What is the most general antiderivative of ? I'll be you are expecting that:

.

BUT

Note that .

Now, I'll be the first to admit that has no real values. But itdoesmanage to solve the differential equation .

So what, if anything, does this all mean? And what does it mean to have a function with no (real) domain, but that has a real valued derivative? There's something I'm just not picturing right here.

-Dan