For the vector field vec$(G)=(y{e}^{xy}+3cos(3x+y))vec(i)+(x{e}^{xy}+cos(3x+y))vec(j),$ find the line integral of vec$(G)$ along the curve $C$ from the origin along the $x-$axis to the point $(5,0)$ and then counterclockwise around the circumference of the circle $x^2+y^2=25$ to the point $(\frac{5}{\sqrt[\phantom{2}]{2}},\frac{5}{\sqrt[\phantom{2}]{2}}).$

${\displaystyle \underset{C}{\overset{\phantom{}}{}}}$vec$(G)*dvec(r)=$

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