rather than an integral problem, it's actually a trig. identity problem.
You hit the nail on the head with this puzzle that was in the puzzle section. Even with the integral sign, it was really a trig problem that's easy to transform by working with both the numerator and denominator, changing it into another problem which is easy to integrate (with one more slight transformation into tan2x).
Moderator edit: Yes, it was in the Puzzles section. And it was explained very clearly to the OP why the Puzzles subforum was not appropriate. In fact, this issue has been explained several times now.