If $\int \frac{1}{x} \sqrt{\frac{1-\sqrt{x}}{1+\sqrt{x}}} d x=2 f(x)-2 \sin ^{-1} \sqrt{x}+c$, then $f(x)=$
- A
$\operatorname{sech}^{-1} \sqrt{x}$
- B
$\operatorname{cosec}^{-1} \sqrt{x}$
- C
$\log \left(\frac{1+x}{\sqrt{x}}\right)$
- D
$\log \left(\frac{\sqrt{1+x}-1}{\sqrt{x}}\right)$
✓ Correct answer: A
Want the full step-by-step reasoning?