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(Sqrt[a]*Sqrt[2*Pi]*x^(3/2)*FresnelS[Sqrt[a]*Sqrt[2/Pi]*Sqrt[x]])/(a*x)^(3/2)


Integrate[Sin[a*x]/Sqrt[a*x], x] ==
(Sqrt[a]*Sqrt[2*Pi]*x^(3/2)* FresnelS[Sqrt[a]*Sqrt[2/Pi]*Sqrt[x]])/(a*x)^(3/2)



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

                     3/2
(Sqrt[a] Sqrt[2 Pi] x    
 
                          2                    3/2
    FresnelS[Sqrt[a] Sqrt[--] Sqrt[x]]) / (a x)
                          Pi

Time to compute: 0.04 second

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