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

Lemma for Primitive of Reciprocal of $\cos a x \paren {1 + \sin a x}$
The Weierstrass Substitution of $\ds \int \frac {\d x} {\cos a x \paren {1 + \sin a x} }$ is:
 * $\ds \frac 2 a \int \frac {\d u} {\paren {1 - u} \paren {1 + u}^3}$

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