Antiderivative of hyperbolic cosecant

Theorem

The following formula holds: $$\displaystyle\int \mathrm{csch}(z)\mathrm{d}z = \log\left(\tanh\left(\frac{z}{2}\right)\right)+C,$$ where $\mathrm{csch}$ denotes the hyperbolic cosecant, $\log$ denotes the logarithm, and $\tanh$ denotes the hyperbolic tangent.