$\int \frac{\sin 2 x}{\sin ^2 x+3 \cos x-3} d x$

• A

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

  $\log \left(\frac{(\cos x-2)^2}{(\cos x-1)^4}\right)+c$
• C

  $\log \left(\frac{(\cos x-2)^2}{|\cos x-1|}\right)+c$
• Correct answer
  D

  $\log \left(\frac{(\cos x-2)^4}{(\cos x-1)^2}\right)+c$

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