Manipulating The Integral

Calculus Level pending

\[\text{When} \int _{ 0 }^{ \pi }{ \frac { x\sin { x } }{ 1+\cos ^{ 2 }{ x } } } dx \text{ is written in the form} \frac { a\pi^b }{ c }\] \[\text{Where a, b, and c are positive integers such that a and c are prime,}\] \[\text{What is the value of } a+b+c?\]

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