let-give-f-x-0-1-ln-1-x-2-t-2-t-2-dt-with-x-lt-1-by-using-derivation-under-find-the-value-of-f-x-

Tinku Tara June 4, 2023 Integration 0 Comments

Question Number 28819 by abdo imad last updated on 30/Jan/18

let give f(x)= ∫_0 ^1 ((ln(1−x^2 t^2 ))/t^2 )dt with ∣x∣<1 by using derivation under ∫ find the value of f(x).

$${let}\:{give}\:{f}\left({x}\right)=\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{ln}\left(\mathrm{1}−{x}^{\mathrm{2}} {t}^{\mathrm{2}} \right)}{{t}^{\mathrm{2}} }{dt}\:\:\:\:{with}\:\mid{x}\mid<\mathrm{1} \\ $$$${by}\:{using}\:{derivation}\:{under}\:\int\:\:{find}\:{the}\:{value}\:{of}\:{f}\left({x}\right). \\ $$

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