Antiderivative of sech

Theorem

The following formula holds: $$\displaystyle\int \mathrm{sech}(z) \mathrm{d}z=\arctan(\sinh(z)) + C,$$ where $\mathrm{sech}$ denotes the hyperbolic secant, $\arctan$ denotes the inverse tangent, and $\sinh$ denotes the hyperbolic sine.