I am trying to represent and compute integrals of closed 1-forms in 2 variables (the result of the integral does not depend on the path chosen), I would like them to display in the usual way

$$\int f(x,y) dx + g(x,y) dy$$

ideally both in the inert form (equivalent to the function Int) and active form (int, where Maple would if possible try to express the integral). The only computation requirement for the inert form would be that the x derivative gives $f$, and the y derivative gives $g$.

Is it possible to modify the possible arguments of the functions Int, int, such that they accept to represent such integral and implement a program to compute them if possible?

I know how to write a program to compute this, but the output display will not use the symbol $\int$ and will not behave nicely when differentiating.