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Author: Tinku Tara

let-0-lt-a-lt-1-calculate-0-ln-t-t-a-1-1-t-dt-and-0-ln-2-t-t-a-1-1-t-dt-

Question Number 73238 by mathmax by abdo last updated on 08/Nov/19 $${let}\:\mathrm{0}<{a}<\mathrm{1}\:{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\frac{{ln}\left({t}\right){t}^{{a}−\mathrm{1}} }{\mathrm{1}+{t}}{dt}\:\:{and}\:\int_{\mathrm{0}} ^{\infty} \:\frac{{ln}^{\mathrm{2}} \left({t}\right){t}^{{a}−\mathrm{1}} }{\mathrm{1}+{t}}{dt} \\ $$ Commented by mathmax by…