First of all, you have a sign error in $\displaystyle \begin{align*} \frac{\mathrm{d}}{\mathrm{d}x} \left[ \mathrm{e}^{-3x}\cos{ \left( 2x \right) } \right] = -3\mathrm{e}^{-3x}\cos{ \left( 2x \right) } - 2\mathrm{e}^{-3x}\sin{ \left( 2x \right) } = -\mathrm{e}^{-3x} \left[ 3\cos{ \left( 2x \right) } + 2 \sin{ \left( 2x \right) } \right] \end{align*}$. This might have affected your chances to get further...