# Why is my integral not being evaluated?

I am trying to integrate a function Gamma, but the output returns the input. I have the following code:

valuesfs = {r -> 50*10^-6, c -> 3*10^8*10^-15, Δt -> 55,
m -> 9.11*10^-31, ϵ -> 8.85*10^-12*10^30, ϵip ->
5.2*1.602*10^-19,
e -> 1.602*10^-19, λ -> 1300*10^-9, ℏ ->
1.054*10^-34*10^15, Γ0 -> 5, t0 -> 100, n -> 0.48,
Ip -> 5*10^17*10^-15};(*list of constants*)

E0 = Sqrt[(2 Ip)/(c*n*ϵ)] //. valuesfs;
Eenv[t_] = E0*E^-((t - t0)/(0.5*Δt))^2 //. valuesfs;
Ef[t_] = Cos[ω*t] //. valuesfs;
El[t_] = Eenv[t]*Ef[t];

Eexp = 1/(ℏ e) Sqrt[2 m] ϵip^(3/2) //. valuesfs;
El[t0] //. valuesfs;
(Eexp/Eenv[t0])^-1 //. valuesfs;

Γ[t_] = Exp[Eexp/Eenv[t]] Γ0 //. valuesfs
Ne = Integrate[Γ[tp], {tp, 0, 200}]


I want to know what value of Ne becomes when Gamma is integrated, but the output of Ne equals the unevaluated input. Can someone tell me what I am doing wrong?

• NIntegrateevaluates 4.964292696444819*10^521122. If this magnitude is expected try to Rationalizethe integrand! – Ulrich Neumann Mar 27 '19 at 11:27
• Note that the value of the integral from tp = 0 to tp = 199.999 is negligible compared to the integral from tp = 199.999 totp = 200, at machine precision. (The ratio is less than 10^-16.) – Michael E2 Dec 22 '19 at 17:29

// N

Ne = Integrate[Γ[tp], {tp, 0, 200}] // N

• Much neater to use NIntegrate then, no? – MarcoB Mar 27 '19 at 15:51