If $\int \frac{\mathrm{dx}}{\sin ^3 \mathrm{x}+\cos ^3 \mathrm{x}}=\mathrm{A} \log \left|\frac{\sqrt{2}+\mathrm{t}}{\sqrt{2}-\mathrm{t}}\right|+\mathrm{B} \operatorname{Tan}^{-1}(\mathrm{t})+\mathrm{c}$, then $\left(\frac{\mathrm{B}}{\mathrm{A}}, \mathrm{t}\right)=$

• A

  $(3 \sqrt{2}, \sin x-\cos x)$
• Correct answer
  B

  $(2 \sqrt{2}, \sin x-\cos x)$
• C

  $\left(\frac{\sqrt{2}}{3}, \sin x-\cos x\right)$
• D

  $\left(\frac{3}{\sqrt{2}}, \sin x+\cos x\right)$

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