If $\frac{5 \pi}{4} < x < \frac{7 \pi}{4}$, then $\int \sqrt{\frac{1-\sin 2 x}{1+\sin 2 x}} d x=$

• A

  $-\sec ^2\left(\frac{\pi}{4}-x\right)+\mathrm{c}$
• B

  $-\log \left|\sec \left(\frac{\pi}{4}-x\right)\right|+c$
• C

  $\sec ^2\left(\frac{\pi}{4}-x\right)+c$
• Correct answer
  D

  $\log \left|\sec \left(\frac{\pi}{4}-x\right)\right|+c$

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