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find-f-0-1-arctan-x-1-x-2-dx-

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Question Number 169930 by Mathspace last updated on 12/May/22
find f(α)=∫_0 ^1 ((arctan(αx))/(1+x^2 ))dx
$${find}\:{f}\left(\alpha\right)=\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{arctan}\left(\alpha{x}\right)}{\mathrm{1}+{x}^{\mathrm{2}} }{dx} \\ $$

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