You could try rewriting it as:
Use the weierstrass substitution: The Weierstrass Substitution Example
Just in case a picture helps...
Spoiler:
Straight continuous lines differentiate downwards, the straight dashed line likewise but with respect to the dashed balloon expression. So the triangular network on the right satifies the chain rule. The Weierstrass substitution is 't = tan of half the angle', from which are derived the formulae for sin x and cos x in terms of t.
Don't integrate - balloontegrate!
Balloon Calculus Forum
Well, anti-clockwise from bottom-left, we do the Weierstrass subs for cos and sin (Mr Fantastic's link), simplify, then spot that
is like the bottom end of the standard result for tanh-1...
So complete the square...