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The relationship between the force and the potential energy is this:

##F=-\nabla V(q_{1},q_{2},...,q_{i})##

If I want to know the potential energy, what do I do? I had an idea, but I don't know if it is correct:

If ##F=-\nabla V(x,y,z)##, then V(x) is just minus the integral of F over x by treating y and z as a constant, and so on and so forth, and then if you want to know what V(x,y,z) is, you just add everything together. But then you'd get 3 different constants of integration that I don't know what they are.

Any help would be appreciated.