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-(x*(3 + 2*a*x^2))/(4*a^2*E^(a*x^2)) + (3*Sqrt[Pi]*Erf[Sqrt[a]*x])/(8*a^(5/2))

Integrate[x^4/E^(a*x^2), x] ==
-(x*(3 + 2*a*x^2))/(4*a^2*E^(a*x^2)) + (3*Sqrt[Pi]*Erf[Sqrt[a]*x])/(8*a^(5/2)) 

            4
           x
Integrate[-----, x] == 
              2
           a x
          E

              2
-(x (3 + 2 a x ))   3 Sqrt[Pi] Erf[Sqrt[a] x]
----------------- + -------------------------
            2                   5/2
      2  a x                 8 a
   4 a  E
Time to compute: 0.05 second
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