"Scope of the concept of even baby integration of a function is much much larger, and OP is talking about that." The OP said the opposite, that differentiation

"Scope of the concept of even baby integration of a function is much much larger, and OP is talking about that." The OP said the opposite, that differentiation is harder 'more finicky.' I agree that the concept of integration is much richer. Also, I didn't mean 'closed form solution' when I said 'analytic.' I also didn't mean 'analytic functions.' I meant that the analytic machinery you have to develop in order to have a theory of integration is far richer than for differentiation - i.e, proving the multivariate change of variable theorem.