Subtraction isn’t much harder than addition. Division isn’t much harder than multiplication. Logarithmization isn’t much harder than exponentiation. Then, what fundamentally makes integration so much more difficult than differentiation?

Question

Subtraction isn’t much harder than addition. Division isn’t much harder than multiplication. Logarithmization isn’t much harder than exponentiation. Then, what fundamentally makes integration so much more difficult than differentiation?

In: Mathematics

Answer 1

There’s some good discussion here:

https://math.stackexchange.com/questions/20578/why-is-integration-so-much-harder-than-differentiation

One main answer is that differentiation is local while integration is more global.

Also, this isn’t what you’re asking but funnily enough, it’s much more likely for a function to be integrable than differentiable (in some sense). “Most” functions are integrable but “most” functions aren’t differentiable.