How do I integrate ∫21∫21∫21∫21x1+x2+x3−x4x1+x2+x3+x4dx1dx2dx3dx4?

Answer 1

Your notation does not quite work, but I can say that when you integrate a function of multiple INDEPENDENT variables, you do so one variable at a time, treating all other variables as constants, just as when taking mixed partial derivatives of such a function.