Evaluate the integral using substitution $\begin{align*}\int\limits_0^1\sin^{-1}\bigg(\frac{2x}{1+x^2}\bigg)dx \end{align*}$

Question

$\begin{array}{1 1} \frac{\pi}{2}-\log 2 \\\frac{\pi}{2}+\log 2 \\\frac{\pi}{4}-\log 4\\\frac{\pi}{4}+\log 4 \end{array} $