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Integral Sum


Does any know why mathematica won't combine these integrals
Integrate[
  2*Exp[-z[1]*x]*x*V[x]/(z[1]*(z[1] + z[j])^2), {x, 0, Infinity}] + 
 Integrate[
  Exp[-z[1]*x]*x*V[x]/(z[1]^2*(z[1] + z[j])^2), {x, 0, Infinity}]
and how I can get it to?

I am assuming that V[x] is simply a polynomial in x, so that the integrals are convergent.

I would like to see this expression simplify to be
Integrate[
 2*Exp[-z[1]*x]*x*V[x]/(z[1]*(z[1] + z[j])^2) + 
  Exp[-z[1]*x]*x*V[x]/(z[1]^2*(z[1] + z[j])^2), {x, 0, Infinity}], so that I can ultimately get to the simplified expression
FullSimplify[
 Integrate[
  2*Exp[-z[1]*x]*x*V[x]/(z[1]*(z[1] + z[j])^2) + 
   Exp[-z[1]*x]*x*V[x]/(z[1]^2*(z[1] + z[j])^2), {x, 0, Infinity}]].

Any tips?
Thanks.



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