Just by looking at it, have a few good ones.

Do you see why, say 2, will not work?.

If r=2, then you have an integrating factor of .

Then

Which is not integrable by elementary means.

Actually, are generally not easily integrated.

Trying to integrate can be a booger.

Then you have for r=0

If r=-1, then

And so on. Just something to think about. See if you can find others in the interval that will or will not work.