# Hot Integral - 2

Calculus Level 5

$\large \displaystyle \int\limits_{0}^{\infty} \left(\frac{\sin x}{x}\right)^{102} \cos(100x) \, dx = \frac{\pi^A}{B\times \Gamma(C)}$

If the equation above holds true for positive integers $$A,B$$ and $$C$$ with $$C$$ maximized, evaluate $$A^{B^C}+C^{B^A}$$.

Notation: $$\Gamma(\cdot)$$ denotes the Gamma function.

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