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

• A

  $\log \left|\frac{\sqrt{2-x^2}+1}{\sqrt{2-x^2}-1}\right|+c$
• B

  $\frac{1}{2} \log \left|\frac{\sqrt{2-x^2}}{1-x^2}\right|+c$
• Correct answer
  C

  $\frac{1}{2} \log \left|\frac{1+\sqrt{2-x^2}}{1-\sqrt{2-x^2}}\right|+c$
• D

  $\log \left|\frac{1-x^2}{\sqrt{2-x^2}}\right|+c$

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