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Math Help - What is the integral of e^1/x?

  1. #1
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    What is the integral of e^1/x?

    Hi, I seem to be stumped with calculating this indefinite integral:

    e^1/x6x^2dx

    I'm using integration by parts, but I can't find how to take the integral of e^1/x...how does it work?

    Thank you, kind sirs!



    Last edited by UBCBOY; February 17th 2013 at 03:12 PM.
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  2. #2
    Super Member ILikeSerena's Avatar
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    Re: What is the integral of e^1/x?

    Quote Originally Posted by UBCBOY View Post
    Hi, I seem to be stumped with calculating this indefinite integral:

    e^1/x6x^2dx

    I'm using integration by parts, but I can't find how to take the integral of e^1/x...how does it work?

    Thank you, kind sirs!



    Hey UBCBOY!

    It doesn't work very well.
    You won't be able to find an indefinite integral of e^{1/x}.
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  3. #3
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    Re: What is the integral of e^1/x?

    It doesn't exist?

    I tried putting DNE on the system but it does not work.
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  4. #4
    Super Member ILikeSerena's Avatar
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    Re: What is the integral of e^1/x?

    As they say, it cannot be expressed with a finite number of standard functions.
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  5. #5
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    Re: What is the integral of e^1/x?

    Hi !

    The integral of exp(1/x) cannot be expressed as a combination of a finite number of elementary functions. It's formal expression requires a special function, namely Ei(x).
    integrate exp(1/x) - Wolfram|Alpha
    Of course, it is possible to express the integral of exp(1/x) on the form of infinite series.
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