I came across the following:
$ F(x) = \int x^3 \cos(x)dx $
where $F$ is understood to be a primitive of $x^3 \cos(x)$. I find this confusing, because of the "same" $x$ appearing on both sides of the equality. To me, $x$ is "integrated out" on the right side, and I prefer the notation:
$ F(x) = \int_{0}^{x} u^3 \cos(u) du $
or possibly:
$ F = \int x^3 \cos(x) dx $
without mentioning the variable for F.
Is the first notation widely used?