Consider the contour \(C\) shown in the figure below. For the vector \(\vec{F} = (x+2y)\hat{e}_x + (2x+4y)\hat{e}_y\), the integral \(\oint_C \vec{F}\cdot d\vec{l} =\)________.
Here \(d\vec{l}\) represents an infinitesimal length along the contour \(C\).
