Primitive of Hyperbolic Cosecant Function/Logarithm Form

Theorem

 * $\displaystyle \int \operatorname{csch} x \ \mathrm d x = -\ln \left \vert {\operatorname{csch} x + \coth x} \right \vert + C$

where $\operatorname{csch} x + \coth x \ne 0$.

Proof
Let:

Then:

Also see

 * Primitive of Hyperbolic Secant Function