It's an even function right?

Calculus Level 4

\[ \large \int_{-\frac \pi 2}^{\frac \pi 2} \left [ \cos(x) \left(x^2 + \ln \left( \frac{\pi-x}{\pi+x} \right)\right) \right ] \, dx \]

If the integral above equals to \( \frac{\pi^A - B}{A} \) for integers \(A,B\), what is the value of \(A+B\)?

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