Another integration problem

Calculus Level 5

\[ \int _{ 0 }^{ \pi /2 }{ \frac { x\cos { (x) } }{ 1+\sin ^{ 2 }{ x } } \ \mathrm{d}x } \]

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

This is original

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