Integral, cylindrical coordinates and Gauss

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I'm stuck with a problem that is looking like this:

Use Gauss theorem to determine to flow of the vectorfield:

$z(ρ^{2}-1/ρ)e_ρ$

out of the region:

$x^{2} + y^{2} + (z-2)^{2} \leq 4$

I realize I have to calculate the undefined region first (that is along the z-axis), but how do I do this? Thanks in advance!