Primitive of Reciprocal of p squared plus square of q by Sine of a x

Theorem

 * $\displaystyle \int \frac {\mathrm d x} {p^2 + q^2 \sin^2 a x} = \frac 1 {a p \sqrt{p^2 + q^2} } \arctan \frac {\sqrt{p^2 + q^2} \tan a x} p + C$

where $C$ is an arbitrary constant.

Also see

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