As practical advice (not addressing your enjoyment), learn how to use a CAS effectively. That will have a ton more bang for the buck in studying physics than being able to occasionally impress yourself with a Feynman trick or obscure application of the King property.
what CAS do you recommend? Are the open source alternatives at the same level as licensed ones? I know Mathematica from Wolfram is well used in the territory.
And how does one learn how to use those?
I personally use Maxima and Sage. They're not as polished as Mathematica by a long shot, but they're free and very useful when it you get enough practice with them.
