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

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Theorem

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


Proof


Sources