Find the potential function f(x,y)f(x,y)f(x,y) for the conservative field F(x,y)=⟨2xy+1,x2+2y⟩\mathbf{F}(x,y) = \langle 2xy + 1, x^2 + 2y \rangleF(x,y)=⟨2xy+1,x2+2y⟩.
f(x,y)=x2y+x+y2+Cf(x,y) = x^2 y + x + y^2 + Cf(x,y)=x2y+x+y2+C
f(x,y)=xy2+x+y2+Cf(x,y) = xy^2 + x + y^2 + Cf(x,y)=xy2+x+y2+C
f(x,y)=x2y+y+y2+Cf(x,y) = x^2 y + y + y^2 + Cf(x,y)=x2y+y+y2+C
f(x,y)=x2y+xy+y2+Cf(x,y) = x^2 y + xy + y^2 + Cf(x,y)=x2y+xy+y2+C