Integrate It Man!

Calculus Level 4

π2π2x2cosx1+exdx=πnab\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,ba,b and nn. Find a+b+na+b+n.

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