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Integrate[Sin[a + b*x + c*x^2], x] ==
(Sqrt[Pi/2]*(Cos[a - b^2/(4*c)]* FresnelS[(b + 2*c*x)/(Sqrt[c]*Sqrt[2*Pi])] + FresnelC[(b + 2*c*x)/(Sqrt[c]*Sqrt[2*Pi])]* Sin[a - b^2/(4*c)]))/Sqrt[c]



                           2
Integrate[Sin[a + b x + c x ], x] == 

                    2
      Pi           b
(Sqrt[--] (Cos[a - ---] 
      2            4 c
 
                    b + 2 c x
       FresnelS[------------------] + 
                Sqrt[c] Sqrt[2 Pi]
 
                                            2
                   b + 2 c x               b
      FresnelC[------------------] Sin[a - ---])) / 
               Sqrt[c] Sqrt[2 Pi]          4 c
 
  Sqrt[c]

Time to compute: 0.14 second

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