519 Schaums and Axiom agree
  14:520 Schaums and Axiom agree
  14:521 Schaums and Axiom agree
  14:522 Schaums and Axiom agree by definition
  14:523 Axiom cannot compute this integral
  14:524 Axiom cannot compute this integral
  14:525 Schaums and Axiom agree
  14:526 Schaums and Axiom agree
  14:527 Schaums and Axiom agree
  14:528 Schaums and Axiom agree
  14:529 Schaums and Axiom agree
  14:530 Schaums and Axiom agree
  14:531 Schaums and Axiom agree
  14:532 Schaums and Axiom agree
  14:533 Schaums and Axiom agree by definition
  14:534 Axiom cannot compute this integral
  14:535 Axiom cannot compute this integral
  14:536 Axiom cannot compute this integral
  14:537 Schaums and Axiom agree
  14:538 Schaums and Axiom agree
  14:539 Axiom cannot compute this integral
  14:540 Schaums and Axiom agree
  14:541 Schaums and Axiom agree
  14:542 Schaums and Axiom agree
  14:543 Axiom cannot compute this integral
  14:544 Axiom cannot compute this integral
  14:545 Axiom cannot simplify this expression
  14:546 Axiom cannot compute this integral
  14:547 Schaums and Axiom agree
  14:548 Schaums and Axiom agree
  14:549 Schaums and Axiom differ by a constant
  14:550 Axiom cannot simplify this expression
  14:551 Schaums and Axiom agree
  14:552 Schaums and Axiom agree
  14:553 Axiom cannot simplify this expression
  14:554 Axiom cannot simplify this expression
  14:555 Axiom cannot simplify this expression
  14:556 Axiom cannot simplify this expression
  14:557 Axiom cannot compute this integral
  14:558 Axiom cannot compute this integral
  14:559 Axiom cannot compute this integral
  14:560 Axiom cannot compute this integral
  14:561 Axiom cannot compute this integral
  14:562 Schaums and Axiom agree
  14:563 Schaums and Axiom agree
  14:564 Schaums and Axiom agree
  14:565 Axiom cannot compute this integral
  14:566 Axiom cannot compute this integral
  14:567 Schaums and Axiom agree
  14:568 Axiom cannot compute this integral
  14:569 Schaums and Axiom agree
  14:570 Schaums and Axiom agree
  14:571 Schaums and Axiom differ by a constant
  14:572 Axiom cannot simplify this expression
  14:573 Schaums and Axiom agree
  14:574 Schaums and Axiom agree
  14:575 Schaums and Axiom differ by a constant
  14:576 Schaums and Axiom differ by a constant
  14:577 Schaums and Axiom differ by a constant
  14:578 Schaums and Axiom differ by a constant
  14:579 Axiom cannot compute this integral
  14:580 Axiom cannot simplify this expression
  14:581 Axiom cannot simplify this expression
  14:582 Axiom cannot simplify this expression
  14:583 Axiom cannot simplify this expression
  14:584 Axiom cannot simplify this expression
  14:585 Axiom cannot compute this integral
  14:586 Axiom cannot compute this integral
  14:587 Axiom cannot compute this integral
  14:588 Axiom cannot compute this integral
  14:589 Axiom cannot compute this integral
  14:590 Schaums and Axiom differ by a constant
  14:591 Axiom cannot simplify this expression
  14:592 Axiom cannot simplify this expression
  14:593 Axiom cannot simplify this expression
  14:594 Schaums and Axiom agree
  14:595 Schaums and Axiom agree
  14:596 Axiom cannot simplify this expression
  14:597 Schaums and Axiom agree
  14:598 Axiom cannot simplify this expression
  14:599 Axiom cannot simplify this expression
  14:600 Axiom cannot simplify this expression
  14:601 Schaums and Axiom agree
  14:602 Schaums and Axiom agree
  14:603 Schaums and Axiom agree
  14:604 Schaums and Axiom differ by a constant
  14:605 Schaums and Axiom differ by a constant
  14:606 Axiom cannot simplify this expression
  14:607 Axiom cannot simplify this expression
  14:608 Schaums and Axiom agree
  14:609 Schaums and Axiom differ by a constant
  14:610 Axiom cannot compute this integral
  14:611 Schaums and Axiom differ by a constant
  14:612 Axiom cannot compute this integral
  14:613 Schaums and Axiom differ by a constant
  14:614 Axiom cannot compute this integral
  14:615 Schaums and Axiom differ by a constant
  14:616 Schaums and Axiom differ by a constant
  14:617 Axiom cannot simplify this expression
  14:618 Schaums and Axiom agree
  14:619 Schaums and Axiom agree
  14:620 Schaums and Axiom differ by a constant
  14:621 Axiom cannot compute this integral
  14:622 Schaums and Axiom differ by a constant
  14:623 Axiom cannot compute this integral
  14:624 Schaums and Axiom differ by a constant
  14:625 Axiom cannot compute this integral
  14:626 Schaums and Axiom agree
  14:627 Schaums and Axiom differ by a constant
  14:628 Axiom cannot simplify this expression
  14:629 Schaums and Axiom agree
  14:630 Schaums and Axiom agree
  14:631 Axiom cannot compute this integral
  14:632 Schaums and Axiom differ by a constant
  14:633 Axiom cannot compute this integral
  14:634 Schaums and Axiom agree
  14:635 Axiom cannot compute this integral
  14:636 Schaums and Axiom agree
  14:637 Axiom cannot simplify this expression
  14:638 Axiom cannot simplify this expression
  14:639 Schaums and Axiom agree
  14:640 Schaums and Axiom agree
  14:641 Axiom cannot compute this integral
  14:642 Schaums and Axiom differ by a constant
  14:643 Axiom cannot compute this integral
  14:644 Schaums and Axiom differ by a constant
  14:645 Axiom cannot compute this integral
  14:646 Schaums and Axiom agree
  14:647 Schaums and Axiom agree
  14:648 Schaums and Axiom agree
  14:649 Axiom cannot compute this integral
  14:650 Schaums and Axiom differ by a constant
  14:651 Schaums and Axiom agree
  14:652 Schaums and Axiom agree
  14:653 Schaums and Axiom agree
  14:654 Axiom cannot compute this integral
  14:655 Axiom cannot simplify these expressions
  14:656 Schaums and Axiom differ by a constant
  14:657 Schaums and Axiom agree
  14:658 Schaums and Axiom differ by a constant
  14:659 Axiom cannot compute this integral
  14:660 Schaums and Axiom agree
  14:661 Schaums and Axiom agree
  14:662 Schaums and Axiom agree
  14:663 Schaums and Axiom agree
  14:664 Axiom cannot compute this integral
  14:665 Schaums and Axiom agree
  14:666 Schaums and Axiom agree
  14:667 Schaums and Axiom differ by a constant
  14:668 SCHAUMS AND AXIOM DIFFER (Axiom has closed form)
  14:669 Axiom cannot simplify these expressions
  14:670 Axiom cannot simplify these expressions
  14:671 SCHAUMS AND AXIOM DIFFER (Axiom has closed form)
  14:672 Axiom cannot compute this integral
  14:673 Axiom cannot compute this integral
  14:674 Axiom cannot compute this integral
  14:675 Axiom cannot compute this integral
  14:676 Axiom cannot compute this integral
  14:677 Axiom cannot compute this integral


