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Math Help - Integrate x^(x)

  1. #1
    Senior Member nycmath's Avatar
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    Integrate x^(x)

    What is the definite integral of x^(x)
    from 0 to 1?
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  2. #2
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    Re: Integrate x^(x)

    Quote Originally Posted by nycmath View Post
    What is the definite integral of x^(x)
    from 0 to 1?
    There's no closed form for this. A quick google show's you're not the first to run up against this function.

    Numerically it integrates to roughly 0.783431.
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  3. #3
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    Re: Integrate x^(x)

    As usual for special functions, there is no closed form until a closed form is defined and referenced.
    "The Sophomores Dream Function" on Scribd : JJacquelin's Documents | Scribd
    Sphd(1;x) is an antiderivative of x^x .
    Before saying "This is a vicious circle", one have to think at the role played by all special functions in maths. On this subject, the paper : "Safari in the country of special functions", pp.18-36, same link on Scribd.
    Last edited by JJacquelin; March 31st 2014 at 10:21 PM.
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