You gotta pick your most favorite poison: If you already ate math for the most parts you can have one good laugh after another with your prof in quantum physics about some ppl. not getting it that well :) . You can even call out the "classical" physicists as numbnuts bc. of their questionable "use" and assumptions (in statistical mechanics, e.g. also) in stochastic methods.

And measure theory imo is actually easy once you understood the concept of zero-measure sets in different measures thoroughly.

The integration part then is hard again bc. integration is an form of art. I often refer to this one in this: https://en.wikipedia.org/wiki/Bronshtein_and_Semendyayev .

The Russians were and are the big wizards of so many integrals and function theory that i stopped counting them and just look them up, if maple (https://www.maplesoft.com/) doesn't solve them fast enough or the solution seems irrational or "too" complex to write down or understand.

Above that there are numeric methods which i just wrote here as a reminder, if you really can't find a closed, beautiful enough solution.