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How to simplify to a result that is real


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


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