Integrate me

Using integration by parts, we have:

$\begin{aligned} \int_0^{1.5} {e^x \sin{(2x)}} dx & =\left[ - \frac{e^x \cos{2x}}{2} \right]_0^{1.5} + \frac{1}{2} \int_0^{1.5} {e^x \cos{(2x)}} dx \\ & = \ -\frac{e^{1.5} \cos{3}}{2} + 1 + \left[\frac{e^x \sin{2x}}{4} \right]_0^{1.5} \\ & \quad \quad - \frac{1}{4}\int_0^{1.5} {e^x \sin{(2x)}} dx \\ \Rightarrow \frac{5}{4} \int_0^{1.5} {e^x \sin{(2x)}} dx & = -\frac{e^{1.5} \cos{3}}{2} + 1 + \frac{e^{1.5} \sin{3}}{4} - 0 \\ \Rightarrow \int_0^{1.5} {e^x \sin{(2x)}} dx & = \frac{4 + e^{1.5}( \sin{3} - 2\cos{3})}{5} = \boxed{2.301} \end{aligned}$