## Calculus 8th Edition

$F$ is conservative with potential function $$f(x,y)=xe^{xy}+e^y+C$$
$F(x,y)=(1+xy)e^{xy}i+(e^y+x^2e^{xy})j$ $F(x,y)=(Pi+Qj)$ will be conservative when $P_y=Q_x$ Thus, $P_y=(2+xy)xe^{xy}$ and $Q_x=(2+xy)xe^{xy}$ Hence, the given vector field $F$ is conservative with potential function $$f(x,y)=xe^{xy}+e^y+C$$