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Integrate[E^x/Cos[x]]

  • To: mathgroup at smc.vnet.net
  • Subject: [mg38008] Integrate[E^x/Cos[x]]
  • From: Peter Breitfeld <phbrf at t-online.de>
  • Date: Mon, 25 Nov 2002 01:57:44 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

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.
	 	 
Gruß Peter
-- 
=--=--=--=--=--=--=--=--=--=--=--=--=--= http://home.t-online.de/home/phbrf
 Peter Breitfeld, Bad Saulgau, Germany   Meinen GnuPG/PGP-5x Key gibts dort



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