How to Determine the Potential of a Conservative, Central-Symmetric Force?

[Uku]

Homework Statement

Find the potential of the following conservative and central-symmetric force

$\vec{F(\vec{r})}=\vec{r}f(\vec{r})$

Homework Equations

$\vec{F}=-\nabla U$

The Attempt at a Solution

I can integrate by components?

$F_{x}=-\frac{\partial U}{\partial x}$

Getting: $U_{x}=-\int xf(x)dx$

Not sure on this..

 

[dextercioby]

It's a system of PDE's for the same function U_x doesn't exist, since U is a scalar. You should have$$U = - \int x f(x,y,z) dx + g(y,z)$$