How this integral could be solved? Mathematica and Rubi failed.
$$\int _{-\infty }^{\infty }\int _{-\infty }^{\infty }\int _{-\infty }^{\infty }\int _{-\infty }^{\infty }\int _{-\infty }^{\infty }\int _{-\infty }^{\infty }a \cdot e^{-\frac{1}{2} \left(z_1^2+z_2^2+z_3^2+z_4^2+z_5^2+z_6^2\right)}dx_6dx_5dx_4dx_3dx_2dx_1$$
with
$a =\sqrt{(z_1 z_5 - z_2 z_4)^2 + (z_3 z_4 - z_1 z_6)^2 + (z_2 z_6 - z_3 z_5)^2}$
$z1 = p1 + x1$
$z2 = p2 + x2$
$z3 = p3 + x3$
$z4 = p4 + x4$
$z5 = p5 + x5$
$z6 = p6 + x6$
where $p_1$,...,$p_6$ are free variables.