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

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

                  2
          Sin[a x]
Integrate[---------, x] == 
          Sqrt[a x]

(2 Sqrt[a] x - Sqrt[Pi] Sqrt[x] 
 
              2 Sqrt[a] Sqrt[x]
     FresnelC[-----------------]) / 
                  Sqrt[Pi]
 
  (2 Sqrt[a] Sqrt[a x])
Time to compute: 0.03 second
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