If $\int \frac{x}{x \tan x+1} \mathrm{~d} x=\log \mathrm{f}(x)+\mathrm{k}$, then $\mathrm{f}\left(\frac{\pi}{4}\right)=$

• A

  $\frac{\pi}{4 \sqrt{2}}$
• B

  $\pi+\frac{\pi}{2 \sqrt{2}}$
• Correct answer
  C

  $\frac{\pi+4}{4 \sqrt{2}}$
• D

  $\frac{\pi-4}{4 \sqrt{2}}$

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