That's a nasty little integral you have there. I'm not surprised TI's CAS couldn't solve it. From what I'm aware, the CAS on the 89 and the Nspire is a modern form of TI's old DERIVE CAS. That CAS wasn't particularly good, but it's also not entirely horrible. The calcs probably use a limited form that has more problems.
On the other hand, HPs are better for math because HP spends a lot of time programming those calcs to do math very well. They really are the best calcs for math. Good thing calculators were never meant for math, eh?
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Hayleia: No solutions exist for that one.