Reduction Formula for Integral of Power of Tangent

Theorem
For all $n \in \Z_{> 1}$:
 * $\displaystyle \int \tan^n\left({x}\right) \mathrm dx = \frac{\tan^{n-1}\left({x}\right)}{n-1} - \int \tan^{n-2}\left({x}\right) \mathrm dx$

Proof
Let:

Then:

Also see

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