Calculating Potential Energy from Force for Non-Linear Systems

[RubroCP]

Homework Statement

$F(x)=\alpha x-\beta x^3$

Relevant Equations

$-\frac{\mathrm{d}V(x)}{\mathrm{d}x}=F(x)$

If I have a force that behaves according to the formula $F(x)=\alpha x-\beta x^3$, how can I get the potential energy from it? I know that:
$$-\frac{\mathrm{d}V(x)}{\mathrm{d}x}=F(x),$$
but what about the limits of the integration?

 

[Orodruin]

The integration constant is not physical as it does not affect the force. It is up to you to choose the zero-level of the potential.

 

[RubroCP]

The integration constant is not physical as it does not affect the force. It is up to you to choose the zero-level of the potential.

So can I say without loss of generality that for x = 0 the potential is also null?

 

[Orodruin]

Yes, this will not affect the physics.

 

[RubroCP]

Yes, this will not affect the physics.

Thanks!