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
It isn’t a general rule that operations should be roughly as easy as their inverses. Encryption algorithms, for example, are very difficult to reverse, as is multiplication when you use prime factorization as the inverse.
Anyway, differentiation only needs to know how the function behaves on a tiny interval (barely more than a single point).
But integration needs to know how the function behaves on large ranges (sometimes everywhere)
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