Primitive of Reciprocal of Hyperbolic Cosine of a x by 1 plus Hyperbolic Sine of a x

Theorem

 * $\displaystyle \int \frac {\rd x} {\cosh a x \paren {1 + \sinh a x} } = \frac 1 {2 a} \ln \size {\frac {1 + \sinh a x} {\cosh a x} } + \frac 1 a \map \arctan {e^{a x} } + C$