5.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{79ac81c3-cd05-4f28-8840-3c8a6960e7b7-14_600_1022_255_461}
\captionsetup{labelformat=empty}
\caption{Figure 3}
\end{figure}
- Find \(\int \frac { \ln x } { x ^ { 2 } } \mathrm {~d} x\)
Figure 3 shows a sketch of part of the curve with equation
$$y = \frac { 3 + 2 x + \ln x } { x ^ { 2 } } \quad x > 0.5$$
The finite region \(R\), shown shaded in Figure 3, is bounded by the curve, the line with equation \(x = 2\), the \(x\)-axis and the line with equation \(x = 4\)
- Use the answer to part (a) to find the exact area of \(R\), writing your answer in simplest form.