Not everything works like integrals. Some things don't have a standard process that everyone follows the same way.

Editing is one of these things. There can be lots of different processes, informed by lots of different things, and getting similar output is no guarantee of a similar process.

Even if the visualization of the integration process via steps typed out in the chat interface is the same as what you would have done on paper, the way the steps were obtained is likely very different for you and LLM. You recognized the integral's type and applied corresponding technique to solve it. LLM found the most likely continuation of tokens after your input among all the data it has been fed, and those tokens happen to be the typography for the integral steps. It is very unlikely are you doing the same, i.e. calculating probabilities of all the words you know and then choosing the one with the highest probability of being correct.