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Integral of polynomial to some power

  1. Jul 30, 2009 #1
    Does anybody know in general how (if) one can perform the integral of a general polynomial to some, not necessarily integer, power? I.e.

    [tex]\int \left(\Sigma_{i=0} ^n c_i x^i \right)^a dx [/tex]

    with [itex] c_i [/itex] and [itex] a [/itex]arbitrary (real) numbers,

    [tex]\int \left(1+x + x^2 + 2x^5 \right)^{1.7} dx [/tex].

    Maybe what I'm looking for is some generalization of Newton's binomium?
     
  2. jcsd
  3. Jul 30, 2009 #2

    HallsofIvy

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    There is no simple way to do that.
     
  4. Jul 30, 2009 #3
    I already thought it would be difficult, if not impossible. Too bad. Thanks anyway.
     
  5. Jul 30, 2009 #4
    [itex]\int\sqrt{\text{fourth degree}}[/itex] = elliptic integral

    [itex]\int_0^1 [x(1-x)]^a\,dx[/itex] = Beta function
     
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