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Question Number 34253 by math khazana by abdo last updated on 03/May/18

 let F(x)= ∫_0 ^x   ((ln(1+t^2 ))/t^2 )dt  1) calculate F(x)  2) find the value of  ∫_0 ^∞    ((ln(1+t^2 ))/t^2 )dt

$$\:{let}\:{F}\left({x}\right)=\:\int_{\mathrm{0}} ^{{x}} \:\:\frac{{ln}\left(\mathrm{1}+{t}^{\mathrm{2}} \right)}{{t}^{\mathrm{2}} }{dt} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{F}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{ln}\left(\mathrm{1}+{t}^{\mathrm{2}} \right)}{{t}^{\mathrm{2}} }{dt} \\ $$

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