A power, a cosine, an exponential, oh my!

Calculus Level 4

π2π2x2cos(x)ex+1 dx=πABC\large \int_{-\frac{\pi}{2}}^\frac{\pi}{2}\dfrac{x^2\cos (x)}{e^x+1}\text{ }dx=\frac{\pi^A}{B}-C

If the equation above is true for positive integers A,A, B,B, and CC, find A+B+CA+B+C.

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