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Question Number 120898 by talminator2856791 last updated on 03/Nov/20

$$$$$$$$$$$$$$\mathrm{evaluate}:{\int }_0^{\mathrm{\infty }}{(\frac{x}{x+1}-\underset{k\to \mathrm{\infty }}{\lim }{\left(\frac{k}{k+1}\right)}^{\lfloor k\rfloor })}^{\lfloor x\rfloor }dx$$$$$$$$$$

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