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[Axiom-developer] 20080413.01.tpd.patch (CATS integration regression tes
|
From: |
daly |
|
Subject: |
[Axiom-developer] 20080413.01.tpd.patch (CATS integration regression testing) |
|
Date: |
Mon, 14 Apr 2008 01:34:03 -0500 |
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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