They can already do this just by downloading Mathematica.

Solving integrals is the original selling point of Mathematica: https://www.wolfram.com/mathematica/scrapbook/1988/03/04/198...

And yes, I memorized a bunch of integrals for my calculus class and then promptly forgot them all after the final exam. It's not worth it to remember how to do integrals other than simple cases like polynomials or sin/cos on their own.