let-give-F-x-0-arctan-1-x-1-t-2-1-t-2-dt-and-x-gt-0-calculate-dF-dx-x-

Tinku Tara June 4, 2023 Integration 0 Comments

Question Number 28827 by abdo imad last updated on 30/Jan/18

let give F(x)=∫_0 ^∞ ((arctan(1+x(1+t^2 )))/(1+t^2 ))dt and x>0 calculate (dF/dx)(x).

$${let}\:{give}\:{F}\left({x}\right)=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{arctan}\left(\mathrm{1}+{x}\left(\mathrm{1}+{t}^{\mathrm{2}} \right)\right)}{\mathrm{1}+{t}^{\mathrm{2}} }{dt}\:\:{and}\:{x}>\mathrm{0} \\ $$$${calculate}\:\frac{{dF}}{{dx}}\left({x}\right).\:\: \\ $$

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let-give-F-x-0-arctan-1-x-1-t-2-1-t-2-dt-and-x-gt-0-calculate-dF-dx-x-

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