Re: Which symbolic method for this Integral ?
- To: mathgroup at smc.vnet.net
- Subject: [mg82863] Re: Which symbolic method for this Integral ?
- From: Thierry Mella <thierry.mella at skynet.be>
- Date: Thu, 1 Nov 2007 05:22:55 -0500 (EST)
- References: <email@example.com> <firstname.lastname@example.org>
samuel.blake at maths.monash.edu.au wrote: > So I'll give > it a go using the good old method of substitution. > > It's late in Australia, so PLEASE check this!! I believe that using > the substitutions > > u = 1 - x > > then > > t = Sqrt[u] > > then > > t = Sqrt Sin[v] > > This will result in a trig rational integral which can be converted to > a rational integral using the trick given in every calculus book. Then > the rational integral can be calculated using the partial fraction > method. I would not expect the answer to be as nice as that given by > Mathematica, mainly because integrating a rational function using the > partial fraction method does not produce an answer in the minimal > algebraic extension field, whereas the Hermite reduction followed by > Lazard-Rothstein-Trager-Rioboo algorithm will! Also, I assumed t = > Sqrt[u] inverts to u = t^2 which causes further complications.... Hello, Thanks for your answer. The substitutions that you suggest are the ones that I thought about also ... The problem to have a "clean" answer after calculating the rational integral is to invert the substitutions and the result seems to be "heavy" ... But I'm an engineer, not a mathematician ... :-) Thanks, Thierry