Why do some people place the differential at the beginning of their integral? I've seen several times on this site people writing integrals like 
$
\int \! dxf(x)
$. This seems confusing to me, especially in an iterated integral or next to a long integrand and it's nonstandard compared to my own personal experience. I'm wondering what are the reasons people use this notation swap and if it has broader support than I'm aware of.
 A: When you have multiple variables, it's often not clear what bounds belong to which variable. Putting the differential at the beginning helps the reader immediately see what the appropriate integration limits for each of the variables are.
I'll add that this notation is often used by physicists, where triple integrals or even infinite dimensional integrals are often used. As an example, here is a relatively short expression taken from an old physics paper:
$$\sigma_t(E_s,E_p,T)=\int_0^T\frac{dt}{T}\int_{E_{smin}(E'_s)}^{E_s}dE'_s\int_{E_p}^{E_{pmax}(E'_p)}dE'_p\ I_e(E_s, E'_s,t)\sigma(E'_s,E'_p)I_e(E'_p, E_p,T-t)$$
Now try and write this expression with the differentials at the end. How do you know which belongs to what bounds? arguably, in this case the variables were helpfully named, but this is far from always being the case.
A: I suspect that it's because with the "dx" at the end, you don't know what's the var of integration until you get there. Imagine that the integrand is some complicated expression involving $x$ and $t$; it's nice to know whether you're integrating with respect to $x$ or $t$ as you read the integrand. In multiple integrals, it's also nice to know in which order you're integrating so that you can see whether there's a constant (wrt the variable of integration) that can be dragged outside the integral. 
All that said, I still find the notation a bit confusing at times, esp. since I tend to think of the $\int$ and the $dx$ as being like "open" and "close" parentheses, and hence used for grouping. 
