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
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Peter Breitfeld, Bad Saulgau, Germany Meinen GnuPG/PGP-5x Key gibts dort