5.5 The Substitution Rule/33

$\int {\sqrt {\cot(x)}}\csc ^{2}{(x)}dx$

${\begin{aligned}u&=\cot {(x)}\\[2ex]du&=-csc^{2}{(x)}dx\\[2ex]dx&={\frac {du}{-csc^{2}{(x)}}}\\[2ex]\end{aligned}}$

Failed to parse (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle {\begin{aligned}&=\int {\sqrt {u}}\csc ^{2}{(x)}{\frac {du}{-csc{(x)}}}&=-\int {({\sqrt {u}})}du\\[2ex]&=\int u^{\frac {1}{2}}\end{aligned}}}