$\int \frac{3 x+2}{4 x^2+4 x+5} d x=\mathrm{A} \log \left(4 x^2+4 x+5\right)+\mathrm{BTan}^{-1}\left(\frac{2 x+1}{2}\right)+\mathrm{c}$, then $\mathrm{A}+\mathrm{B}=$

• Correct answer
  A

  $\frac{1}{2}$
• B

  $\frac{3}{4}$
• C

  $\frac{3}{8}$
• D

  $\frac{1}{8}$

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