# Evaluate the integral using the indicated substitution. \int\cot x \cos ec^{2}xdx,\ u=\cot x

Evaluate the integral using the indicated substitution.
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faldduE
Consider the integrals,
$\int \mathrm{cot}x\cdot \mathrm{cos}e{c}^{2}x\cdot dx$
Let, $u=\mathrm{cot}x$
$du=-\mathrm{cos}e{c}^{2}xdx$
Substitute all value in given integrals,
$\int \mathrm{cot}x\cdot \mathrm{cos}e{c}^{2}x\cdot dx=-\int u\cdot du$
$=-\frac{{u}^{2}}{2}+C$
$=-\frac{1}{2}{\mathrm{cot}}^{2}x+C$