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