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E^(c + b*x + a*x^2)/(2*a) - (b*E^(-b^2/(4*a) + c)*Sqrt[Pi]*Erfi[(b + 2*a*x)/(2*Sqrt[a])])/(4*a^(3/2))


Integrate[E^(c + b*x + a*x^2)*x, x] ==
E^(c + b*x + a*x^2)/(2*a) - (b*E^(-b^2/(4*a) + c)*Sqrt[Pi]* Erfi[(b + 2*a*x)/(2*Sqrt[a])])/(4*a^(3/2))



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

              2
 c + b x + a x
E
--------------- - 
      2 a
 
        2
      -b /(4 a) + c               b + 2 a x
   b E              Sqrt[Pi] Erfi[---------]
                                  2 Sqrt[a]
   -----------------------------------------
                       3/2
                    4 a

Time to compute: 0.10 second

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