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-(E^(x^2/2)*(1 + Sqrt[2]*Pi*DawsonF[x/Sqrt[2]]))

Integrate[-(E^(x^2/2)*(Pi + x)), x] ==
-(E^(x^2/2)*(1 + Sqrt[2]*Pi*DawsonF[x/Sqrt[2]])) 

              2
             x /2
Integrate[-(E     (Pi + x)), x] == 

    2
   x /2                            x
-(E     (1 + Sqrt[2] Pi DawsonF[-------]))
                                Sqrt[2]
Time to compute: 0.01 second
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