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evaluate-0-x-x-1-lim-k-k-k-1-k-x-dx-




Question Number 120898 by talminator2856791 last updated on 03/Nov/20
         evaluate: ∫_0 ^( ∞) ((x/(x+1)) − lim_(k→∞)  ((k/(k+1)))^(⌊k⌋) )^(⌊x⌋) dx
$$\: \\ $$$$\: \\ $$$$\: \\ $$$$\mathrm{evaluate}:\:\int_{\mathrm{0}} ^{\:\infty} \left(\frac{{x}}{{x}+\mathrm{1}}\:−\:\underset{{k}\rightarrow\infty} {\mathrm{lim}}\:\left(\frac{{k}}{{k}+\mathrm{1}}\right)^{\lfloor{k}\rfloor} \right)^{\lfloor{x}\rfloor} {dx} \\ $$$$\: \\ $$$$\: \\ $$

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