- #1

Tony1

- 17

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Prove that,

$$\int_{0}^{\pi/2}\ln^2\left(\ln^2 (\sin x)\over \pi^2+\ln^2 (\sin x)\right){\mathrm dx\over \tan x}=\color{blue}{(2\pi)^2\ln 2}$$

$$\int_{0}^{\pi/2}\ln^2\left(\ln^2 (\sin x)\over \pi^2+\ln^2 (\sin x)\right){\mathrm dx\over \tan x}=\color{blue}{(2\pi)^2\ln 2}$$

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