Nested NIntegrate problem

Question

So I've been trying to evaluate the following integral in Mathematica 8.0 Student version:

opsnum[a_, \[Omega]_] := (c^5*(3*10^25))/\[HBar]*
      NIntegrate[\[Rho][y, \[Omega]]/
        Hubble[y, \[Omega]]*(1/Hubble[z, \[Omega]])^3, {y, 
        a, \[Infinity]}, {z, a, y}]

with

    Hubble[z_, \[Omega]_] := 
 H0 Sqrt[\[CapitalOmega]M (1 + z)^3 + \[CapitalOmega]\[Gamma] (1 + 
      z)^4 + \[CapitalOmega]\[CapitalLambda] ((1 + 
       z)^(3*(1 + \[Omega])))]

\[Chi][a_, \[Omega]_] := 
 NIntegrate[c/Hubble[z, \[Omega]], {z, a, \[Infinity]}]
\[Rho][a_, \[Omega]_] := (3*Matter[a, \[Omega]])/(
 4 \[Pi]*(\[Chi][a, \[Omega]])^3)

My problem is that this refuses to converge, and gives me an NIntegrate::inumr error, due to the nested integral nature of the function. Furthermore, I cannot think of another definition for the function as it relies on the cube of an integral which has limits different from the limits of the total integrand, of which it is a part.

Anyone got any ideas? I would be eternally grateful!

Answer 1

The NIntegrates should be combined into one call:

NIntegrate[\[Rho][ y, \[Omega]]*(c/Hubble[z, \[Omega]])^3, {y, a, \[Infinity]}, {z, a, y}]

Otherwise, the inner integral remains in symbolic form when the outer integral is run.