You don't have to talk about integrating higher degree polynomials, because a polynomial is just a sum of monomials, and you just end up integrating monomials over and over again. If you can integrate a single monomial, you can integrate all polynomials.

That makes your objection seem weak, as though you don't know how to integrate, and you're just imagining that it is hard. That undermines your point because there are actually things in math that are hard, but you'd be woefully unprepared to understand them if you don't see the value in memorizing the absolutely trivial stuff.

It's like a child saying "I don't want to be forced to memorize the shapes of the letters, because that's not what makes a good writer." Does a good writer sit around looking up letter shapes in a diagram all day because they can't be bothered to remember them?

Either way, the optimal solution is the same: do the task over and over again until you are so familiar with it that you can recall it from memory. Memorization is a necessary part of learning.