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Re: Integrate[E^x/Cos[x]]

  • To: mathgroup at smc.vnet.net
  • Subject: [mg38015] Re: Integrate[E^x/Cos[x]]
  • From: Hendrik van Hees <hees at physik.uni-bielefeld.de>
  • Date: Tue, 26 Nov 2002 00:48:36 -0500 (EST)
  • References: <arsip9$een$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Peter Breitfeld wrote:

> I want to evaluate the integral:
> 
> f[u_] = Integrate[E^x/Cos[x], {x, 0, u},
>     Assumptions -> {x \[Element] Reals, u < Pi/2}]
> 
> Mathematica 4.2 on Linux returns
> 
> (1 - I)*E^((1 + I)*u)*Hypergeometric2F1[
>     1/2 - I/2, 1, 3/2 - I/2, -E^(2*I*u)] +
>   (1/2)*((-I)*PolyGamma[0, 1/4 - I/4] +
>     I*PolyGamma[0, 3/4 - I/4])
> 
> so far so good. This integral should be real-valued, at least in the
> Range 0<=u<Pi/2. And that is my problem. How can I get a real result
> with no imaginary I's. Neither FunctionExpand or FullSimplify did it.

As far as I can see the imaginary parts of the numerical evaluation of the 
above expression are numerical artifacts. They are around <10^(-15). So you 
should use Chop[f[u]] to suppress these numerical uncertainties.

-- 
Hendrik van Hees                        Fakultät für Physik 
Phone: +49 521/106-6221                 Universität Bielefeld 
Fax:   +49 521/106-2961                 Universitätsstraße 
http://theory.gsi.de/~vanhees/          D-33615 Bielefeld 


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