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(2*Sqrt[-x]*x)/3 - 2*EllipticE[(Pi - 2*x)/4, 2]

Integrate[Sqrt[-x] + Sqrt[Sin[x]], x] ==
(2*Sqrt[-x]*x)/3 - 2*EllipticE[(Pi - 2*x)/4, 2] 

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

2 Sqrt[-x] x               Pi - 2 x
------------ - 2 EllipticE[--------, 2]
     3                        4
Time to compute: 1.14 second
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