Table

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Table 1: TABLE 1 Guidelines for Choosing

$u$ and

$dv$

Integral; $n$ is a positive integer	$u$	$dv$
$\left. \begin{array}{l} \int x^{n}e^{ax}\,dx \\ \int x^{n}\cos (ax) \,dx \\ \int x^{n}\sin (ax) \,dx \end{array} \right\}$	$u=x^{n}$	$dv= \hbox{what remains}$
$\begin{array}{l} \int x^{n}\sin ^{-1}x\,dx \\ \int x^{n}\cos ^{-1}x\,dx \\ \int x^{n}\tan ^{-1}x\,dx \end{array}$	$\begin{array}{l} u=\sin ^{-1}x \\ u=\cos ^{-1}x \\ u=\tan ^{-1}x \end{array}$	$dv=x^{n}\,dx$
$\int x^{m}( \ln x) ^{n}\,dx;$ $m$ is a real number, $m ≠ -1$	$u=( \ln x) ^{n}$	$dv=x^{m}\,dx$