Answer
\[\ln |x^2+3x+4|+C\]
Where $C$ is constant of integration
Work Step by Step
Let \[I=\int\frac{2x+3}{x^2+3x+4}dx\]
Let \[t=x^2+3x+4\;\;\;...(1)\]
\[\Rightarrow dt=(2x+3)\: dx\]
\[\Rightarrow I=\int\frac{1}{t}dt\]
\[I=\ln |t|+C\]
Where $C$ is constant of integration
From (1)
\[I=\ln |x^2+3x+4|+C\]
Hence ,
\[I=\ln |x^2+3x+4|+C\]
