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 (unknown function "\u"): {\displaystyle \begin{align} &= \int {\sqrt{u}} \csc^2{(x)} \frac{du}{-csc{(x)}} &= - \int{(\sqrt{u})}du \\[2ex] &= \int (u^{\frac{1}{2}})du &= -\frac{2}{3} \u + c \end{align} }