Re: How to simplify to a result that is real

• To: mathgroup at smc.vnet.net
• Subject: [mg50716] Re: [mg50679] How to simplify to a result that is real
• From: Andrzej Kozlowski <andrzej at akikoz.net>
• Date: Sat, 18 Sep 2004 05:48:03 -0400 (EDT)
• References: <200409170515.BAA11699@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```On 17 Sep 2004, at 14:15, 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
>
>

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

-((2*ArcTan[((e - 1)*Tan[a/2])/Sqrt[1 - e^2]])/
Sqrt[1 - e^2])

Andrzej Kozlowski
Chiba, Japan
http://www.akikoz.net/~andrzej/
http://www.mimuw.edu.pl/~akoz/

```

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