What does the "3" in $d^3x_1d^3p_1\ldots d^3x_Nd^3p_N$ mean here?

Question

On page 4 of this online lecture notes, I find the following notation: $$d^3x_1d^3p_1\ldots d^3x_Nd^3p_N$$

What does the raised "3" next to the "d" mean?

Answer 1

It's just an index indicating that you are considering a volume (3D) integral. Each of the $x_j$ and $p_j$ is a vector with $3$ components.

Answer 2

The explanation may be found on page 2 of the document. Here is an image:

It's the same number as the 6N here:

You have $N$ particles with 3 position and 3 momentum values each.