I have a very simple, possibly silly question...
Can this integral make sense in some way? $$ \int \frac{dx}{dx}$$ And does it actually mean something to write things like $$ \int f(x)$$ without the differential?
I just got an expression of this type and I probably made some mistake along the way, but I'm still curious... my intuition from my limited knowledge of differential forms suggests that the last integral should simply evaluate to $f(x)$. How much sense does this make? I pretty much have no idea what to do here, so any help would be appreciated, especially if it includes intuitively pleasing explanations! :)
EDIT: To clarify my question some more, consider an ordinary integral $$\int f(x) dx = F(x) + c$$ where $\frac{dF}{dx} = f$(x).
We could write it as $$\int \frac{dF}{dx}dx = \int dF = F +c$$ Then, going back to my original integral, I could write it as $$\int \frac{1}{dx} dx = \int 1$$ Or for an arbitrary function: $$\int f = \int \frac{f}{dx} dx$$ But does that mean anything or is it just (incorrect) notation gymnastics? Does it make sense for "$1$" to be a differential of something? What about $f$?