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

Lemma for Primitive of Reciprocal of $\paren {p + q \sin a x}^2$
The Weierstrass Substitution of $\ds \int \frac {\d x} {p^2 + q^2 \sin^2 a x}$ is:
 * $\ds \frac 2 a \int \frac {\paren {u^2 + 1} \rd u} {p^2 \paren {u^2}^2 + \paren {2 p + 4 q^2} u^2 + p}$