5.5 The Substitution Rule/33

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

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

${\begin{aligned}&=\int {\sqrt {u}}x\csc ^{2}{(x)}x{\frac {du}{-csc{(x)}}}\end{aligned}}$