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0-1-0-1-ln-1-x-y-dxdy-5-2-ln2-1-2-lnpi-9-4-




Question Number 137939 by Ñï= last updated on 08/Apr/21
               ∫_0 ^1 ∫_0 ^1 lnΓ(1+x+y)dxdy=(5/2)ln2+(1/2)lnπ−(9/4)
$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \int_{\mathrm{0}} ^{\mathrm{1}} {ln}\Gamma\left(\mathrm{1}+{x}+{y}\right){dxdy}=\frac{\mathrm{5}}{\mathrm{2}}{ln}\mathrm{2}+\frac{\mathrm{1}}{\mathrm{2}}{ln}\pi−\frac{\mathrm{9}}{\mathrm{4}} \\ $$

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