Determine the value of the line integral $\oint_C \mathbf{F} \cdot d\mathbf{r}$ for $\mathbf{F}(x, y) = \langle e^x \sin y + 3y, e^x \cos y + 3x + 5 \rangle$ where $C$ is the circle $x^2 + y^2 = 9$ oriented counter-clockwise.