Primitive of Sine of p x by Cosine of q x

Theorem

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

for $p, q \in \R: p \ne q$

Also see

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


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