Some integrals with problematic evaluation

[parisse]

You should enter the commandlines in plain text if you want other to be able to reproduce easily your inputs, screenshots can not be copied/pasted.
Now, the status of your examples is not completly clear. Did you find *wrong* answers or is it just more complicated than it could ideally be?
I did not look at all your examples, but one of your expected answer (4th screenshot) requires complex logarithms for x>sqrt(6)/3 which would be considered as bad by many users, while the Prime answer does not, thanks to absolute values.
You should also consider that there are several ways to express an antiderivative, and an automatic system can obviously not always find the simplest way to return it. Note also that the answer on the Prime might look complicated just because some expressions are sometimes added to ensure that the antiderivative is continuous (floor) or to ensure that it is defined in the real domain (ln(abs(..))).