Need help with Integral: e^(-1/x)?

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Discussion Overview

The discussion revolves around the integral of the function e^(-1/x), specifically focusing on methods of integration and the challenges associated with finding an anti-derivative for this expression. Participants explore various approaches and substitutions related to this integral.

Discussion Character

  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant requests assistance with the integral e^(-1/x).
  • Another participant suggests following the rules for exponential integration, but later clarifies that the integral does not fit the standard form for simple substitution.
  • A participant notes that the integral \int e^{-1/x}dx does not have an anti-derivative in terms of elementary functions.
  • One participant introduces the concept of using the exponential integral function to express the integral.
  • There is a correction regarding the applicability of a simple substitution for this integral.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the method to solve the integral, with some suggesting that it cannot be expressed in elementary terms while others propose alternative approaches. The discussion remains unresolved regarding the best method to tackle the integral.

Contextual Notes

Participants express uncertainty about the applicability of standard integration techniques and the limitations of substitutions for this specific integral.

Alexx1
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Can someone help me with this integral?

e^(-1/x)
 
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Just follow the rules for exponential integration.

\int e^{u} du = e^{u} + C

Thanks
Matt
 
Last edited:
If this is the integral:
\int e^{-1/x}dx

an ordinary substitution is not much help. Alexx1, can you show us the complete integral you're trying to do?
 
CFDFEAGURU said:
Just follow the rules for exponential integration.

\int e^{u} du = e^{u} + C

Thanks
Matt
If the problem were \int e^u du, but it isn't and there is no good way to change it to that form.

It looks to me like \int e^{1/x} dx does not have an anti-derivative in terms of elementary functions.
 
in terms of an exponential integral function...

<br /> \int \!{{\rm e}^{-{x}^{-1}}}{dx}=x{{\rm e}^{-{x}^{-1}}}-{\rm Ei}_1<br /> \left({x}^{-1} \right) <br /> <br />
 
HallsofIvy,

Yes, now I see that a simple substitution is not the way to proceed. Thanks for correcting me.

Thanks
Matt
 

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