Integrate It Man!

Calculus Level 4

\[\large \int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \frac{x^2 \cos x}{1+e^x} \, dx = \frac{\pi^n}{a}-b\]

The equation above holds true for integers \(a,b\) and \(n\). Find \(a+b+n\).

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