Some integrals with problematic evaluation

[quinyu]

I'm not entirely sure about the Nspire's CAS basis, but (at least according to the developer of that system) it is based on Derive (ref: here, at the bottom of page.) In theory, Derive is/was capable to show steps of the calculation as well, but the Nspire doesn't do so. Whether or not it will later on... no clue, probably if enough students complain about it, they will.
The two integrals that you showed, I tried to time them: on the last CAS version available to me (4.2.0.532) and overclocked to 210MHz base/CPU, 52MHz AHB, the first integral evaluates in a little less than 16s. The second, as you say, is not evaluated, just split into the sum of two integrals. In comparison, the HP Prime results are effectively instantaneous. For added interest: the 50G also solves both integrals. The Classpad II does the first one in ~7s, the second in ~3s. I did not bother actually checking the result from the first, too long for me to compare by hand, but there were no integrals left in it on the CX, 50G or CP. Derive (v6.10) can solve the first as well as the second, and from the displayed steps I can definitely see that it is looking for patterns. Some of the patterns are pretty curious, but they seem to work in the end. So if Derive can solve the second, I'm unsure why the CX cannot, unless they took some earlier branch (that couldn't) as codebase, or trimmed down the available rules...