# Perform convergence tests for a multidimensional integral?

GROUPS:
 Is there a way in Mathematica to test whether the integral converges, i.e. numerical integration is kosher? The variables are q3v = Table[q3[i], {i, 3}]; p3v = Table[p3[i], {i, 3}]; qv = Table[q[i], {i, 3}]; pv = Table[p[i], {i, 3}]; The limits are: intvariables = Flatten[Join[{q3v}, {p3v}, {qv}, {pv}]] intvariables2 = {#, -1, 1} & /@ intvariables The integral to be evaulated is 1/((1 + p[1]^2 + p[2]^2 + p[3]^2)^2* (1 + q[1]^2 + q[2]^2 + q[3]^2)^2* Sqrt[Sqrt[1. + p[1]^2 + p[2]^2 + p[3]^2]* Sqrt[1. + p3[1]^2 + p3[2]^2 + p3[3]^2]* Sqrt[1. + q3[1]^2 + q3[2]^2 + q3[3]^2]* Sqrt[1. + (-p[1] + p3[1] + q3[1])^2 + (-p[2] + p3[2] + q3[2])^2 + (-p[3] + p3[3] + q3[3])^2]]* Sqrt[Sqrt[1. + p3[1]^2 + p3[2]^2 + p3[3]^2]* Sqrt[1. + q[1]^2 + q[2]^2 + q[3]^2]* Sqrt[1. + q3[1]^2 + q3[2]^2 + q3[3]^2]* Sqrt[1. + (p3[1] - q[1] + q3[1])^2 + (p3[2] - q[2] + q3[2])^ 2 + (p3[3] - q[3] + q3[3])^2]]* (Sqrt[1. + q3[1]^2 + q3[2]^2 + q3[3]^2] + Sqrt[1. + (p3[1] - q[1] + q3[1])^2 + (p3[2] - q[2] + q3[2])^ 2 + (p3[3] - q[3] + q3[3])^2])) The results are different if the integration limits are changed to -10, 10 for example. Is there a way to test that the integral converges, without being able to perform a symbolic integration (which Mathematica will not do)?