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Re: General expression of this definite integral ?


Here's an antiderivative:

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

(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])

But look up AppellF1 to see where its singularities and branch-cut discontinuities lie, before using that to compute a definite integral.

Bobby

On Wed, 18 Aug 2004 01:20:07 -0400 (EDT), Jeffrey Tan <M.L.Tan at open.ac.uk> 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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