# Error on the evaluation of an integral

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.

I would be grateful if someone can explain what is the problem.

• 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 – Mariusz Iwaniuk Jan 6 '17 at 15:41
• 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. – Mounia Hamidouche Jan 6 '17 at 16:07
• If I put Integrate[eq, {r0,-Infinity,Infinity}] = 0. !!!.Solution is Zero. – Mariusz Iwaniuk Jan 6 '17 at 18:40