Show that one-form got an antiderivative

Let $F:{\mathbb{R}}^{d}\setminus \{0\}\to {\mathbb{R}}^{d}$ be a continous vector field with

$F(x)=\phi (\Vert x{\Vert}^{2})x$ for a continous $\phi :(0,\mathrm{\infty})\to \mathbb{R}$. Show that the one-form ${\omega}^{F}(p)(v):=\u27e8F(p),v\u27e9$, got an antiderivative.

I have no idea. Do i have to show that ${\mathbb{R}}^{d}\setminus \{0\}$ is star-like and that F is closed?

Let $F:{\mathbb{R}}^{d}\setminus \{0\}\to {\mathbb{R}}^{d}$ be a continous vector field with

$F(x)=\phi (\Vert x{\Vert}^{2})x$ for a continous $\phi :(0,\mathrm{\infty})\to \mathbb{R}$. Show that the one-form ${\omega}^{F}(p)(v):=\u27e8F(p),v\u27e9$, got an antiderivative.

I have no idea. Do i have to show that ${\mathbb{R}}^{d}\setminus \{0\}$ is star-like and that F is closed?