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: <firstname.lastname@example.org>
- Reply-to: kuska at informatik.uni-leipzig.de
- 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