Results 1 to 6 of 6

Math Help - How to integrate x^x?

  1. #1
    Senior Member
    Joined
    Jan 2009
    Posts
    290

    How to integrate x^x?

    I'm bored today so I tried to integratel x^x, but I couldn't. How do you integrate that?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Jun 2008
    Posts
    792
    You can't express it in elementary functions.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member
    Joined
    Jan 2009
    Posts
    290
    Quote Originally Posted by Chop Suey View Post
    You can't express it in elementary functions.
    What does that mean? What is elementary functions? So does that mean you can express it in another function?

    Also, the derivative of x^x is x^x(\ln x+1)

    How would you integrate that if you don't know that formula?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Math Engineering Student
    Krizalid's Avatar
    Joined
    Mar 2007
    From
    Santiago, Chile
    Posts
    3,654
    Thanks
    13
    it means that you'll never find a certain function whose derivative yields the integrand.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by Krizalid View Post
    it means that you'll never find a certain function whose derivative yields the integrand.
    Actually it's not difficult. It's just that nobody bothered to think of defining a special function to account for its antiderivative.

    There is a solution - the function F such that dF/dx is x^x. This function is also known as the Fantastic F-function.

    It can't be written anymore nicely than that. There is nothing surprising about this. Almost no functions have integrals that can be written out nicely and explicitly in some closed form.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Member
    Joined
    May 2007
    Posts
    237
    Quote Originally Posted by chengbin View Post
    What is elementary functions?
    See this for elementary functions:
    Elementary function - Wikipedia, the free encyclopedia
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Integrate ((x+1)^2)/x
    Posted in the Calculus Forum
    Replies: 1
    Last Post: June 9th 2010, 02:18 PM
  2. Integrate 3 e^x
    Posted in the Calculus Forum
    Replies: 4
    Last Post: June 9th 2010, 01:16 PM
  3. how to integrate this ??
    Posted in the Calculus Forum
    Replies: 8
    Last Post: August 9th 2009, 08:14 PM
  4. Integrate
    Posted in the Calculus Forum
    Replies: 7
    Last Post: April 28th 2009, 07:54 PM
  5. Integrate
    Posted in the Calculus Forum
    Replies: 8
    Last Post: April 15th 2009, 03:50 PM

Search Tags


/mathhelpforum @mathhelpforum