When You're High on Math

Calculus Level 5

k=1(1+2cos(2x3k)3)\prod_{k=1}^{\infty}\left(\frac{1+2 \cos \left(\frac{2x}{3^k}\right)}{3}\right)

Define the expression above as 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

where AA and BB are coprime positive integers. Find the value of A+BA+B.

Image Credit: Wikimedia Psychedelic Dingbats by Hendrike
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