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(E^(a*x)*(-5040 + 5040*a*x - 2520*a^2*x^2 + 840*a^3*x^3 - 210*a^4*x^4 + 42*a^5*x^5 - 7*a^6*x^6 + a^7*x^7))/a^8

Integrate[E^(a*x)*x^7, x] ==
(E^(a*x)*(-5040 + 5040*a*x - 2520*a^2*x^2 + 840*a^3*x^3 - 210*a^4*x^4 + 42*a^5*x^5 - 7*a^6*x^6 + a^7*x^7))/a^8 

           a x  7
Integrate[E    x , x] == 

  a x                           2  2        3  3
(E    (-5040 + 5040 a x - 2520 a  x  + 840 a  x  - 
 
           4  4       5  5      6  6    7  7      8
      210 a  x  + 42 a  x  - 7 a  x  + a  x )) / a
Time to compute: 0.02 second
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