# Stubborn Integral

by qspeechc
Tags: integral, stubborn
 P: 778 Hi I'm trying to evaluate the following indefinite integral, where s is any positive real number $$\int \frac{du}{ \sqrt{Au^{s+2}+Bu^2+Cu+D} }$$ For any A,B,C,D, and u is zero at $$\pm \infty$$ I don't need to know how to do it, you can evaluate it on some computer algebra system. Any help thanks?
 HW Helper P: 3,353 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.
 P: 778 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.
HW Helper
P: 3,353

## 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.
 P: 778 Er, yea, wolframalpha gives a strange answer, what is # supposed to represent? But thanks anyway.
 HW Helper P: 3,353 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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