In the physics world, the notation is $P\exp(\int_a^b f(t)\,dt)$ or $T\exp(\int_a^b f(t)\,dt)$, where the "$P$" and "$T$" stand for "path ordered" and "time ordered". The idea of time-ordered arithmetic I think is originally due to Feynman:
- R.P. Feynman (1951). An operator calculus having applications in quantum electrodynamics. Physical Review. vol. 84 (1) pp. 108-128.
In the UC Berkeley 2008 course on Lie theory by Mark Haiman (my edited lecture notes are available as a PDF), we called it just $\int$, which was a bit of an abuse of notation. Or rather, for any ODE, we referred to the corresponding "flow" as $\int$: $\int_p(\vec x)(t)$ was the point that you get to by starting at a point $p$ and flowing via the vector field $\vec x$ by $t$ seconds. I'm not a fan of this notation, myself, whereas I'm reasonably happy with "$T\exp$".
