$\int \frac{d x}{(1+\sqrt{x}) \sqrt{x-x^2}}=$

• A

  $-2 \sqrt{\frac{1+\sqrt{x}}{1-\sqrt{x}}}+c$
• B

  $-\sqrt{\frac{1-\sqrt{x}}{1+\sqrt{x}}}+c$
• Correct answer
  C

  $-2 \sqrt{\frac{1-\sqrt{x}}{1+\sqrt{x}}}+c$
• D

  $2 \sqrt{\frac{1+\sqrt{x}}{1-\sqrt{x}}}+c$

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