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I am trying to compute the following integral:

    Integrate[ConditionalExpression[-4 I E^(-\[Pi] r0^2 - 32/5 I \[Pi] r0^4 s - 
 2 \[Pi] (-((300540195 \[Pi] Sqrt[s])/67108864) + 
  2 (1/Sqrt[1/ r0^4] - ((r0^4)^(33/2)
       Hypergeometric2F1[16, 33/2, 35/2, -(r0^4/s)])/(
     33 s^16)))) \[Pi]^2 r0 s (-1 + 1/(1 + s)), r0 != 0], {s,-Infinity,Infinity}]

But I got an error given as:

       PolynomialGCD::lrgexp: Exponent is out of bounds for function PolynomialGCD.
       PolynomialGCD::lrgexp: Exponent is out of bounds for function PolynomialGCD.
       PolynomialGCD::lrgexp: Exponent is out of bounds for function PolynomialGCD.
        Factor::lrgexp: Exponent is out of bounds for function Factor.
       General::stop: Further output of PolynomialGCD::lrgexp will be suppressed during this calculation.

I add a screen shot to be more clear.

enter image description here I would be grateful if someone can explain what is the problem.

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  • $\begingroup$ Firstly, you should use NIntegrate with the method Method -> {"DoubleExponentialOscillatory", "SymbolicProcessing" -> 0} because your integral is highly oscillatory over -infinity to infinity. Unfortunately NIntegrate says evaluated to Overflow, Indeterminate, or Infinity for all sampling points in the region with boundaries $\endgroup$ – Mariusz Iwaniuk Jan 6 '17 at 15:41
  • $\begingroup$ Thank you, so the integral is complicated to be evaluated ? Actually this is a double integral with variables {s,- Infinity, Infinity} and {r0,-Infinity,Infinity}. I f I do the evaluation for the double integral it is teh same. $\endgroup$ – Mounia Hamidouche Jan 6 '17 at 16:07
  • $\begingroup$ If I put Integrate[eq, {r0,-Infinity,Infinity}] = 0. !!!.Solution is Zero. $\endgroup$ – Mariusz Iwaniuk Jan 6 '17 at 18:40

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