Use Green's theorem to evaluate

$o{\displaystyle \underset{C}{\overset{\phantom{}}{}}}(ln(x^2)+x{y}^2-6xy)dx+(y^3+x^{2}y+x^2)dy,$

where $C$ is the boundary of a region bounded by $(x-1{)}^2+y^2=1,y=x$ and the $x-$axis oriented in the anticlockwise manner.