If $\int \frac{3 x+1}{(x-1)^3(x+1)} d x=\mathrm{A} \cdot \log \left|\frac{x+1}{x-1}\right|+\frac{\mathrm{B}}{x-1}+\frac{\mathrm{C}}{(x-1)^2}+\mathrm{D}$ then $\mathrm{A}+\mathrm{B}+\mathrm{C}=$

• Correct answer
  A

  $\frac{-5}{4}$
• B

  $\frac{5}{4}$
• C

  $\frac{-5}{2}$
• D

  $\frac{5}{2}$

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