If $\int \frac{1}{x} \sqrt{\frac{1-\sqrt{x}}{1+\sqrt{x}}} d x=2 f(x)-2 \operatorname{Sin}^{-1} \sqrt{x}+\mathrm{c}$, then $f(x)=$

• Correct answer
  A

  $\operatorname{Sech}^{-1} \sqrt{x}$
• B

  $\operatorname{Cosec}^{-1} \sqrt{x}$
• C

  $\log \left(\frac{1+x}{\sqrt{x}}\right)$
• D

  $\log \left(\frac{\sqrt{1+x}-1}{\sqrt{x}}\right)$

Hence, the correct answer is option: 'A'.