Primitive of Power of Sine of a x by Power of Cosine of a x/Reduction of Power of Sine

Theorem

 * $\displaystyle \int \sin^m a x \cos^n a x \ \mathrm d x = \frac {-\sin^{m - 1} a x \cos^{n + 1} a x} {a \left({m + n}\right)} + \frac {m - 1} {m + n} \int \sin^{m - 2} a x \cos^n a x \ \mathrm d x$