Some integrals with problematic evaluation

[parisse]

(04-03-2016 04:37 PM)quinyu Wrote:  Once again, we agree that many math teachers simply don't take the time to understand what's going on under the surface. Nevertheless, for the general high school teacher, it might well be a bit too high expectation to know and fully understand for example the Hermite-Kronecker-Brioschi characterization (which in itself isn't a particularly complicated one, at least in terms of programming),

?? Never heard of that.
I don't think math teachers should learn very specialized algorithms, but they should learn when a problem can be solved by a CAS with full confidence, and what they can expect from a CAS. Things like you can not expect a CAS to make a particular case when simplifying x^2/x. Or know that you can use a CAS with full confidence when computing with polynomials and rational fractions. Or the difference between exact and approx representations...