Evaluate: `intsec^n xtanx\ dx`

Explanation

`I=int sec ^{n-1} x sec x tan x d x `

`text { Let } sec x=t `

`therefore sec x tan x d x=d t `

`I=int t^{n-1} d t `

`=frac{t^{n}}{n}+c `

`=frac{sec ^{n} x}{n}+C`