5.5 The Substitution Rule/33

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

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