Chọn A

Ta có:

$\int{\frac{\left( 2x+3 \right)dx}{{{x}^{2}}+5x+6}=\int{\frac{3\left( x+2 \right)-\left( x+3 \right)}{\left( x+2 \right)\left( x+3 \right)}dx}=\int{\left( \frac{3}{x-2}-\frac{1}{x+3} \right)}dx}$

$=3\ln \left| x+2 \right|-\ln \left| x+3 \right|=\ln \left| \frac{{{\left( x+2 \right)}^{3}}}{x+3} \right|+C$

Vậy $\int{\frac{2x+3}{{{x}^{2}}+5x+6}dx=\ln \left| \frac{{{\left( x+3 \right)}^{3}}}{x+2} \right|+C}$