Solution
= Solution
The <partial fraction decomposition> is
$$
\frac{2x+1}{x(x+1)}=\frac1x+\frac1{x+1}.
$$
Taking <antiderivatives> and using the positive endpoints gives
$$
\int_2^3\frac{2x+1}{x(x+1)}\,dx=[\ln x+\ln(x+1)]_2^3=\ln\frac{3\cdot4}{2\cdot3}=\ln2.
$$
Hence $\boxed{n=2}$.