I’m afraid that computerized anti-differentiation looks like black magic to me as it is. I might argue, OTOH, that functionally it is no different than using a table of integrals, and that a way to exploit it legitimately might be to have the student prove the integral that comes out of the machine by differentiating it, before using it. Wouldn’t that be enough?You can certainly expose the student to the old manual process, but I have the feeling that the new math apps probably don’t even work the same way internally as the process we learned. In which case, what actually is the point in grinding out a lot of moot examples of the way you would do it on a desert island?
People on desert islands don’t use calculus!
No the math apps do work differently, but on a fundamental level it’s still reasoning doing some level of mental pattern matching, some more reasoning again until you get the answer. I think it’s good for you!