Primitive of Product of Hyperbolic Cosecant and Cotangent

Theorem

 * $\displaystyle \int \operatorname{csch} x \coth x \ \mathrm d x = - \operatorname{csch} x + C$

where $C$ is an arbitrary constant.

Proof
From Derivative of Hyperbolic Cosecant Function:
 * $\dfrac{\mathrm d}{\mathrm dx} \operatorname{csch} x = - \operatorname{csch} x \coth x$

The result follows from the definition of primitive.