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-2*EllipticE[(Pi - 2*x)/4, 2]

Integrate[Sqrt[Sin[x]], x] ==
-2*EllipticE[(Pi - 2*x)/4, 2] 

Integrate[Sqrt[Sin[x]], x] == 

             Pi - 2 x
-2 EllipticE[--------, 2]
                4
Time to compute: 0.99 second
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