How to further simplify the result of this indefinite integral

The following result of indefinite integral contains hypergeometric series, but the reference answer is $-frac{1}{2}left(e^{-2 x} arctan e^{x}+e^{-x}+arctan e^{x}right)$.

Integrate[ArcTan[E^x]/E^(2 x), x, 
  GeneratedParameters -> C] // FullSimplify
D[Integrate[ArcTan[E^x]/E^(2 x), 
    x] - (-(1/2) (E^(-2 x) ArcTan[E^x] + E^-x + ArcTan[E^x])), 
  x] // FullSimplify

How can I further simplify the above indefinite integral result into the form of reference answer?

Integrate[ArcTan[E^x]/E^(2 x), x]//FunctionExpand //PowerExpand //Expand