- #1

DrWahoo

- 53

- 0

Code:

```
\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}
```