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[Axiom-developer] 20080409.03.tpd.patch (CATS integration regression tes
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From: |
daly |
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Subject: |
[Axiom-developer] 20080409.03.tpd.patch (CATS integration regression testing) |
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Date: |
Thu, 10 Apr 2008 01:41:40 -0500 |
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 <address@hidden>
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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