If $\frac{x+1}{(x-1)^2\left(x^2+1\right)}=\frac{A}{x-1}+\frac{B}{(x-1)^2}+\frac{C x+D}{x^2+1}$, then $\sqrt{3 A^2+4 D^2+5 C^2+B^2}=$

• A

  $\frac{3}{2}$
• B

  $\frac{1}{2}$
• C

  1
• Correct answer
  D

  2

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