       Re: General expression of this definite integral ?

• To: mathgroup at smc.vnet.net
• Subject: [mg50172] Re: General expression of this definite integral ?
• From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
• Date: Wed, 18 Aug 2004 04:34:07 -0400 (EDT)
• Organization: Universitaet Leipzig
• References: <cfupl8\$627\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Hi,

Mathematica say
In[]:=Integrate[x^n*Sqrt[(c + x)/(c - x)], x]

Out[]=(x^(1 + n)*Sqrt[(c + x)/(c - x)]*Sqrt[1 - x/c]*
AppellF1[1 + n, 1/2, -1/2, 2 + n, x/c, -(x/c)])/
((1 + n)*Sqrt[1 + x/c])

In[]:= Integrate[x^n*Sqrt[(c - x)/(c + x)], x]

Out[]=(x^(1 + n)*Sqrt[(c - x)/(c + x)]*Sqrt[1 + x/c]*
AppellF1[1 + n, -1/2, 1/2, 2 + n, x/c, -(x/c)])/
((1 + n)*Sqrt[1 - x/c])

depending on a and b you may simply insert the boundaries
but for cases where a,b > c you should look for the
branch cuts in the complex plane.

Regards
Jens

Jeffrey Tan wrote:
>
> Dear all,
> I am looking for the general expressions of the following definite
> integrals
>           Int [ x^n * sqrt[(c + x)/(c - x)]]
> and     Int [ x^n * sqrt[(c - x)/(c + x)]]
> with the integration range from a to b,
> where a, b, c = constants
> n = n-th degree power
>
> I try in several mathematical packages but only specific solutions are
> computed by putting n= 0,1,2... seperately in the above expression.
> Besides that, no information available from many famous integral
> handbooks, e.g. W. Grobner and N. Hofreiter, Integraltafel, Zweiter Teil,
> Bestimmte Integrale (Springer, Wien, 1958).
>
> Could anyone suggests how tackle this problems ?
>
> Looking forward your helping hands as soon as possible! Thanks!
> Cheers,
> Jeffrey M.L.Tan
> -----------------------------------------------------------
> Department of Materials Engineering
> Faculty of Technology
> The Open University
> Walton Hall, Milton Keynes  MK7 6AA
> Buckinghamshire
> United Kingdom

```

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