  



   



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To: daly@axiom-developer.org
Subject: Re: [Axiom-developer] Re: About Schaums.
References: <48186FDF.5070409@nerim.fr>
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From: Martin Rubey <martin.rubey@univie.ac.at>
Date: 30 Apr 2008 19:52:59 +0200
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root <daly@axiom-developer.org> writes:
>   Axiom has a closed form for 2 integrals where Schaums has series.

But at least one of them seems to be wrong. Since it seems that my message was
overlooked, I repeat it here:

daly@axiom-developer.org writes:

>   14:668 SCHAUMS AND AXIOM DIFFER (Axiom has closed form)

But I'm not so sure that it is correct, at least not for a=1 and x in 0..1.

draw(D(integrate(asech(x)/x,x),x)-asech(x)/x, x=0..1)

I'm an absolute nobody on this stuff, so I may well be missing something.  On
the other hand, the power series for (asech x)/x + (log x - log 2)/x is
Dfinite:

(76) -> guessPRec [coefficient(series normalize((asech x + log x - log 2) / x)::GSERIES(EXPR INT, x, 0), i) for i in 0..30]

   (76)
   [
     [
       function =
         BRACKET
            f(n):
                2                         2                                  1
              (n  + 6n + 9)f(n + 2) + (- n  - 3n - 2)f(n)= 0,f(0)= 0,f(1)= - -
                                                                             4
       ,
      order= 0]
     ]
    Type: List Record(function: Expression Integer,order: NonNegativeInteger)

and this doesn't agree at all with the power series you get from
D(integrate(asech(x)/x,x),x).

