Primitive of Sine of p x by Sine of q x

Theorem
For $p \ne q$:


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

Also see

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


 * For $p = q$, see Primitive of $\sin^2 a x$