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Re: How to simplify to a result that is real


Richard Chen <richard at doubleprime.com> wrote in message news:<cidt38$brv$1 at smc.vnet.net>...
> 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



Richard,

I think this will work:


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

FullSimplify[ComplexExpand[ch, TargetFunctions -> {Re, Im}], {-1 < e <
1, 0 < a < Pi}]


The result is

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


Peter


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