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find-F-0-1-arctan-x-1-x-2-dx-with-R-1-1-




Question Number 31465 by abdo imad last updated on 08/Mar/18
find  F(α)= ∫_0 ^1   ((arctan(αx))/(1+x^2 )) dx  with α ∈ R−{1,−1}
$${find}\:\:{F}\left(\alpha\right)=\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{arctan}\left(\alpha{x}\right)}{\mathrm{1}+{x}^{\mathrm{2}} }\:{dx}\:\:{with}\:\alpha\:\in\:{R}−\left\{\mathrm{1},−\mathrm{1}\right\} \\ $$

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