# Integration problem: lrgexp

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?

• 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? – Histograms May 28 '15 at 18:48
• 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. – Farhad May 28 '15 at 19:05
• All the Greek characters mean I cannot cut and paste this into Mathematica. At least not with a Ubuntu Linux clipboard. – Daniel Lichtblau May 28 '15 at 22:52