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Math Help - integration of (e^x)/x ?

  1. #1
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    integration of (e^x)/x ?

    Hi all,
    can anybody find a solution for the integration of (e^x)/x ?

    Best regards.
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  2. #2
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by raladin View Post
    Hi all,
    can anybody find a solution for the integration of (e^x)/x ?

    Best regards.
    It has no closed form solution...by try converting to power series \frac{e^x}{x}=\sum_{n=1}^{\infty}\frac{x^{n-1}}{n!}
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  3. #3
    Eater of Worlds
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    Just as an aside, this particular integral is known as the Exponential Integral

    and is represented by Ei(x).

    Actually, \int_{x}^{\infty}\frac{e^{-t}}{t}dt is called the exponential integral and can be represented as an 'incomplete' Gamma function.

    An incomplete Gamma function is \int_{x}^{\infty}t^{n-1}e^{-t}dt for x\neq 0

    By repeated integration by parts we can find several terms of the asymptotic series for the above integral.

    Just some useless information for you

    mathstuds series is easier.
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  4. #4
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    thanks a lot guys for your help, I really appreciate it.
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