This isn’t really an ELI5 question but basically there isn’t a closed formula for this:
Let’s start with an easier example:
W=ydx+xdy
We integrate the first part and get F=xy but there is another part which is a function of y which we don’t know yet. We can repeat the process for y and get that
F=xy+c which you can check gives us W=ydx+xdy.
The problem with your example is that there isn’t any function that can give this differential form. An easy way to check is to differentiate again. For most regular functions, differentiations by x and then y is the same as y and then x.
But in your case we get x in one case and y in the other.
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