6
\includegraphics[max width=\textwidth, alt={}, center]{68f4b2dc-a05d-4061-aaf0-de15cfe186a9-08_616_531_269_799} The diagram shows the curves \(y = \frac { 6 } { 3 x + 2 }\) and \(y = 3 \mathrm { e } ^ { - x } - 3\) for values of \(x\) between 0 and 4. The shaded region is bounded by the two curves and the lines \(x = 0\) and \(x = 4\). Find the exact area of the shaded region, giving your answer in the form \(\ln a + b + c \mathrm { e } ^ { d }\).