Evaluate: `int{1+2tanx(tanx-secx)}^(1/2)dx`

Explanation

`int(1+2tan^(2)x+ 2tan x sec x)^(1//2)dx`
`=int(sec^(2)x +tan^(2)x +2tanx secx)^(1//2)dx`
`=int(secx +tanx)dx`
`=log|secx+tanx|+log|secx|+c`
`=log|secx(secx+tanx)|+c`