Primitive of x over Power of Hyperbolic Cosine of a x

Theorem

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

Also see

 * Primitive of $\dfrac x {\sinh^n a x}$