This problem is deceiving and needs three rounds of rearrangements/manipulations to get the answer.
1) the problem has a radical function inside an inverse trig function, so we use u sub to get rid of the radical.
2) we use integration by parts to pull out the inverse trigonometric function and are left with something that resembles the derivative of inverse tangent of x. However, we must manipulate the function to make it fit the derivative of arctan(x).
3) We do this by adding 0. Bear with me. Adding by 0 means we are actually adding a number and subtracting by that same number to split up the integral into two. In this case we add and subtract by 1. This gives us two very tame integrals from one very ferocious one.