Primitive of Hyperbolic Sine of p x by Hyperbolic Cosine of q x

Theorem

 * $\displaystyle \int \sinh p x \cosh q x \ \mathrm d x = \frac {\cosh \left({p + q}\right) x} {2 \left({p + q}\right)} + \frac {\cosh \left({p - q}\right) x} {2 \left({p - q}\right)} + C$

Also see

 * Primitive of $\sinh a x \sinh p x$
 * Primitive of $\sinh a x \cosh a x$
 * Primitive of $\cosh a x \cosh p x$