# Find the antiderivative of \csc^{2}x

Find the antiderivative of ${\mathrm{csc}}^{2}x$
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Jeremy Merritt
$\frac{d}{dx}\left(\mathrm{cot}\left(x\right)\right)=-{\mathrm{csc}}^{2}\left(x\right)$
$\frac{d}{dx}\left(-\mathrm{cot}\left(x\right)\right)=-\left(-{\mathrm{csc}}^{2}\left(x\right)\right)$
$={\mathrm{csc}}^{2}\left(x\right)$
$-\mathrm{cot}\left(x\right)+C$ is the antiderivative

Hattie Schaeffer
${\mathrm{csc}}^{2}x$
Use the common integral
$\int {\mathrm{csc}}^{2}\left(x\right)dx=-\mathrm{cot}\left(x\right)$
$-\mathrm{cot}\left(x\right)+C$