I tried using it but didn't get very far, any chance you give me any further hints. The substitution I've done so far hasn't used trig but the standard $\displaystyle u$.
When you substitute $\displaystyle x=2sec\theta$, you will face ( Assuming $\displaystyle tan\theta > 0$ ):
$\displaystyle \int \frac{2 sec\theta tan\theta}{2 tan\theta} d\theta$