$\int_{0}^{1/2} \frac{dx}{(1+x^2)\sqrt{1-x^2}}$ is equal to
$\frac{1}{\sqrt{2}} \tan^{-1} \left(\frac{\sqrt{2}}{3}\right)$
$\frac{2}{\sqrt{2}} \tan^{-1} \left(\frac{3}{\sqrt{2}}\right)$
$\frac{\sqrt{2}}{2} \tan^{-1} \left(\frac{3}{2}\right)$
$\frac{\sqrt{2}}{2} \tan^{-1} \left(\frac{\sqrt{3}}{2}\right)$
