Solution
= Solution
Use <integration by substitution> $u=\ln x$, $du=dx/x$. The bounds become $3$ and $4$, and the remaining denominator factorizes as $(u-1)(u-2)$. The <partial fraction decomposition> is
$$
\frac{3u-4}{(u-1)(u-2)}=\frac1{u-1}+\frac2{u-2}.
$$
Consequently the <definite integral> is
$$
\boxed{\left[\ln(u-1)+2\ln(u-2)\right]_3^4
=\ln\frac32+2\ln2=\ln6.}
$$
All logarithm arguments here are positive on the integration interval.