Primitive of Reciprocal of Cosine of a x by 1 plus Sine of a x/Weierstrass Substitution

Lemma for Primitive of Reciprocal of $\cos a x \left({1 + \sin a x}\right)$
The Weierstrass Substitution of $\displaystyle \int \frac {\mathrm d x} {\cos a x \left({1 + \sin a x}\right)}$ is:
 * $\displaystyle \frac 2 a \int \frac {\mathrm d u} {\left({1 - u}\right) \left({1 + u}\right)^3}$

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