[jordan_curve]

I’ll disagree with everyone else here. There’s not really a good reason to understand them, no. It’s good to have a broad understanding of what tricks are out there and to get a general sense of what techniques might work where, but no reason to know them in depth or learn all the tricks.

Computer Algebra is actually not great at solving integrals (and the problem is unsolvable in general). But it’s not extremely common that one needs to symbolically integrate gnarly expressions and you can look up the tricks when it comes up.

Much in the same way that I believe introductory linear algebra is bogged down by endless matrix computation without a computer, I think forcing students to compute a million different gross integrals quickly has diminishing returns.