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0-1-0-1-log-1-x-log-1-y-log-log-1-x-log-log-1-y-2-dxdy-




Question Number 155135 by amin96 last updated on 25/Sep/21
∫_0 ^1 ∫_0 ^1 (((log((1/x))−log((1/y)))/(log(log((1/x)))−log(log((1/y))))))^2 dxdy=?
$$\int_{\mathrm{0}} ^{\mathrm{1}} \int_{\mathrm{0}} ^{\mathrm{1}} \left(\frac{\boldsymbol{\mathrm{log}}\left(\frac{\mathrm{1}}{\boldsymbol{\mathrm{x}}}\right)−\boldsymbol{\mathrm{log}}\left(\frac{\mathrm{1}}{\boldsymbol{\mathrm{y}}}\right)}{\boldsymbol{\mathrm{log}}\left(\boldsymbol{\mathrm{log}}\left(\frac{\mathrm{1}}{\boldsymbol{\mathrm{x}}}\right)\right)−\boldsymbol{\mathrm{log}}\left(\boldsymbol{\mathrm{log}}\left(\frac{\mathrm{1}}{\boldsymbol{\mathrm{y}}}\right)\right)}\right)^{\mathrm{2}} \boldsymbol{\mathrm{dxdy}}=? \\ $$

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