You have no idea. This is tame compared to some of the shit I seen in my masters.

I remember one time we had an exercise where the calculation yielded a violently nonconvergent improper integral.

Now, we had already been introduced to some “tricks” to “deal with” those. And I do mean “tricks” as in magic. Arcane spells best described as “praying to the obscure gods of Borel summation until some incantation accidentally summoned untold horrors that would swallow infinities into fractional dimensions converging to zero” or some bullshit like that.

But this one was so bizarre that the whole class was stumped. Our runes were powerless, what remained of our sanities was fraying and disappearing into the abyss that kept lookingback for more.

Then the TA just tsk’d at our collective weakness, deadass looked into each of our eyeballs and wrote this on the blackboard

I almost puked on the spot

If anyone’s curious, the first step is wrong. e^x minus its integral is a constant. Not necessarily zero.

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.