Problem

Figure 3 shows a sketch of part of the curve with equation

$$y=\frac{3+2x+\ln x}{x^2}\qquad x>0.5$$

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 $x=4$

(a) Find

$$\int \frac{\ln x}{x^2}\,dx$$

(b) Use the answer to part (a) to find the exact area of $R$, writing your answer in simplest form.