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

Lemma for Primitive of Reciprocal of $\left({p + q \sin a x}\right)^2$
The Weierstrass Substitution of $\displaystyle \int \frac {\mathrm d x} {p^2 + q^2 \sin^2 a x}$ is:
 * $\displaystyle \frac 2 a \int \frac {\left({u^2 + 1}\right) \ \mathrm d u} {p^2 \left({u^2}\right)^2 + \left({2 p + 4 q^2}\right) u^2 + p}$.