Question Number 219456 by Nicholas666 last updated on 25/Apr/25
$$ \\ $$$$\:\int_{\mathrm{1}} ^{\:\mathrm{3}} \int_{\mathrm{1}} ^{\:\mathrm{3}} \int_{\mathrm{1}} ^{\:\mathrm{3}} \int_{\mathrm{1}} ^{\:\mathrm{3}} \int_{\mathrm{1}} ^{\:\mathrm{3}} \:\frac{{x}_{\mathrm{1}} +{x}_{\mathrm{2}} +{x}_{\mathrm{3}} +{x}_{\mathrm{4}} −{x}_{\mathrm{5}} }{{x}_{\mathrm{1}} +{x}_{\mathrm{2}} +{x}_{\mathrm{3}} +{x}_{\mathrm{4}} +{x}_{\mathrm{5}} }\:{dx}_{\mathrm{1}} {dx}_{\mathrm{2}} {dx}_{\mathrm{3}} {dx}_{\mathrm{4}} {dx}_{\mathrm{5}} \:\:\:\:\:\:\:\:\: \\ $$$$ \\ $$
Commented by mr W last updated on 26/Apr/25
$$=\left(\mathrm{1}−\frac{\mathrm{2}}{\mathrm{5}}\right)\left(\mathrm{3}−\mathrm{1}\right)^{\mathrm{5}} =\frac{\mathrm{96}}{\mathrm{5}} \\ $$
Commented by Nicholas666 last updated on 26/Apr/25
$${thanks} \\ $$