Is it possible to predict equality/inequality, of indefinite integrals of multivariable fucntions, over a domain from equality/inequality respectively of those functions over the same domain?
Does f(x,y,z) ≠ g(x,y,z) for say x,y,z belonging to the set of natural numbers ⇒ ∫∫∫ f(x,y,z) dx dy dz ≠ ∫∫∫ g(x,y,z) dx dy dz for x,y,z belonging to the set of natural numbers?
While this should hold for definite integrals, this does not look binding for indefinite integrals. But, I was just wondering if it was possible, if not in general, then in some special cases.