Primitive of Hyperbolic Cosecant Function

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Theorem

Logarithm Form

$\displaystyle \int \csch x \rd x = -\ln \size {\csch x + \coth x} + C$

where $\csch x + \coth x \ne 0$.


Inverse Hyperbolic Cotangent Form

$\displaystyle \int \operatorname{csch} x \ \mathrm d x = -2 \coth^{-1} \left({e^x}\right) + C$