I would like to evaluate integrals of the following type (in position space):
$$\int \frac{d^{2\omega}z}{\left[(x_1-z)^2 (x_2-z)^2 (x_3-z)^2 \right]^A} \tag{1}$$
I can introduce three Feynman parameters using the last equation of the section "Formulas" in this wikipedia article, integrate over $z$, then integrate over one Feynman parameter with the delta function in order to obtain:
$$\pi^\omega \frac{\Gamma(3A-\omega)}{\Gamma^3(A)} \int_0^1 d\gamma \int_0^{1-\gamma} d\beta \frac{\left[ \gamma\beta (1-\gamma-\beta) \right]^{A-1}}{\left[\gamma\beta x_{12}^2+\gamma(1-\gamma-\beta)x_{13}^2 +\beta(1-\gamma-\beta)x_{23}^2\right]^{3A-\omega}} \tag{2}$$
where $x_{ij}:=x_i-x_j$. Is it possible to go further with this integral? If yes, in what way? If not, is there at least a way to extract the divergent part for $\omega \rightarrow 2$ and $A=\omega-1$?
EDIT:
So far the answers seem to not be addressing my problem, so I would like to emphasize the issue: I can do the loop integral, but am stuck at solving the remaining integral with the Feynman parameters. I have also posted the same question at math.stackexchange but did not receive any attention so far. I am starting to believe that this integral is solvable only numerically, because of this quote of Sidney Coleman from the book "Lectures of Sidney Coleman on Quantum Field Theory":
In principle you can reduce any Feynman graph to an integral over Feynman parameters. At that point, typically, you are stuck, but you can always work it out numerically with a computer.