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!