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Question Number 151062 by qaz last updated on 18/Aug/21

$$\mathrm{Calculate}::{\int }_0^{\mathrm{\infty }}\frac{\mathrm{dx}}{\sqrt{{\mathrm{x}}^2+\mathrm{x}}\cdot \sqrt[4]{{8\mathrm{x}}^2+8\mathrm{x}+1}}=\frac{{\mathrm{\Gamma }}^2\left(\frac{1}{8}\right)}{2^{\frac{11}{4}}\mathrm{\Gamma }\left(\frac{1}{4}\right)}$$

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