Think back to the discussion of where the parts table comes from. Recall that you can stop a table at any point by integrating the product of the terms in the last row . In this case, the product of the terms in the last row is 0, and the antiderivative of 0 is a constant. Thus, if you get 0 by differentiating, your table stops automatically at the 0-row. This is usually a good thing.
Parts is often useful when an integral contains different kinds of functions.