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 (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \begin{align} &= \int {\sqrt{u}} \csc^2{(x)} \frac{du}{-csc{(x)}} &= - \int{\sqrt{u}}du }