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Stubborn Integral

by qspeechc
Tags: integral, stubborn
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qspeechc
#1
Oct30-09, 03:58 AM
P: 792
Hi

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?
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Gib Z
#2
Oct30-09, 07:22 AM
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P: 3,348
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.
qspeechc
#3
Oct30-09, 07:35 AM
P: 792
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.

Gib Z
#4
Oct30-09, 07:50 AM
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P: 3,348
Stubborn Integral

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.
qspeechc
#5
Oct30-09, 07:54 AM
P: 792
Er, yea, wolframalpha gives a strange answer, what is # supposed to represent? But thanks anyway.
Gib Z
#6
Oct30-09, 08:01 AM
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P: 3,348
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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