Different Results from Integrate & NIntegrate

Question

Strangely enough, I believe I am getting different results from Mathematica's Integrate and NIntegrate[] functions when they are evaluated at some point.

Here is the function I am integrating:

Integrate[-((E^(2 n x μ) (-1 + 
         Gamma[2, 
          n x μ]) (λR^2))/((λR^2 + (E^(n x μ) ((n \
μ - λR^2)))))^2) (n μ E^(-n x μ)), {x, 
  0, ∞}]

and here is the result from symbolic integration:

ConditionalExpression[(λR^2)/(n^2 μ^2 - 
    n μ (λR^2)), Re[n μ] > 0]

So, when I campare analytic result with one that is obtained numerically, I get

(λR^2)/(n^2 μ^2 - n μ (λR^2)) /. {n -> 
   1, μ -> 1.0, λR -> 0.99}

49.2513

And, when I integrate numerically, I get

NIntegrate[-((E^(2 n x μ) (-1 + 
          Gamma[2, 
           n x μ]) (λR^2))/((λR^2 + (E^(n x μ) ((n \
μ - λR^2)))))^2) (n μ E^(-n x μ)) /. {n -> 
    1, μ -> 1.0, λR -> 0.99}, {x, 0, ∞}]

40.8463 Am I missing something???

For the analytic result, on different platforms, are people getting a different result than mine?

Mathematica Version: 9.0.1.0, MS Windows 64bit

Answer 1

I guess this is a problem of version 9.0. In Mathematica 10 I get the correct result:

expr = -((E^(2 n x μ) (-1 + 
          Gamma[2, n x μ]) (λR^2))/((λR^2 + (E^(n x μ) ((n μ - λR^2)))))^2) (n μ E^(-n x μ));

Integrate[expr, {x, 0, Infinity}]

(* Out: ConditionalExpression[
           1/(-λR^2 + n*μ) + PolyLog[2, λR^2/(λR^2 - n*μ)]/λR^2, 
           Re[n*μ] > 0] *)

% /. {n -> 1, μ -> 1., λR -> 0.99}
(* Out: 40.84631507906563 *)

Comparing with version 9 one notices the absence of PolyLog function.