Having difficulty with what seems like a standard integral

I am fairly sure the integral I am trying to evaluate has an analytical solution and I am not used to Mathematica not finding the answer relatively easily, I have tried out a few tricks and transformations but doesn’t seem to evaluate it.

Here is the integral:

$$ F(x,y,z)=int_{r=0}^{r=R} int_{phi=0}^{phi=2pi}dr dphi left(frac{r}{sqrt{(z-delta)^2+(x-r cos(phi))^2+(y-r sin(phi))^2}}right)-left(frac{r}{sqrt{(z+delta)^2+(x-r cos(phi))^2+(y-r sin(phi))^2}}right)$$

Here is the code I use for it with assumptions clarified on these parameters (everything is real)

Integrate[ r/Sqrt[(z - [Delta])^2 + (x - r Cos[[Phi]])^2 + (y - 
 r Sin[[Phi]])^2] - r/  Sqrt[(z + [Delta])^2 + (x - r Cos[[Phi]])^2 + (y - 
 r Sin[[Phi]])^2], {r, 0, R}, {[Phi], 0, 2 [Pi]}]

I tried the integration with the following assumptions:

$ {x,y,z,R,delta} in Re $ and $ R>0,delta >0$.

Not sure if this is truly uncomputable or I am missing a simple transformation. Thank you for your suggestions!