let-f-x-y-x-y-ln-t-ln-1-t-t-dt-with-0-lt-x-lt-y-lt-1-give-f-x-y-at-form-of-serie-

Tinku Tara June 4, 2023 Integration 0 Comments

Question Number 35629 by abdo mathsup 649 cc last updated on 21/May/18

let f(x,y) = ∫_x ^y ((ln(t)ln(1−t))/t)dt with 0<x<y<1 give f(x,y) at form of serie .

$${let}\:\:{f}\left({x},{y}\right)\:=\:\int_{{x}} ^{{y}} \:\:\frac{{ln}\left({t}\right){ln}\left(\mathrm{1}−{t}\right)}{{t}}{dt}\:\:{with}\:\mathrm{0}<{x}<{y}<\mathrm{1} \\ $$$${give}\:{f}\left({x},{y}\right)\:{at}\:{form}\:{of}\:{serie}\:. \\ $$

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