5.5 The Substitution Rule/31

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 \int \frac{\cos{(x)}}{\sin^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&=\sin {(x)}\\[2ex]du&=\cos {(x)}dx\end{aligned}}}

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