Question Number 219458 by Nicholas666 last updated on 25/Apr/25
$$ \\ $$$$\:\int_{\mathrm{1}} ^{\:\mathrm{2}} \int_{\mathrm{1}} ^{\:\mathrm{2}} \int_{\mathrm{1}} ^{\:\mathrm{2}} \int_{\mathrm{1}} ^{\:\mathrm{2}} \:{x}_{\mathrm{1}} ^{\:\mathrm{2}} {x}_{\mathrm{2}} ^{\:\mathrm{3}} {x}_{\mathrm{3}} ^{\:\mathrm{4}} {x}_{\mathrm{4}} ^{\:\mathrm{5}} \:{dx}_{\mathrm{1}} {dx}_{\mathrm{2}} {dx}_{\mathrm{3}} {dx}_{\mathrm{4}\:} \\ $$$$\: \\ $$
Answered by mr W last updated on 26/Apr/25
$$=\left(\int_{\mathrm{1}} ^{\mathrm{2}} {x}_{\mathrm{1}} ^{\mathrm{2}} {dx}_{\mathrm{1}} \right)\left(\int_{\mathrm{1}} ^{\mathrm{2}} {x}_{\mathrm{2}} ^{\mathrm{3}} {dx}_{\mathrm{2}} \right)\left(\int_{\mathrm{1}} ^{\mathrm{2}} {x}_{\mathrm{3}} ^{\mathrm{4}} {dx}_{\mathrm{3}} \right)\left(\int_{\mathrm{1}} ^{\mathrm{2}} {x}_{\mathrm{4}} ^{\mathrm{5}} {dx}_{\mathrm{4}} \right) \\ $$$$=\frac{\mathrm{2}^{\mathrm{3}} −\mathrm{1}^{\mathrm{3}} }{\mathrm{3}}×\frac{\mathrm{2}^{\mathrm{4}} −\mathrm{1}^{\mathrm{4}} }{\mathrm{4}}×\frac{\mathrm{2}^{\mathrm{5}} −\mathrm{1}^{\mathrm{5}} }{\mathrm{5}}×\frac{\mathrm{2}^{\mathrm{6}} −\mathrm{1}^{\mathrm{6}} }{\mathrm{6}} \\ $$$$=\frac{\mathrm{4557}}{\mathrm{8}} \\ $$
Commented by Nicholas666 last updated on 26/Apr/25
$${tanks} \\ $$