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%  Equation array
\def\eqa#1;{\hbox{$\displaystyle{}#1$}}
%
%   A set of integrals and other useful math-type stuff
%
\centerline{\bf A Set of Integrals}
\centerline{\sc and Other Useful Math-Type Stuff}
\medskip
\centerline{Compiled by Andrew Marc Greene}
\medskip
\hrule
\medskip
\centerline{\tt This file lives in /mit/amgreene/texhax/integrals.tex}
\medskip
\hrule
\bigskip
\centerline{\sc Fundamental Forms}
\hbox{\vtop{\hsize=3in
\eqa\int a\,dx=ax;
\eqa\int {dx\over{x}}=\ln{x};
\eqa\int a^x\,dx={a^x\over\ln a};
\eqa\int{dx\over{1+x^2}}=\tan^{-1}x = -\cot^{-1}x;
\eqa\int{dx\over\sqrt{1-x^2}}=\sin^{-1}x = -\cos^{-1}x;
\eqa\int{dx\over{x\sqrt{x^2-1}}}=\sec^{-1}x = -\csc^{-1}x;
\eqa\int\cot{x}\,dx=\ln\,\sin{x};
\eqa\int\tan{x}\,dx=-\ln\,\cos{x};
\eqa\int\tan{x}\sec{x}\,dx=\sec{x};
\eqa\int\sec^2x\,dx=\tan{x};
\eqa\int\csc^2x\,dx=-\cot{x};}%
\vtop{\hsize=2in

\vskip 2in

\psgraph4.71;rads sin;
\centerline{$y=\sin{x}$}}}
\centerline{\sc Rational Expressions}
\end
