8. (10 points) Compute the line integral

$$\oint_C \vec{F}\cdot d\vec{r},$$

where

$$\vec{F}(x,y)=(4y+6ye^{2x},6x+3e^{2x})$$

and $C$ is the closed loop formed by traveling from $(-2,0)$ to $(4,0)$ to $(3,3)$ to $(-1,3)$ and back to $(-2,0)$ by straight lines.