Calculation of $\mathrm{E}[\sqrt{X^2+Y^2} \sqrt{(X+d)^2+Y^2}]$ with X and Y uncorrelated Normal random variables

Question

I am trying to solve the following integral:

$$\frac{1}{2\pi\sigma^2}\int_{-\infty}^{\infty}\int_{-\infty}^{\infty} \sqrt{x^2+y^2} \sqrt{(x+d)^2+y^2} \exp\left[\frac{-1}{2\sigma^2} ((x-\mu_x)^2+(y-\mu_y)^2) \right] dx dy$$

Is the previous integral solvable analytically?