Question Number 57948 by maxmathsup by imad last updated on 14/Apr/19
$${let}\:{A}\left(\xi\right)\:=\int_{\xi} ^{\xi^{\mathrm{2}} } \:\:\:\:\frac{{arctan}\left(\mathrm{1}+\xi{t}\right)−\frac{\pi}{\mathrm{4}}}{\:\sqrt{\mathrm{2}+\xi{t}}−\sqrt{\mathrm{2}−\xi{t}}}\:{dt} \\ $$$${find}\:{lim}_{\xi\:\rightarrow\mathrm{0}} \:\:{A}\left(\xi\right)\:. \\ $$$$ \\ $$