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

Theorem

 * $\displaystyle \int \frac {\mathrm d x} {\cosh a x \left({1 + \sinh a x}\right)} = \frac 1 {2 a} \ln \left\vert{\frac {1 + \sinh a x} {\cosh a x} }\right\vert + \frac 1 a \arctan \left({e^{a x} }\right) + C$