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Question Number 100235 by mathmax by abdo last updated on 25/Jun/20
$$\mathrm{calculate}\sum_{\mathrm{n}=\mathrm{0}} ^{\infty} \:\left(−\mathrm{1}\right)^{\mathrm{n}} \:\int_{\mathrm{1}} ^{\mathrm{e}} \:\mathrm{x}^{\mathrm{n}} \:\mathrm{lnx}\:\mathrm{dx} \\ $$