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

• A

  $\frac{\pi}{8} \log 2$
• B

  $-\frac{\pi}{2} \log 2$
• C

  $-\frac{\pi}{4} \log 2$
• Correct answer
  D

  $2 \pi \log 2$

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