5.5 The Substitution Rule/37

$\int \cot(x)dx=\int {\frac {\cos(x)}{\sin(x)}}dx$

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 &= \sin(x) \\[2ex] du &= \cos(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 \frac{\cos(x)}{\sin(x)}dx &= \int \frac{1}{\sin(x)}\cos(x)\;dx = \int \frac{1}{\sin(x)}(\cos(x)\;dx) \\[2ex] &= \int \frac{1}{{u}}(du) \\[2ex] &= \left| \ln(u) \right| + C \\[2ex] &= \left| \ln(\sin(x)) \right| + C \\[2ex] \end{align} }