Question Number 120898 by talminator2856791 last updated on 03/Nov/20
$$\: \\ $$$$\: \\ $$$$\: \\ $$$$\mathrm{evaluate}:\:\int_{\mathrm{0}} ^{\:\infty} \left(\frac{{x}}{{x}+\mathrm{1}}\:−\:\underset{{k}\rightarrow\infty} {\mathrm{lim}}\:\left(\frac{{k}}{{k}+\mathrm{1}}\right)^{\lfloor{k}\rfloor} \right)^{\lfloor{x}\rfloor} {dx} \\ $$$$\: \\ $$$$\: \\ $$