Evaluate Integral for Reduced Green's Function: Semi-Infinite Plates

[AxiomOfChoice]

Can someone help me evaluate this integral?

$$\int\limits_{-\infty}^{\infty} dz' \frac{1}{\sqrt{(x-x')^2 + (y-y')^2 + (z-z')^2}}$$

Mathematica is telling me that this guy diverges. But it CAN'T! This is supposed to give me the reduced Green's function for two semi-infinite plates that meet at a right angle on the z-axis.

 

[mathman]

For large z' the integrand behaves like 1/|z'|, leading to divergence.

 

[Gerenuk]

It does indeed diverge.

To solve you could use
$$z-z'=\sqrt{(x-x')^2+(y-y')^2}\sinh t$$