If \( \int \sin ^{-1} \sqrt{\frac{x}{1+x}} d x=A(x) \tan ^{-1} \sqrt{x}+B(x)+C \), where \( C \)....

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



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