# 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) |