Re: General expression of this definite integral ?

*To*: mathgroup at smc.vnet.net*Subject*: [mg50173] Re: [mg50158] General expression of this definite integral ?*From*: DrBob <drbob at bigfoot.com>*Date*: Wed, 18 Aug 2004 04:47:24 -0400 (EDT)*References*: <200408180520.BAA05979@smc.vnet.net>*Reply-to*: drbob at bigfoot.com*Sender*: owner-wri-mathgroup at wolfram.com

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 > > > -- DrBob at bigfoot.com www.eclecticdreams.net

**References**:**General expression of this definite integral ?***From:*Jeffrey Tan <M.L.Tan@open.ac.uk>