Evaluate: `inttan^3xsec^4x\ dx`

Explanation

`1+tan^2x = sec^2x`

`I = int tan^3x sec^2x sec^2x dx`

` = int tan^3x (1 + tan^2x) sec^2x dx`

Put `tanx = t` which means `sec^2xdx = dt`

`=int t^3(1+t^2)dt`

`=frac{t^5}{5}+frac{t^6}{6}`

`=frac{tan^5x}{5}+frac{tan^6x}{6}`