Julian, as usual, sent this only to me. I don't know how to make the question rigorous, but I think one answer is that differentiation is a local operation, and integration isn't. This contributes significantly to the practical fact of the chain rule, which is what usually makes differentiation easy (often via product, inverse, etc. which are easily derived from it). The "chain rule" for integration would be change-of-variables, which has ickiness both in how it changes the domain and the Jacobian involving inverse functions. (You need to consider multivariable because that's where the product rule comes from.) Julian (per rwg) Date: 2016-12-16 13:54 From: Dan Asimov <asimov@msri.org> Why is it usually so easy to differentiate a function defined by an exact formula, but so much more difficult to integrate? If this question can be made rigorous, how might that be done? (And if so, what is the rigorous answer, or at least a method of approaching it?) —Dan