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

$\displaystyle \int \frac {\d x} {p \sin a x + q \cos a x - \sqrt {p^2 + q^2} } = \frac {-1} {a \sqrt {p^2 + q^2} } \map \tan {\frac \pi 4 + \frac {a x + \arctan \frac q p} 2} + C$