Reduction Formula for Integral of Power of Sine

Theorem
Let $n \in \Z_{> 0}$ be a (strictly) positive integer.

Then:
 * $\displaystyle \int \sin^n x \rd x = \dfrac {n - 1} n \int \sin^{n - 2} x \rd x - \dfrac {\sin^{n - 1} x \cos x} n$

is a reduction formula for $\displaystyle \int \sin^n x \rd x$.

Also see

 * Reduction Formula for Integral of Power of Cosine
 * Reduction Formula for Integral of Power of Tangent