If \( \int \sin ^{-1}\left(\sqrt{\frac{x}{1+x}}\right) d x=A(x) \tan ^{-1}(\sqrt{x})+B(x)+C \) where \( C \) is a consta…

If \( \int \sin ^{-1}\left(\sqrt{\frac{x}{1+x}}\right) d x=A(x) \tan ^{-1}(\sqrt{x})+B(x)+C \) where \( C \) is a constant of integration, then the ordered pair \( (A(x), B(x)) \) can be

[JEE Main 2020, 3 Sep (Shift 2)]