Re: How to simplify to a result that is real

*To*: mathgroup at smc.vnet.net*Subject*: [mg50735] Re: How to simplify to a result that is real*From*: p-valko at tamu.edu (Peter Valko)*Date*: Sat, 18 Sep 2004 05:48:55 -0400 (EDT)*References*: <cidt38$brv$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

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

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

**Re: Re: How to simplify to a result that is real***From:*DrBob <drbob@bigfoot.com>