Primitive of Reciprocal of Square of Sine of a x by Cosine of a x

Theorem

 * $\displaystyle \int \frac {\mathrm d x} {\sin^2 a x \cos a x} = \frac 1 a \ln \left\vert{\tan \left({\frac \pi 4 + \frac {a x} 2}\right)}\right\vert - \frac 1 {a \sin a x} + C$

Also see

 * Primitive of $\dfrac 1 {\sin a x \cos^2 a x}$