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.

> the way the steps were obtained is likely very different for you and LLM

this is not true, any examples?