Reduction Formula for Integral of Power of Tangent

Theorem
For all $n \in \Z_{> 1}$:
 * $\displaystyle \int \map {\tan^n} x \rd x = \frac {\map {\tan^{n - 1} } x} {n - 1} - \int \map {\tan^{n - 2} } x \rd x$

Proof
Let:

Then:

Also see

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