$\int_0^{\pi / 4} \frac{1}{5 \cos ^2 x+16 \sin ^2 x+8 \sin x \cos x} d x=$

• A

  $\operatorname{Tan}^{-1}\left(\frac{4}{5}\right)$
• B

  $2 \operatorname{Tan}^{-1}\left(\frac{3}{5}\right)$
• Correct answer
  C

  $\frac{1}{8} \operatorname{Tan}^{-1}\left(\frac{8}{9}\right)$
• D

  $\frac{1}{4} \operatorname{Tan}^{-1}\left(\frac{7}{8}\right)$

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