How to solve this integral for three-point correlation function?

Question

I need to solve the following integral as part of the computation of a three-point correlation function in a charged massless quantum field theory, where I can also assume conformal invariance. $$ \begin{align} (\star)= \int\frac{d^{d}x}{(|x-x_a|^2|x-x_b||x-x_c|)^{d-2}} \end{align} $$ Using Feynman parameters, I arrive at the following form $$ \begin{align} (\star)= \frac{\Gamma(2d-4)}{\Gamma(d-2)(\Gamma(\frac{d-2}{2})^2)}&\int_{0}^{1}d{u_1}d{u_2}{u_1^{d-3}}{u_2}^{\frac{d-4}{2}}({1-u_1-u_2})^{\frac{d-4}{2}} \\ \times&\int\frac{d^{d}x}{(u_1(x-x_a)^2+u_2(x-x_b)^2+(1-u_1-u_2)(x-x_c)^2)^{2d-4}} \end{align} $$ and through Schwinger parameterization I arrive at $$ \begin{align} \begin{split} (\star)&=\frac{\Gamma(\frac{3d}{2}-4)}{\Gamma(d-2)(\Gamma(\frac{d-2}{2})^2)}\int_{0}^{1}d{u_1}d{u_2}{u_1^{d-3}}{u_2}^{\frac{d-4}{2}}({1-u_1-u_2})^{\frac{d-4}{2}} \\ &\times ({u_1}{u_2}(x_a-x_b)^2+{u_1}(1-u_1-u_2)(x_a-x_c)^2+{u_2}(1-u_1-u_2)(x_b-x_c)^2)^{4-\frac{3d}{2}}, \end{split} \end{align} $$ which I have been unable to simplify. I was advised to use the result for the four-point integral $\int\frac{d^dx}{|x-x_1|^a|x-x_2|^b|x-x_3|^c|x-x_4|^d}$ and send one point to infinity but I haven't been able to find a simple reference for either this four-point integral or this procedure of sending points to infinity. Any tips or references welcome.