Should be investigated,

Martin




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This is similar to other (old) problems I saw on the list archives.  This is
regarding axiom pulled from git on April 29th 2008 (which I guess is a
Silver source, my bad, I was looking for a Gold, but whatever).  Basically
something from graph wants to link against libXpm.a.  However, my
installatio (and I haven't touched it for the most part), not only doesn't
contain libXpm.a in /usr/X11R6/lib, it doesn't have this library at all
AFAIK.  It only has a libtoolized archive, i.e. libXpm.la, and the shared
libraries libXpm.so.<version>.  I don't know much about libtool, but from
what I can tell this is a script wrapper that hides the actually archive.
Anyway, I should be able to use the shared library files, right?  Here is
some info:

smithzv@marco:~$ uname -a
Linux marco 2.6.23.9MYTH-TV #4 SMP Mon Dec 17 05:46:46 MST 2007 i686 AMD
Duron(tm) Processor AuthenticAMD GNU/Linux
smithzv@marco:~$ locate libXpm.a
smithzv@marco:~$ locate libXpm
/var/log/packages/libXpm-3.5.6-i486-1
/var/log/scripts/libXpm-3.5.6-i486-1
/usr/lib/libXpm.so.4.11.0
/usr/lib/libXpm.so.4
/usr/lib/libXpm.la
/usr/lib/libXpm.so
smithzv@marco:~$ file /usr/lib/libXp
libXp.la                   libXpm.so.4                libXprintUtil.la
libXp.so                   libXpm.so.4.11.0           libXprintUtil.so
libXp.so.6                 libXprintAppUtil.la        libXprintUtil.so.1
libXp.so.6.2.0             libXprintAppUtil.so        libXprintUtil.so.1.0.0
libXpm.la                  libXprintAppUtil.so.1
libXpm.so                  libXprintAppUtil.so.1.0.0
smithzv@marco:~$ file /usr/lib/libXpm.la
/usr/lib/libXpm.la: libtool library file

Similar to the approach in another thread, I replaced all occurrences of
${XLIB}/libXpm.a with -lXpm in the Makefile.pamphlet file.  I believe that
such a replacement will make this work on my system (and others like it) but
not break any other installations.  The linker should automatically look for
libXpm.a and libXpm.so on the linker directories when it encounters a -l
flag, right?  Why is the libXpm archive's path hard coded into makefile
maker?

I am still working on the build (old computer), but it appears to be on the
testing stage without problems, so it seems to have worked.

Zach

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This is similar to other (old) problems I saw on the list archives.&nbsp;
This is regarding axiom pulled from git on April 29th 2008 (which I
guess is a Silver source, my bad, I was looking for a Gold, but
whatever).&nbsp; Basically something from graph wants to link against
libXpm.a.&nbsp; However, my installatio (and I haven&#39;t touched it for the
most part), not only doesn&#39;t contain libXpm.a in /usr/X11R6/lib, it
doesn&#39;t have this library at all AFAIK.&nbsp; It only has a libtoolized
archive, i.e. libXpm.la, and the shared libraries
libXpm.so.&lt;version&gt;.&nbsp; I don&#39;t know much about libtool, but from
what I can tell this is a script wrapper that hides the actually
archive.&nbsp; Anyway, I should be able to use the shared library files,
right?&nbsp; Here is some info:<br>
<br>smithzv@marco:~$ uname -a<br>Linux marco 2.6.23.9MYTH-TV #4 SMP Mon Dec 17 05:46:46 MST 2007 i686 AMD Duron(tm) Processor AuthenticAMD GNU/Linux<br>smithzv@marco:~$ locate libXpm.a<br>smithzv@marco:~$ locate libXpm<br>

/var/log/packages/libXpm-3.5.6<div id="1fcv" class="ArwC7c ckChnd">-i486-1<br>/var/log/scripts/libXpm-3.5.6-i486-1<br>/usr/lib/libXpm.so.4.11.0<br>/usr/lib/libXpm.so.4<br>/usr/lib/libXpm.la<br>/usr/lib/libXpm.so<br>smithzv@marco:~$ file /usr/lib/libXp<br>
libXp.la&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; libXpm.so.4&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; libXprintUtil.la<br>
libXp.so&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; libXpm.so.4.11.0&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; libXprintUtil.so<br>libXp.so.6&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; libXprintAppUtil.la&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; libXprintUtil.so.1<br>libXp.so.6.2.0&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; libXprintAppUtil.so&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; libXprintUtil.so.1.0.0<br>

libXpm.la&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; libXprintAppUtil.so.1&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <br>libXpm.so&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; libXprintAppUtil.so.1.0.0&nbsp; <br>smithzv@marco:~$ file /usr/lib/libXpm.la<br>/usr/lib/libXpm.la: libtool library file<br><br>Similar
to the approach in another thread, I replaced all occurrences of
${XLIB}/libXpm.a with -lXpm in the Makefile.pamphlet file.&nbsp; I believe
that such a replacement will make this work on my system (and others
like it) but not break any other installations.&nbsp; The linker should
automatically look for libXpm.a and libXpm.so on the linker directories
when it encounters a -l flag, right?&nbsp; Why is the libXpm archive&#39;s path
hard coded into makefile maker?<br>
<br>I am still working on the build (old computer), but it appears to
be on the testing stage without problems, so it seems to have worked.<br><br>Zach<font color="#888888"><br><br></font></div>

