Integral of gauge field bulk to boundary propagator in AdS

I’m studying from the book "Introduction to the AdS/CFT Correspondance" by Horatiu Nastase.
In page 190, he defines the gauge field bulk-to-boundary propagator in Euclidean $AdS_{d+1}$ given by
$$A_mu(z) = int text{d}^dvec{x} G_{mu i}(z,vec{x})a_i(vec{x}) $$
Where $G_{mu i}(z,vec{x})$ is
$$G_{mu i}(z,vec{x}) = C^d frac{z_0^{d-2}}{[z_0^2 + |vec{z}-vec{x}|^2 ]^{d-1}} I_{mu i}(z-vec{x})$$
here $I_{mu i}(z-vec{x})$ is the inversion tensor
$$I_{mu i }(z-vec{x}) = delta_{mu i } – 2 frac{(z-vec{x})_mu(z-vec{x})_i}{[z_0^2+|vec{z}-vec{x}|^2]}$$
He claims that the normalization constant $C^d$, such that $A_i to a_i$ at the boundary is given by
$$C^d = frac{Gamma(d)}{2 pi^{d/2} Gamma(d/2)}$$
I wanted to verify this, but I encounter the integral
$$-2 int text{d}^dvec{x} frac{z_0^{d-2}(z-vec{x})_mu(z-vec{x})_i}{[z_0^2+|vec{x}-vec{x}’|^2]^{d}} a_i(vec{x})$$
Which I have no idea how to deal with.
$textbf{Disclaimer}$: the greek indices are in d+1-dimensions and the latin indices in d-dimensions, also $z$ is a vector in d+1-dimensions and $vec{x}$ a vector in d-dimensions