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

Theorem

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