Primitive of Reciprocal of p by Sine of a x plus q by Cosine of a x plus or minus Root of p squared plus q squared

Theorem

 * $\displaystyle \int \frac {\mathrm d x} {p \sin a x + q \cos a x \pm \sqrt {p^2 + q^2} } = \frac {-1} {a \sqrt {p^2 + q^2} } \tan \left({\frac \pi 4 \mp \frac {a x + \arctan \frac q p} 2}\right) + C$