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Comment by cperciva | Hacker News Reader

Yes, I did know that the Risch algorithm existed; and I've implemented it (or at least most of it).

I wonder why it's never mentioned in high school Calculus classes.

Because there's no way in hell that you want to ever apply the Risch algorithm by hand. As the wikipedia page says, it takes more than 100 pages to describe the algorithm; even just using it to compute the integral of x + 1/x would probably take hours without a computer.

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But rather than focus on symbolic integration done by hand in high school, why not focus on higher level problem solving involving symbolic integration done by computer?

Integration itself is quite a bit of problem solving itself, and much more fundamentally understandable.

I'd rather students understand the fundamentals of that integration than have a computer apply an algorithm they don't understand. You can construct problems plenty complicated enough in intro calculus courses for students without resorting to functions they can't integrate with the methods they learn.

Have you looked at the syllabus of a numerical analysis course recently? There is plenty to learn at that level, even for students who had an exceptionally good calculus course beforehand.

Funny, I just forwarded this to my numerical analysis prof. we mostly studied solutions based on laplace in my course, but this is quite interesting (as it appeals to my inner hacker)

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