Except the first assumption that e^x = its own integral, everything else actually makes sense (except the DX are in the wrong powers). You simply treat the “1” and “integral dx” as operators, formally functions from R^R into R^R and “(0)” as calculating the value of the operator on a constant-valued function 0. EDIT: the step 1/(1-integral) = the limit of a certain series is slightly dubious, but I believe it can be formally proven as well. EDIT 2: I was proven wrong, read the comments
Yeah I don’t remember if the result is correct, but the process is definitely sus.
the result is correct
I don’t believe you can just factor our e^x in the second step like that. That seems in incorrect to me. Then again I’ve been out of calculus for years now.