Integral of e^1/x

Integral of e^1/x

Indefinite integral
integral e^(1/x) dx = e^(1/x) x – Ei(1/x) + constant
Series expansion of the integral at x=0
e^(1/x) (-x + O(x^2)) + e^(1/x) (x + O(x^2)) + i pi ceiling((arg(x))/(2 pi)) + i pi floor((arg(x))/(2 pi)) – i pi floor((arg(x) + pi)/(2 pi))
Series expansion of the integral at x=∞
x + (log(x) – gamma + 1) – 1/(2 x) + O((1/x)^2)
(generalized Puiseux series)

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