Re: Re: How to simplify to a result that is real

• To: mathgroup at smc.vnet.net
• Subject: [mg50752] Re: [mg50725] Re: How to simplify to a result that is real
• From: DrBob <drbob at bigfoot.com>
• Date: Sun, 19 Sep 2004 03:56:00 -0400 (EDT)
• References: <cidt38\$brv\$1@smc.vnet.net> <200409180948.FAA00517@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```But that's not what MY 5.0.1.0 says:

Integrate[1/(1 + e*Cos[t]), {t, 0, a}, Assumptions -> {-1 < e < 1, 0 < a < Pi}]

-((1/Sqrt[1 - e^2])*(I*Log[Sqrt[1 - e^2] - I*(-1 + e)*Tan[a/2]])) +
(1/Sqrt[1 - e^2])*(I*Log[Sqrt[1 - e^2] + I*(-1 + e)*Tan[a/2]])

Bobby

On Sat, 18 Sep 2004 05:48:16 -0400 (EDT), Jens-Peer Kuska <kuska at informatik.uni-leipzig.de> wrote:

> Hi,
>
> my Mathematica 5.0.1 say
>
> (-2*ArcTan[((-1 + e)*Tan[a/2])/Sqrt[1 - e^2]])/
>  Sqrt[1 - e^2]
>
> and it looks real ?
>
> Regards
>   Jens
>
> Richard Chen wrote:
>>
>> The command:
>>
>> Integrate[1/(1 + e Cos[t]), {t, 0, a},
>>   Assumptions -> {-1 < e < 1, 0 < a < Pi}]
>>
>> leads to a complex valued result. I could not make
>> mathematica to render the result in a form that is
>> purely real. ComplexExpand, Refine all do not seem to work.
>>
>> Does anyone know how to make mathematica to simplify this
>> result into a real form?
>>
>> Thanks for any info.
>>
>> Richard
>
>
>

--
DrBob at bigfoot.com
www.eclecticdreams.net

```

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