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

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

Also see

 * Primitive of $\cos^n a x$
 * Primitive of $\tan^n a x$
 * Primitive of $\cot^n a x$
 * Primitive of $\sec^n a x$
 * Primitive of $\csc^n a x$