Question Number 105771 by malwaan last updated on 31/Jul/20
$$\underset{{n}\rightarrow\infty} {{lim}}\:\left(\frac{\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:{x}^{\mathrm{2}} \left({x}+{n}\right)^{{n}} }{\left({n}+\mathrm{1}\right)^{{n}} }\:{dx}\right)=? \\ $$