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Finding the closed form of the integral of a closed form, yes then what you say is true (this is different from 'analytic' which in mathematics has a different meaning). Scope of the concept of even baby integration of a function is much much larger, and OP is talking about that.

Note the key word there is a function not a function with a closed form that's a tiny subset.

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"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.

Thanks for clarifying what you meant by 'analytic'.

To me, 'harder, more finicky' means exactly that it is of a more constrained scope, so I don't think I interpreted OP wrong.

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