> They're comparing their algorithm's accuracy (solution correctness vs. incorrectness), with Mathematica's ability to find the correct solution in less than 30 seconds. This is a very important distinction!
I had the same initial reaction as you, but then I realized that this is still extremely useful. In a ton of examples, only one direction of differentiation/integration is hard while the other direction is easy. You could build a system that attempted to solve it directly, and failing that attempted to guess-and-verify using this approach. My intuition is that such an overall system would be strictly superior to Mathematica's approach as it exists today.
I had the same initial reaction as you, but then I realized that this is still extremely useful. In a ton of examples, only one direction of differentiation/integration is hard while the other direction is easy. You could build a system that attempted to solve it directly, and failing that attempted to guess-and-verify using this approach. My intuition is that such an overall system would be strictly superior to Mathematica's approach as it exists today.