I did quite a bit at university but have barely done any since.
I went to the campus bookstore and it looks like every Electrical Engineering book is full of integrals. EE, maybe?
Dentistry.
Hahaha?
the most practical part of calculus it isn’t in integrals and derivatives but rather manipulating them in differential equations to model things.
Well, it violates conventions (of etiquette, let’s say) about contexts in which x[sup]x[/sup] ought be taken to be uniquely defined. But at any rate, even limiting ourselves to positive numbers, this (definite) integral clearly goes off to infinity rather than converging.
(Of course, you really meant to ask about the indefinite integral instead. To which the answer is simply “It’s the antiderivative of x[sup]x[/sup]”. If pressed further, one might admit that one lacks a better way of expressing the answer, or perhaps even prove that it can’t be expressed in some particular format or another, but no matter… until someone settled on names like “sine”, “logarithm”, and so on, those functions lacked nice names too, but no one considers them any the worse for it now.)
Just for the record, I did know what calculus was in this sense. The dentists have found lots of it in my mouth, you see… =(
That’s easy: it’s the antiderivative of f(x)=x[sup]x[/sup]. 
ETA: Or what Indistinguishable said. 