The diagram shows the curves \(y=\dfrac6{3x+2}\) and \(y=3e^{-x}-3\) 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 \(\ln a+b+ce^d\). [9]