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I need more help

  1. Apr 24, 2005 #1
    i came acreoss a problem thats red like this ,wats the integral of x^x i gev it all i could so can anyone help me,furthermore wats the integral ,of a fuction raised 2 another e.g x^x,e^[x^2],cos[x]^[sin[x].and so on
     
  2. jcsd
  3. Apr 24, 2005 #2

    dextercioby

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    One of them,viz.[itex] \int \mbox{exp} \left(x^{2}\right) \ dx [/itex],can be expressed as function of the "common" special functions (the erf of imaginary argument).The other that u mentioned cannot...


    Daniel.
     
  4. Apr 24, 2005 #3

    HallsofIvy

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    Where are you getting these problems? None of these functions can be integrated in terms of elementary functions.
     
  5. Apr 25, 2005 #4
    Just a quick thought: what about breaking x^x into a product. For instance x^x = [x^(x-1)]*x^1 and then try integration by parts. It's been a while since my calculus days but that sounds like something I might have tried.
     
  6. Apr 25, 2005 #5

    dextercioby

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    It's usless.Here's why.

    [tex] \int x^{x} \ dx =\int x^{x-1} x \ dx=\frac{x^{x-1}x^{2}}{2}-\frac{1}{2}\int x^{x-1}\left[x(x-1)+x^{2}\ln x\right] \ dx [/tex]

    and the second integral looks horrible...


    Daniel.
     
  7. Apr 27, 2005 #6
    hey thnxs for all but they still do not help ,
     
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