Primitive of Reciprocal of square of p plus 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 $\displaystyle \int \frac {\mathrm d x} {\left({p + q \sin a x}\right)^2}$ is:
 * $\displaystyle \frac 2 a \int \frac {\left({u^2 + 1}\right) \ \mathrm d u} {\left({p u^2 + 2 q u + p}\right)^2}$

where $u = \tan \dfrac {a x} 2$.