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calculatef-a-0-ln-a-2-x-2-a-2-x-2-dx-with-gt-0-1-calculate-0-ln-2-x-2-2-x-2-dx-and-0-ln-3-x-2-3-x-2-dx-




Question Number 59161 by maxmathsup by imad last updated on 05/May/19
calculatef(a)=  ∫_0 ^∞    ((ln(a^2 +x^2 ))/(a^2 +x^2 ))dx   with >0  1) calculate ∫_0 ^∞   ((ln(2+x^2 ))/(2+x^2 ))dx  and ∫_0 ^∞   ((ln(3+x^2 ))/(3+x^2 )) dx .
$${calculatef}\left({a}\right)=\:\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{ln}\left({a}^{\mathrm{2}} +{x}^{\mathrm{2}} \right)}{{a}^{\mathrm{2}} +{x}^{\mathrm{2}} }{dx}\:\:\:{with}\:>\mathrm{0} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{ln}\left(\mathrm{2}+{x}^{\mathrm{2}} \right)}{\mathrm{2}+{x}^{\mathrm{2}} }{dx}\:\:{and}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{ln}\left(\mathrm{3}+{x}^{\mathrm{2}} \right)}{\mathrm{3}+{x}^{\mathrm{2}} }\:{dx}\:. \\ $$

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