For the vector field $\vec G = (ye^{xy}+2\cos\!\left(2x+y\right))\,\vec i + (xe^{xy}+\cos\!\left(2x+y\right))\,\vec j$, find the line integral of $\vec G$ along the curve $C$ from the origin along the $x$-axis to the point $(4,0)$ and then counterclockwise around the circumference of the circle $x^2+y^2=16$ to the point $(4/\sqrt{2},4/\sqrt{2})$.

$\int_C\vec G\cdot d\vec r =$