I noticed a couple of things on sage-devel recently about integration
with Maxima. It appears Maxima can't do either of these two. (Well, it
does the second one, but leaves it in a overly complex form, that
Sage's n(). can't even use).

integrate( sqrt(x^2+4)/(x^2+1), x )

integrate(log(1+x)/(x^2+1),(x,0,1)) # (This one from the Putman 2005 challenge)

I noticed that if one sticks that exact syntax into Wolfram|Alpha, it
evaluates the integrals. There's no need to re-write the integrals in
Mathematica's syntax.. If one was to use Mathematica directly, then
the sage syntax would not be understood.

I guess none of this is not totally surprising, but can be useful to
get a second opinion on something, without even taking the trouble to
rewrite the problem in Mathematica's syntax.

See:


http://www.wolframalpha.com/input/?i=integrate%28%20sqrt%28x^2%2B4%29%2F%28x^2%2B1%29%2C%20x%20%29&t=ff3tb01

http://www.wolframalpha.com/input/?i=integrate%28log%281%2Bx%29%2F%28x^2%2B1%29%2C%28x%2C0%2C1%29%29&t=ff3tb01


Dave

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