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

Theorem

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

for $n \ne -1$.

Also see

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


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