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/

**References**:**How to simplify to a result that is real***From:*Richard Chen <richard@doubleprime.com>