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From: root <daly@axiom-developer.org>
To: martin.rubey@univie.ac.at
In-reply-to: <9q63tzjklg.fsf@aquin.mat.univie.ac.at> (message from Martin
	Rubey on 30 Apr 2008 19:52:59 +0200)
Subject: Re: [Axiom-developer] Re: About Schaums.
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>>   Axiom has a closed form for 2 integrals where Schaums has series.
>
>But at least one of them seems to be wrong. Since it seems that my message was
>overlooked, I repeat it here:
>
>daly@axiom-developer.org writes:
>
>>   14:668 SCHAUMS AND AXIOM DIFFER (Axiom has closed form)
>
>But I'm not so sure that it is correct, at least not for a=1 and x in 0..1.
>
>draw(D(integrate(asech(x)/x,x),x)-asech(x)/x, x=0..1)
>
>I'm an absolute nobody on this stuff, so I may well be missing something.  On
>the other hand, the power series for (asech x)/x + (log x - log 2)/x is
>Dfinite:
>
>(76) -> guessPRec [coefficient(series normalize((asech x + log x - log 2) / x)::GSERIES(EXPR INT, x, 0), i) for i in 0..30]
>
>   (76)
>   [
>     [
>       function =
>         BRACKET
>            f(n):
>                2                         2                                  1
>              (n  + 6n + 9)f(n + 2) + (- n  - 3n - 2)f(n)= 0,f(0)= 0,f(1)= - -
>                                                                             4
>       ,
>      order= 0]
>     ]
>    Type: List Record(function: Expression Integer,order: NonNegativeInteger)
>
>and this doesn't agree at all with the power series you get from
>D(integrate(asech(x)/x,x),x).
>
>Should be investigated,

Martin,

I saw your note but haven't yet had the time to prove the result
one way or the other. I just finished the last integrals and did a
bug-catching, "check my homework" review last night. I plan to use
the 3 Ms to check both Axiom and Schaums. Ultimately, I suspect they
are both "right" under some as-yet-unstated set of assumptions.
But I have much more to learn about branch cuts, which ones are
assumed, and how they propagate before I think I have a solid clue.
These assumptions should really be written down someplace but they
are not.

Tim



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To: Martin Rubey <martin.rubey@univie.ac.at>
Subject: Re: [Axiom-developer] 20080427.01.tpd.patch (CATS Schaums-Axiom
	equivalence testing (29-34))
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I investigated a tiny bit further, but only to notice that this result is
*not* produced by the pattern matcher, but rather by the general integration
algorithm. 

I'm a bit worried.

Martin

Martin Rubey <martin.rubey@univie.ac.at> writes:

> daly@axiom-developer.org writes:
> 
> >   14:668 SCHAUMS AND AXIOM DIFFER (Axiom has closed form)
> 
> But I'm not so sure that it is correct, at least not for a=1 and x in 0..1.
> 
> draw(D(integrate(asech(x)/x,x),x)-asech(x)/x, x=0..1)
> 
> I'm an absolute nobody on this stuff, so I may well be missing something.  On
> the other hand, the power series for (asech x)/x + (log x - log 2)/x is
> Dfinite:
> 
> (76) -> guessPRec [coefficient(series normalize((asech x + log x - log 2) / x)::GSERIES(EXPR INT, x, 0), i) for i in 0..30]
> 
>    (76)
>    [
>      [
>        function =
>          BRACKET
>             f(n):
>                 2                         2                                  1
>               (n  + 6n + 9)f(n + 2) + (- n  - 3n - 2)f(n)= 0,f(0)= 0,f(1)= - -
>                                                                              4
>        ,
>       order= 0]
>      ]
>     Type: List Record(function: Expression Integer,order: NonNegativeInteger)
> 
> and this doesn't agree at all with the power series you get from
> D(integrate(asech(x)/x,x),x).
> 
> Should be investigated,
> 
> Martin
> 
> 
> 
> 
> _______________________________________________
> Axiom-developer mailing list
> Axiom-developer@nongnu.org
> http://lists.nongnu.org/mailman/listinfo/axiom-developer




