alt Hacker NewsI think that's more about integrations/differentials not producing them (generally speaking). Physics likes to deal with integrals and differentiation as you calculate change over time or over spatial dimensions.
Eg. the integral of x^10 is x^11 / 11 + c. No hyper-operation appears and it's just another exponential (with a division).
The integral of log(x) is xlog(x) - x + c. So still basically just a logarithm
Even the integral of 2^x is just 2^x / log(2). Still basically the same thing.
There's no easy way to pull a hyper-operation out.
I'd say integrals or differentials are not as important on their own as the kinds of differential equations that come up in physics. Integrals and differentials don't produce hyperoperations from non-hyperoperations, but a solution to something as simple as y' - e^x y = 0 will have a double exponential.
However a lot of DEs in physics are linear second-order with coefficients that are most often constants or polynomials, and if they're not polynomial they are made to be so using series expansions, under reasonable assumptions. This already brings you a long way towards solving the problem. The resulting equations usually have trigonometric/exponential/special function solutions.
It's still possible that hyper-operations like a double exponential might come up in the study of some specific non-linear problems. As in the example above, if you have an exponential function as a coefficient in your differential equation you might get a double exponential in the solution somewhere. I'm not familiar with any specific physics examples though.