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∏k=1∞(1+2cos(2x3k)3)\prod_{k=1}^{\infty}\left(\frac{1+2 \cos \left(\frac{2x}{3^k}\right)}{3}\right)k=1∏∞(31+2cos(3k2x))
Define the expression above as f(x)f(x)f(x) and if
∫0∞(f(x)+f2(x)+f3(x)+f4(x)) dx=ABπ\int_{0}^{\infty}(f(x)+f^2(x)+f^3(x)+f^4(x)) \ \mathrm dx=\frac{A}{B}\pi∫0∞(f(x)+f2(x)+f3(x)+f4(x)) dx=BAπ
where AAA and BBB are coprime positive integers. Find the value of A+BA+BA+B.
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