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

• A

  $\log (x+1)-\log (x-2) \sqrt{1-x}+c$
• B

  $\log (\mathrm{x}-2) \sqrt{1-\mathrm{x}}+\mathrm{c}$
• Correct answer
  C

  $6 \operatorname{Tan}^{-1} \sqrt{1-x}-2 \sqrt{1-x}+c$
• D

  $4 \operatorname{Tan}^{-1} \sqrt{1-x}-2 \sqrt{1-x}+c$

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