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-(ExpIntegralEi[a*x]/a) + (E^(a*x)*Log[x])/a

Integrate[E^(a*x)*Log[x], x] ==
-(ExpIntegralEi[a*x]/a) + (E^(a*x)*Log[x])/a 

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

                         a x
  ExpIntegralEi[a x]    E    Log[x]
-(------------------) + -----------
          a                  a
Time to compute: 0.01 second
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