Reduction Formula for Integral of Power of Sine/Corollary

Corollary to Reduction Formula for Integral of Power of Sine
Let $n \in \Z_{> 0}$ be a (strictly) positive integer.

Let $a \in \R_{\ne 0}$ be a non-zero real number

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

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

Also see

 * Reduction Formula for Integral of Power of Cosine/Corollary