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(Sqrt[2*Pi]*Sqrt[x]*FresnelS[Sqrt[a]*Sqrt[2/Pi]*Sqrt[x]])/(Sqrt[a]*Sqrt[a*x])


Integrate[Sin[a*x]/Sqrt[a*x], x] ==
(Sqrt[2*Pi]*Sqrt[x]*FresnelS[Sqrt[a]*Sqrt[2/Pi]* Sqrt[x]])/(Sqrt[a]*Sqrt[a*x])



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

                                          2
(Sqrt[2 Pi] Sqrt[x] FresnelS[Sqrt[a] Sqrt[--] 
                                          Pi
 
      Sqrt[x]]) / (Sqrt[a] Sqrt[a x])

Time to compute: 0.04 second

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