Solving Stubborn Integral: Help Needed

[qspeechc]

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?

 

[Gib Z]

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]

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]

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]

Er, yea, wolframalpha gives a strange answer, what is # supposed to represent? But thanks anyway.

 

[Gib Z]

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.