Some integrals with problematic evaluation

[quinyu]

Yes, I know it is table lookup, and it is certainly less valuable as far as education is concerned; but it has its own strengths. I am not trying to argue away the educational value of XCAS' approach.

In fact I would love to see such step by step explanation coming from the calculator itself, and preferably know all the tricks that XCAS employs as well - seeing that unfortunately that's not the case.

As of table lookup, well, the rule set that I employ has close to 6000 such "rules" encoded - roughly 1.8Mb of Mathematica code. I agree it is a lot, and likely not very educational. (By the way, the integral I mentioned was 1/(a^5+x^5), not with a minus, but as far as the technique is concerned, that's close to irrelevant...) But it tends to get to a solution. More frequently so than baseline Mathematica, Maple and Maxima combined.

I agree that elegance also plays a great part in mathematics, and I'm not in position to criticise the XCAS system. If anything, I'm criticising what HP made out of it, which appears to be both less capable and less educational than the original; and precisely these shortcomings am I trying to point out to those who are responsible for what actually gets into a software update, as to make them reconsider. Maybe it's all in vain, I do not know. But I know there's much of hard iron in the HP, it's a shame not to put it to full use.