# How to integrate an expression holding Series[]?

How do you integrate with the Series command in the Integral?

I.e., it looks something like:

NIntegrate[(E^x α)/(Series[E^(x α), {x, 0, 3}] - Series[E^x, {x, 0, 3}] Subscript[λ, R] +
Subscript[λ, R]) /. {θ -> 1, α -> 1/3, Subscript[λ, R] -> 0.5}, {x, 1, ∞}]

• Series returns a special SeriesData object that is different from what it looks like. Use Normal to convert it to a plain expression. See 2nd item under Possible Issues in Series documentation. – Szabolcs Feb 25 '17 at 14:49

As mentioned by @Szabolcs, the issue is with the structure of Series

Series[E^(x α), {x, 0, 3}] We need to remove O[x]^4 to be able to integrate the expression containing Series. Thus to get "Normal expression", we should use Normal,

a = Normal[Series[E^(x α), {x, 0, 3}]]
b = Normal[Series[E^x, {x, 0, 3}]]
NIntegrate[((E^(x*α))/(a - b Subscript[λ, R] +  Subscript[λ, R])) /. {θ -> 1, α -> 1/3,
Subscript[λ, R] -> 0.5}, {x, 1, ∞}]


But, still we are getting error messages, this is because $\exp{(\infty)}$ is $\infty$.

• I made the expansion finite so it works...Thanks! – PiE Feb 25 '17 at 15:39
• @PMF You are welcome! – zhk Feb 25 '17 at 15:43