Primitive of Product of Hyperbolic Secant and Tangent

Theorem

 * $\displaystyle \int \operatorname{sech} x \tanh x \ \mathrm d x = - \operatorname{sech} x + C$

where $C$ is an arbitrary constant.

Proof
From Derivative of Hyperbolic Secant Function:
 * $\dfrac{\mathrm d}{\mathrm dx} \operatorname{sech} x = - \operatorname{sech} x \tanh x$

The result follows from the definition of primitive.