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I wanted to find the normalization of distribution F2 . 

p = 2.2849;
p1 = 0.938/3;
p2 = 0.938/3;
p3 = 1.6;


F2 = Integrate[(s - s0)*(s + 2^2)^-2/(p^2 - s)^2, {s, s0, Infinity}]/. s0 -> (p1^2/(1 - x2 - x3) + p2^2/x2 + p3^2/x3)

nfactor = NIntegrate[F2, {x2, 0, 1}, {x3, 0, 1}];

why is Mathematica producing complex result? while the result have to be real

J. M.'s missing motivation
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  • Please take a minute to format your post. Put the code in code block. Editing help is on the right of the edit box, or press the (?) button on the edit toolbar for additional help. – Szabolcs Jun 24 '14 at 18:07
  • This is not a very strange issue, see a closely related post explaining why it happens: Why does Integrate declare a convergent integral divergent? – Artes Jun 24 '14 at 18:31
  • If I copy-paste your code, Integrate produces a ConditionalExpression which fails for parts of the rectangle {x2, 0, 1}, {x3, 0, 1}. This means NIntegrate returns unevaluated. Did you F2 correctly? – Greg Hurst Jun 24 '14 at 18:49
  • Why would it be real? The integrand has logs that have negative arguments in ranges 0<x2<1 and 0<x3<1. – Daniel Lichtblau Jun 24 '14 at 19:50
  • In[1]:= p = 2.2849; p1 = 0.938/3; p2 = 0.938/3; p3 = 1.6;

    F2 = Integrate[(s - s0)*(s + 2^2)^-2/(s - p^2)^2, {s, s0, Infinity}, Assumptions -> {s0 [Element] Reals, s0 > 5.22077}] /. s0 -> (p1^2/(1 - x2 - x3) + p2^2/x2 + p3^2/x3)

    In[6]:= nfactor = NIntegrate[F2, {x2, 0, 1}, {x3, 0, 1}, MaxRecursion -> 20, Method -> {GlobalAdaptive, MaxErrorIncreases -> 10000}]

    Out[6]= -0.00145373 - 0.00874148 I

     – asal Jun 24 '14 at 21:06
  • but the result is complex – asal Jun 24 '14 at 21:08

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