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I want to calculate the following integration but it gives the error

PolynomialGCD::lrgexp: Exponent is out of bounds for function PolynomialGCD.

The code is:

        Δ = 0.0001
        γ = 0.01
        ϵ = 10^10
        δ = 10^10
        ω = 10^10
        Λ = 10^12
        k = Sqrt[δ^2 + ω^2]

        Δ^2 γ^2 Integrate[
        E^(I (ϵ τ)/Λ) (((2 k Cos[k τ] + 
        I ω Sin[k τ]) (k^2 - δ^2 Sin[k τ]^2))/(
        k^2 (2 k Cos[k τ] - I ω Sin[k τ]))) (100/(
        1 + τ^2) + I ((2  τ)/(1 + τ^2)^2)), {τ, 
        0, ∞}]

I tried to solve with NIntegrate, but it gives

NIntegrate::ncvb: NIntegrate failed to converge to prescribed accuracy after 9 recursive bisections

How should I solve this integral?

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  • $\begingroup$ Firstly, you should use NIntegrate with the method Method -> {"DoubleExponentialOscillatory", "SymbolicProcessing" -> 0} because your integral is highly oscillatory over 0 to infinity. Unfortunately it is far too oscillatory to converge within any reasonable error. What do you need this integral for? $\endgroup$ – Histograms May 28 '15 at 18:48
  • $\begingroup$ Thanks. It is one of the coefficients of a differential equation describing the dynamics of a physical system. I think that since it contains a decreasing function it must converge somewhere. $\endgroup$ – Farhad May 28 '15 at 19:05
  • $\begingroup$ All the Greek characters mean I cannot cut and paste this into Mathematica. At least not with a Ubuntu Linux clipboard. $\endgroup$ – Daniel Lichtblau May 28 '15 at 22:52

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