Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2019 / Paper 1 / 17 / b / 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 isConsequently the definite integral isAll logarithm arguments here are positive on the integration interval.