$\int \frac{\sin x+\cos x}{\sin x-\cos x} d x=$

• A

  $-x+\log |\cos x-\sin x|+c$
• B

  $x-\log |\cos x-\sin x|+c$
• C

  $-\log |\cos x-\sin x|+c$
• Correct answer
  D

  $\log |\cos x-\sin x|+c$

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