(a) Find $$\(\int \frac{\ln x}{x^{2}} \mathrm{~d} x\)$$ (3) Figure 3 shows a sketch of part of the curve with equation $$\[ y=\frac{3+2 x+\ln x}{x^{2}} \quad x> 0.5 \]$$ The finite region $$\(R\)$$, shown shaded in Figure 3, is bounded by the curve, the line with equation $$\(x=2\)$$, the $$\(x\)$$-axis and the line with equation $$\(x=4\)$$ (b) Use the answer to part (a) to find the exact area of $$\(R\)$$, writing your answer in simplest form. (4)

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