I used a lot of SageMath (https://www.sagemath.org) when I was an undergrad. Very easy to use piece of softawre for Python in case anyone want to explore computer algebra systems.
But what I love about pure SymPy is that it doesn't bring anything new to the language at all. You just write in Python, business as usual, it's just half of your variables are now computable symbols, and you can solve things symbolically whenever you want to.
The best part for me is the SymPy API methods have the same names as the concepts I am trying to teach: solve, expand, simplify, factor, integrate, etc.
Here is a short tutorial to introduce SymPy for anyone who hasn't seen before: https://minireference.com/static/tutorials/sympy_tutorial.pd... also available as notebooks: https://mybinder.org/v2/gh/minireference/sympytut_notebooks/...
It's also worth checking out the SymPy Live Shell, where you can try things out without installing anything: https://live.sympy.org/
For calculus it would make a lot of sense though. You can learn the formulas and general rules so you can do derivative and integrals by hand, but I think we could cut-down significantly on the "integration techniques" topics without any loss. I would love to see a course like that... but I doubt any teacher would be "allowed" to teach it this way, since CALC I and CALC II course curriculum is usually imposed by the university.