Primitive of Power of Hyperbolic Sine of a x by Hyperbolic Cosine of a x

Theorem

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

for $n \ne -1$.

Also see

 * Primitive of $\coth a x$ for the case where $n = -1$.


 * Primitive of $\cosh^n a x \sinh a x$