# Potential of conservative force

## 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..

$$U = - \int x f(x,y,z) dx + g(y,z)$$