Basic Integration Rules

	$\displaystyle \int k f(u)\;du= k\int f(u)\;du$		$\displaystyle \int\left[f(u)\pm g(u)\right]\;du=\int f(u)\;du\pm\int g(u)\;du$
	$\displaystyle \int du=u+C$		$\displaystyle \int u^n\;du=\frac{u^{n+1}}{n+1}+C,\quad n\ne -1$
	$\displaystyle \int\frac{du}{u}=\ln{\left\lvert u \right\rvert }+C$		$\displaystyle \int e^u\;du=e^u+C$
	$\displaystyle \int \sin u\;du= -\cos u+C$		$\displaystyle \int \cos u\;du=\sin u+C$
	$\displaystyle \int \tan u\;du= -\ln{\left\lvert\cos u \right\rvert }+C$		$\displaystyle \int \cot u\;du=\ln{\left\lvert\sin u \right\rvert }+C$
	$\displaystyle \int \sec u\;du=\ln{\left\lvert\sec u+\tan u \right\rvert }+C$		$\displaystyle \int \csc u\;du= -\ln{\left\lvert\csc u+\cot u \right\rvert }+C$
	$\displaystyle \int \sec^2 u\;du=\tan u+C$		$\displaystyle \int \csc^2 u\;du= -\cot u+C$
	$\displaystyle \int \sec u \tan u\;du=\sec u+C$		$\displaystyle \int \csc u \cot u\;du= -\csc u+C$
	$\displaystyle \int \frac{du}{\sqrt{a^2-u^2}}=\arcsin{\frac{u}{a}}+C$		$\displaystyle \int \frac{du}{a^2+u^2}=\frac{1}{a}\arctan{\frac{u}{a}}+C$