# Woww! Integratable

Calculus Level 3

$\large \int_0^{2\pi} \dfrac1{(1+2^{\sin x})(1+2^{\cos x})} \, dx$

If the integral above equals to $$\dfrac {\pi^A}{B}$$ for positive integers $$A$$ and $$B$$, find the value of $$A+B$$.

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