MHB Short table of integrals (.tex file) will include pdf of output.

[DrWahoo]

\documentclass[12pt]{article}
\usepackage{graphicx}

\addtolength{\textwidth}{1.5in}
\addtolength{\hoffset}{-1.in}
\addtolength{\textheight}{2.0in}
%\addtolength{\voffset}{-1.68in}
\addtolength{\voffset}{-0.8in}
\newcommand {\rreal}{\mbox{$R\!\!\!\!\!l\,\,\,\,$}}
\newcommand{\graphspace}{\vspace{2in}}
\newcommand{\eqnspace}{\hspace{.1in}}
\newcommand{\toppageoneexam}{\vspace{-.4in} \mbox{ } \hspace{-.6in}
\parbox[t]{7.8in} 
{\noindent {\bf Name:} \hspace{.01in}
$\underline{\mbox{\hspace{3.5in}}}$\ \ {\bf Section:} \underline{\hspace{.5in}}  }}
%\newcommand{\toppageexam}{\vspace{-.4in} \parbox[t]{7.5in}
%{\noindent {\bf Name:} \hspace{.01in}
%$\underline{\mbox{\hspace{3.5in}}}$\\ }}
\newcommand{\toppageexam}{\vspace{-.6in}  \hspace{-.6in} 
\parbox[t]{6.5in}
{\noindent {\bf Name:} \hspace{.01in}
$\underline{\mbox{\hspace{3.5in}}}$ \ \ {\bf Section:} \underline{\hspace{.5in}} }}

\include{macros} 

\begin{document}\toppageoneexam%Integrals
\ee

\bc {\bf A short table of integrals} \ec

\be
 \item $A$ a constant \  \imp \ $\int Adx = Ax + C$,  
 \item $n \neq 0, 1$ \ \imp \ $\int x^n dx = \frac{x^{n+1}}{n+1} + C$
 \item $\int \frac{dx}{x} = log(x) + C$; \ind \ind Integration by parts: $\int u dv = u v - \int v du $
 \item $\int e^{ax} dx = \frac{1}{a}e^{ax} + C$; \ind \ind 
   Substitution: $u = u(x), \ \int u du = \int u(x) u'(x) dx $ 
 \item $\int xe^{ax} dx = e^{ax}(\frac{x}{a} - \frac{1}{a^2})  + C$
 \item $\int x^2e^{ax} dx = e^{ax}(\frac{x^2}{a} - \frac{2x}{a^2} +
\frac{2}{a^3})  + C$
 \item $\int log(a x) = xlog(a x) -x + C$
 \item $\int x log(a x) = \frac{x^2}{2} log(a x) -\frac{x^2}{4} + C$
 \item $\int \frac{dx}{a^2 + x^2} = \frac{1}{a} arctan(\frac{x}{a}) +
C $
 \item $\int \frac{dx}{a^2 - x^2} = \frac{1}{2a} log(\frac{x+a}{x-a})
+ C$
 \item $\int \frac{dx}{\sqrt{a^2 - x^2}} = arcsin(\frac{x}{a}) + C $
 \item $\int \frac{dx}{\sqrt{x^2 - a^2}} = log(x + \sqrt{x^2 - a^2}) + C$
 \item $\int \frac{dx}{\sqrt{a^2 + x^2}} = arcsinh(\frac{x}{a}) + C $
 \item $\int sin(ax) = - \frac{1}{a} cos(a x) + C$
 \item $\int cos(ax) = \frac{1}{a} sin(a x) + C$
 \item $\int tan(ax) = \frac{1}{a} log(sec(a x))  + C$
 \item $\int cot(ax) = \frac{1}{a} log(sin(a x))  + C$
 \item $\int sec(ax) = \frac{1}{a} log(tan(a x)+sec(a x)) + C$
 \item $\int csc(ax) = -\frac{1}{a} log(csc(a*x)+cot(a*x)) + C$
 \item $\int x \ cos(ax) = \frac{x \ sin(a x)}{a} + \frac{cos(a x)}{a^2}
+ C$
 \item $\int x \ sin(ax) = \frac{sin(a x)}{a^2} - \frac{x \ cos(a x)}{a}
+ C$
\end{document}

 

[DrWahoo]

If anyone wants me to add one to the code and the output, I will gladly do so. Would be nice to have a very comprehensive list so user could check their u-sub, partial fractions, and intg by parts. I think the washer and shell method is left out way to often as well.

 

[DrWahoo]

All code and output is free to use. I will never post anything that I won't allow reproduction of. Thus feel free to copy and edit code as you prefer. Again, we are all here to help one another! If you need anything in particular, feel free to post up a question and I will help to the best of my ability along with others.

 

[Euge]

Hello DrWahoo,

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We discourage such posting behavior because such a post adds no value or content to a thread.