Reduction formula for $\int \tan^n x dx$
You don't need integration by parts at all. Just write $$\tan^nx=\tan^{n-2}x(\sec^2x-1)$$ Multiply out and integrate and get the answer immediately
You don't need integration by parts at all. Just write $$\tan^nx=\tan^{n-2}x(\sec^2x-1)$$ Multiply out and integrate and get the answer immediately