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-(x^(1 + m)*ExpIntegralE[-m, -(a*x)])

Integrate[E^(a*x)*x^m, x] ==
-(x^(1 + m)*ExpIntegralE[-m, -(a*x)]) 

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

   1 + m
-(x      ExpIntegralE[-m, -(a x)])
Time to compute: 0.02 second
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