Primitive of Reciprocal of p squared by square of Sine of a x minus q squared by square of Cosine of a x

Theorem

 * $\displaystyle \int \frac {\mathrm d x} {p^2 \sin^2 a x - q^2 \cos^2 a x} = \frac 1 {2 a p q} \ln \left\vert{\frac {p \tan a x - q} {p \tan a x + q} }\right\vert + C$