Integral: e^(-1/x)

  • Thread starter Alexx1
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Can someone help me with this integral?

e^(-1/x)
 
776
9
Just follow the rules for exponential integration.

[tex]\int[/tex] [tex]e^{u}[/tex] du = [tex]e^{u}[/tex] + C

Thanks
Matt
 
Last edited:
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4,562
If this is the integral:
[tex]\int e^{-1/x}dx[/tex]

an ordinary substitution is not much help. Alexx1, can you show us the complete integral you're trying to do?
 

HallsofIvy

Science Advisor
Homework Helper
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Just follow the rules for exponential integration.

[tex]\int[/tex] [tex]e^{u}[/tex] du = [tex]e^{u}[/tex] + C

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

It looks to me like [itex]\int e^{1/x} dx[/itex] does not have an anti-derivative in terms of elementary functions.
 
607
0
in terms of an exponential integral function...

[itex]
\int \!{{\rm e}^{-{x}^{-1}}}{dx}=x{{\rm e}^{-{x}^{-1}}}-{\rm Ei}_1
\left({x}^{-1} \right)

[/itex]
 
776
9
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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