If $\int \sin ^{-1} \bigg( \large\frac{2x}{1+x^2}\bigg) $$dx-=f(x)-\log (1+x^2)+c$ then $f(x) $ is equal to :

Question

\[\begin {array} {1 1} (a)\;2x \tan ^{-1} x & \quad (b)\;-2x \tan ^{-1} x \\ (c)\;x \tan ^{-1} x & \quad (d)\;-x \tan ^{-1} x \end {array}\]