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find-the-value-of-this-integral-I-0-tan-1-x-1-x-x-2-dx-




Question Number 174610 by Brahimmekkaoui last updated on 05/Aug/22
find the value of this integral:  I=∫_0 ^∞  ((tan^(−1) (x))/(1+x+x^2 )) dx
$${find}\:{the}\:{value}\:{of}\:{this}\:{integral}: \\ $$$${I}=\int_{\mathrm{0}} ^{\infty} \:\frac{{tan}^{−\mathrm{1}} \left({x}\right)}{\mathrm{1}+{x}+{x}^{\mathrm{2}} }\:{dx} \\ $$

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