Primitive of x over Power of Hyperbolic Sine of a x

Theorem

 * $\displaystyle \int \frac {x \rd x} {\sinh^n a x} = \frac {-x \cosh a x} {a \paren {n - 1} \sinh^{n - 1} a x} - \frac 1 {a^2 \paren {n - 1} \paren {n - 2} \sinh^{n - 2} a x} - \frac {n - 2} {n - 1} \int \frac {x \rd x} {\sinh^{n - 2} a x} + C$

Also see

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