Evaluate: `inttan^5xsec^3x\ dx`

Explanation

`=int tan^4x sec^2x.secx tanx dx`

`=int (sec^2x-1)^2.sec^x.secx tanxdx`

`secx=t=>secxtanxdx=dt`

`=int(t^2-1)^2.t^2 dt`

`=int (t^6-2t^4+t^2)dt`

`=frac{t^7}{7}-frac{2t^5}{5}+frac{t^3}{3}+C`

`=1/7 sec^2x-2/5 sec^5x+1/3 sec^3x+C`