Another integration problem

Calculus Level 5

0π/2xcos(x)1+sin2x dx \int _{ 0 }^{ \pi /2 }{ \frac { x\cos { (x) } }{ 1+\sin ^{ 2 }{ x } } \ \mathrm{d}x }

If the above integral can be stated in the form lnA(B+C)D\dfrac { {\ln}^{ A }(B+\sqrt { C } ) }{ D } , find A+B+C+DA+B+C+D where A,B,C,DA,B,C,D are positive integers (not necessarily distinct) and CC not an even perfect power.

This is original

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