Question Number 219553 by Nicholas666 last updated on 28/Apr/25
$$ \\ $$$$\:{I}_{{n}} =\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \int_{\mathrm{0}} ^{\:\mathrm{1}} ….\int_{\mathrm{0}} ^{\:\mathrm{1}} \:\frac{{ln}\left(\mathrm{1}+{x}_{\mathrm{1}} {x}_{\mathrm{2}} \:….{x}_{{n}} \right)}{\left(\mathrm{1}−{x}_{\mathrm{1}} \right)\left(\mathrm{1}−{x}_{\mathrm{2}} \right)….\left(\mathrm{1}−{x}_{{n}\:} \right)}\:{dx}_{\mathrm{1}} {dx}_{\mathrm{2}} \:….{dx}_{{n}} \:\:\:\:\:\:\:\: \\ $$$$ \\ $$