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Stubborn Integral

  1. Oct 30, 2009 #1

    I'm trying to evaluate the following indefinite integral, where s is any positive real number

    [tex] \int \frac{du}{ \sqrt{Au^{s+2}+Bu^2+Cu+D} }[/tex]

    For any A,B,C,D, and u is zero at [tex]\pm \infty[/tex] I don't need to know how to do it, you can evaluate it on some computer algebra system. Any help thanks?
    Last edited: Oct 30, 2009
  2. jcsd
  3. Oct 30, 2009 #2

    Gib Z

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    Mathematica can't do it, doubt any other computer systems will be able to either. If you could specify more of your variables it might help.
  4. Oct 30, 2009 #3
    Ok, s is a positive integer, and A=-1/(1+s)(2+s), that's as specific as I can get. Or, simply looking at the cases s=1,2,3,4. Thanks.
  5. Oct 30, 2009 #4

    Gib Z

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    Even if s=1 it seems like a very complex elliptic integral.

    The simplest it can be made into is evaluated by Mathematica if you enter "integrate 1/( x^3+ ax^2+bx+c)^(1/2) dx" into www.wolframalpha.com .

    I've never seen that "Root" function or notation before though.
  6. Oct 30, 2009 #5
    Er, yea, wolframalpha gives a strange answer, what is # supposed to represent? But thanks anyway.
  7. Oct 30, 2009 #6

    Gib Z

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    I think it may signify a certain root of a high degree polynomial. Although I can't make out more than that. Sorry, I think that integral you have is pretty much not doable.
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