[andomggazzz662]

For the same reason not grinding out the code by hand and copying from your LLM is going to result in you being a less competent programmer in the long run.

I really believe there is something to be said for putting yourself through the mental strain of evaluating the integrals (or code) and that doing so contributes to you having a better feel for how it works on a conceptual level as well, you don't just get better at calculating by doing things the hard way.

If you can easily see the solutions and manipulations you can make to an integral by hand, then you are more able to quickly get a feel for what it represents just by looking at it. If you are not as experienced doing them by hand, just reading them is going to sap some of your brain power and energy, and you will be less able to reason about them abstractly as a result.

I think the whole "just learn the concepts" approach to almost anything is fundamentally misguided and not at all how representative of how humans really learn.

[saghm]

I guess I just fundamentally disagree with you on this one. To me, spending time manually calculating integrals in a timed exam is less similar to copying code from an LLM and more similar to manually translating the source code you write into machine code instead of using a compiler; it might have value, but the amount of work it would take a student in an intro class to do that would drown out their ability to retain anything else.