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

```

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