Evaluate: `int(sec^4x)/(sqrt(tanx))\ dx`

Explanation

`int(sec^4x)/(sqrt(tanx))\ dx`
let `tan x=t`
`=>sec^2x dx=dt`
`=int(sec^2x*sec^2x dx)/sqrt(tanx)`
`=int((1+tan^2x)*sec^2x dx)/sqrt(tanx)`
`=int(1+t^2)/t^(1/2) dt`
`=int(t^(-1/2)+t^2-1/2)dt`
`=intt^(-1/2)dt+int t^(3/2)dt`
`=t^(1/2)/(1/2)+t^(5/2)/(5/2)+c`
`=2sqrt(tanx)+2/5(tanx)^(5/2)+c`