I found a nice paper about inverse vector operators here. I have successfully implemented a Mathematica function for most of them, however I can't figure out how to do inverse gradient (page 7 in the paper). According the paper, the inverse gradient can be computed as a path independent line integral, but in my attempts I got improper results. The paper doesn't show up an example for it and I'm not really familiar with line integrals.
If anyone could help me I would be really thankful.