Some integrals with problematic evaluation

[quinyu]

Sure. Starting from the basic assumption that the HP Prime was meant to be aimed mainly at education (which might be wrong, but from the advertising that it had, that's how it came across): while it might do things, it does not have any step-by-step mode in places where it would matter the most, not even as an optional switch/configuration setting.

This can be integration, solving of general or differential equations, you name it. The calculator spits out a result, do what you will with it - in this respect, the 50g is actually more helpful with the proper settings. The Prime very frequently mashes results together using a common denominator, and from that point on, it needs a disproportionate amount of extra function calls to untangle it. If anything, have a configuration setting for whether you want to unify everything. As I see in Xcas, the output is not automatically put together in a common denominator, at least not in the current version, so it should be possible to preserve them, if it serves as the HP Prime CAS base.

Simplify... well, it might simplify or not, it's hard to measure the "simplicity" of an expression, although if I look at a tree representation of it, it would likely be possible to select the tree with smallest average depth, or something similar (perhaps have a more extended array of settings - prefer sin/cos/tan over cot/csc/sec [though this isn't a too common problem]... separate a denominator if in the numerator there is a function with a fraction on its own... try to avoid using the imaginary unit when the device is not in complex mode. Don't do multi-story fractions and such fractions that are broader than a screen, if you can help it. Stuff like these.) As it stands currently, for my perception, simplify very often fails to live up to its name (and then again, I mentioned one expression crashing the calculator on simplify. That's when I gave up further experiments on using it.) I am sure some would disagree over which expression is simpler than the other... it might worth to make some sort of survey with interested users/students.