Reduction Formula for Integral of Power of Cosine/Corollary

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

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

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

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

Also see

 * Reduction Formula for Integral of Power of Sine/Corollary