You use the anti-derivate OF THE FUNCTION to do the nonlinear processing. Then take the derivative OF THE SIGNAL. This suppresses aliasing products. Of course you need to figure out the anti-derivative of the function which can end up being a much more complex function which then defeats any gains you get by lowering the oversample rate.d/dx of the integral of f(t)dt from 0 to t (that's hard to type out) is just f(x) isn't it? What's the benefit of doing it that way over just using f(x), does it sort of "normalize" the data?
It also means that you are using a waveshaper in the first place. In our case the functions are essentially dynamic so this wouldn't work.