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I think you mean analytically in the same sense as the comment I replied to, of having a closed form you can write down by hand, but that's not right. But that's not the really important thing from a mathematical point of view: you really want to know useful properties about what you get out of integration, and integration gives you nice mathematical objects with good properties, very much unlike differentiation. It's wrong to think of getting a closed form as the goal, that's nice, but not as important as the other stuff. The numerical consequences just follow from the mathematics, so they can illustrate the difference.



Still, that's not what you grade you for in school. Differentiation is much easier than integration, because for the former you have, within the scope of what they can throw at you on the test, a well-defined set of rules you pretty much mechanically apply to the formula until you can't simplify the answer anymore. Whereas integration is a constant guess-work and performing algebraic magic tricks to maybe make the formula look like something you can tackle with one of the two or three generic methods you've been taught.

Sure, school != reality, but it's the former we get tortured by...


>It's wrong to think of getting a closed form as the goal, that's nice, but not as important as the other stuff.

I see you've never had to do Bayesian inference.




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