Let $P\left(x\right)=\int \frac{dx}{e^x+8e^{-x}+4e^{-3x}},$ $Q\left(x\right)=\int \frac{dx}{e^{3x}+8e^x+4e^{-x}}$ and $R\left(x\right)=P\left(x\right)-2Q\left(x\right)$. If $R\left(x\right)=\frac{1}{2}A\left(\frac{B+2e^{-x}}{C}\right)+K,$ then the value of $\left(A,B,C\right)$ is

• A

  $\left({\tan }^{-1},2,e^x\right)$
• Correct answer
  B

  $\left({\tan }^{-1},e^x,2\right)$
• C

  $\left({\tan }^{-1},\frac{1}{2},\frac{1}{e^x}\right)$
• D

  $\left({\tan }^{-1},\frac{1}{e^x},\frac{1}{2}\right)$

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