5.5 The Substitution Rule/33

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

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} u &= \cot{(x)} \\[2ex] du &= -csc^2{(x)}dx \\[2ex] -du &= csc^2{(x)}dx \\[2ex] \end{align} }

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 \\[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} }