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Question Number 155979 by mnjuly1970 last updated on 06/Oct/21
  prove that:  ∫_0 ^( 1) ∫_0 ^( 1) (((√x) +(√y))/((1−xy)((xy))^(1/4) )) dxdy=4 (4 −π)
$$ \\ $$$${prove}\:{that}: \\ $$$$\int_{\mathrm{0}} ^{\:\mathrm{1}} \int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\sqrt{{x}}\:+\sqrt{{y}}}{\left(\mathrm{1}−{xy}\right)\sqrt[{\mathrm{4}}]{{xy}}}\:{dxdy}=\mathrm{4}\:\left(\mathrm{4}\:−\pi\right) \\ $$$$ \\ $$

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