5.5 The Substitution Rule/33

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

Failed to parse (unknown function "\begin{align}"): {\displaystyle \begin{align} u &= \cot{(x)} \\[2ex] du &= \-csc^2{(x)}dx \\[2ex] -du &= \csc^2{(x)}dx \\[2ex] \end{align} }

${\begin{aligned}&=-\int {({\sqrt {u}})}du\\[2ex]&=\int (u^{\frac {1}{2}})du\\[2ex]&=-{\frac {2}{3}}u+C\\[2ex]&=-{\frac {2}{3}}(\cot {(x)})^{\frac {3}{2}}+C\end{aligned}}$