MathGroup Archive 2001

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Integrate[Sqrt[Tan[x]], {x, 0, 1}]


Or even more symmetric:

(Pi - ArcTan[Sqrt[2*Tan[1]]/(Tan[1] - 1)] - 
   ArcTanh[Sqrt[2*Tan[1]]/(Tan[1] + 1)])/Sqrt[2]

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