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Answering your third question, yes they are! However, they are still somewhat loosely integrated in with the main symbolics, primarily because Maxima does not necessarily do a lot of these integrals in the same way; however, search the link for "integrate" and you will see some of them.

As to the simplification question Thierry points out, it turns out that nearly all of the Maxima simplification methods yield this (though just sending it to Maxima and back, simplify, doesn't). (I also don't see this in Maxima proper, and I'm investigating this.) These are, of course, simplifications, which might only be valid over certain domains, but I haven't seen one involving an unevaluated integral before so I'm not sure what's going on there.

Answering your third question, yes they are! However, they are still somewhat extremely loosely integrated in with the main symbolics, primarily because Maxima does not necessarily do a lot of these integrals in the same way; however, search the link for "integrate" and you will see some of them.symbolics.

As to the simplification question Thierry points out, it turns out that nearly all of the Maxima simplification methods yield this (though just sending it to Maxima and back, simplify, doesn't). (I also don't see this in Maxima proper, and I'm investigating this.) These are, of course, simplifications, which might only be valid over certain domains, but I haven't seen one involving an unevaluated integral before so I'm not sure what's going on there.