Primitive of Reciprocal of Square of p plus q by Hyperbolic Sine of a x

Theorem

 * $\ds \int \frac {\d x} {\paren {p + q \sinh a x}^2} = \frac {-q \cosh a x} {a \paren {p^2 + q^2} \paren {p + q \sinh a x} } + \frac p {p^2 + q^2} \int \frac {\d x} {p + q \sinh a x} + C$

Proof
Hence the result.

Also see

 * Primitive of $\dfrac 1 {\paren {p + q \cosh a x}^2}$