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(2*x*(Sqrt[a]*Sqrt[2*Pi]*Sqrt[x]*FresnelC[Sqrt[a]*Sqrt[2/Pi]*Sqrt[x]] - Sin[a*x]))/Sqrt[x^3]

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

          Sin[a x]
Integrate[--------, x] == 
                3
          Sqrt[x ]

(2 x (Sqrt[a] Sqrt[2 Pi] Sqrt[x] 
 
                             2
       FresnelC[Sqrt[a] Sqrt[--] Sqrt[x]] - Sin[a x]))
                             Pi
 
            3
    / Sqrt[x ]
Time to compute: 0.11 second
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