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Integrate[(-r + x)^4/E^(a*x^2), x] ==
(2*Sqrt[a]*(8*r + 8*a*r^3 - 3*x - 12*a*r^2*x + 8*a*r*x^2 - 2*a*x^3) + E^(a*x^2)*Sqrt[Pi]* (3 + 12*a*r^2 + 4*a^2*r^4)*Erf[Sqrt[a]*x])/ (8*a^(5/2)*E^(a*x^2))



                  4
          (-r + x)
Integrate[---------, x] == 
                2
             a x
            E

                       3               2
(2 Sqrt[a] (8 r + 8 a r  - 3 x - 12 a r  x + 
 
              2        3
       8 a r x  - 2 a x ) + 
 
        2
     a x                      2      2  4
    E     Sqrt[Pi] (3 + 12 a r  + 4 a  r ) 
 
                                   2
                           5/2  a x
     Erf[Sqrt[a] x]) / (8 a    E    )

Time to compute: 0.11 second

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