Đáp án:

\( \frac{3x + 2}{(x - 2)(x - 3)} = \frac{A}{x - 2} + \frac{B}{x - 3} \implies  
\begin{cases} 
A = -8 \\ 
B = 11 
\end{cases} \)

\( \int \frac{3x + 2}{x^2 - 5x + 6} \, dx = 11 \int \frac{1}{x - 3} \, dx - 8 \int \frac{1}{x - 2} \, dx \)  

\( = 11 \ln|x - 3| - 8 \ln|x - 2| + C \)