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Question Number 177492 by Shrinava last updated on 06/Oct/22

$$\mathrm{If}0<\mathrm{a}⩽\mathrm{b}\mathrm{then}:$$$${\int }_{\mathbf{a}}^{\mathbf{b}}{\int }_{\mathbf{a}}^{\mathbf{b}}\frac{\mathrm{dx}\mathrm{dy}}{\sqrt{\mathrm{xy}(\mathrm{x}+\mathrm{y})}}⩽\frac{\mathrm{b}-\mathrm{a}}{2}\cdot \log \left(\frac{\mathrm{b}}{\mathrm{a}}\right)+{\log }^2\left(\frac{\mathrm{b}}{\mathrm{a}}\right)$$

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