Solving integrals

*To*: mathgroup at smc.vnet.net*Subject*: [mg68588] Solving integrals*From*: Jens Benecke <jens-news at spamfreemail.de>*Date*: Fri, 11 Aug 2006 04:39:51 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

Hello everybody, I am trying to solve this integral: f :== int ( cos(x) / sqrt[A=C2=B2=C2=B7sin=C2=B2(x/2) + (Bx)=C2=B2 = ] dx, x==0..N*2*pi where N==(int)0..20, and A and B are small fixed values (around 0.0001..0.05). The problem is the additional summand in the sqare root of the denominator (ie., (Bx)=C2=B2). Without this part the integral would be an elliptic one or could be represented with a combination of E(x) and F(x). I have tried developing the sine function into rows (x-x^3/3!+...) but to be precise enough I would have to go up to x^150/150=C2=B0 which is hardly practical. I have also tried seperating the denominator into expressions where either part of the sum is << or >> the other part so that suitable approximations can be made, without much luck. One other system chokes on this integral while another tells me the solution may be inexact because of singularities. Yes, there is a singularity at x==0, but I need to integrate starting at 0, (and singularities do not always imply that integrals diverge, AFAIK). I would really appreciate any kind of hint or idea on how to tackle this problem. Thank you! :) -- Jens Benecke