Primitive of Sine of p x by Sine of q x

Theorem

 * $\displaystyle \int \sin p x \sin q x \ \mathrm d x = \frac {\sin \left({p - q}\right) x} {2 \left({p - q}\right)} - \frac {\sin \left({p + q}\right) x} {2 \left({p + q}\right)} + C$

Also see

 * Primitive of $\cos a x \cos p x$