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(Gamma[1 + n, -Log[a*x]]*Log[a*x]^n)/(a*(-Log[a*x])^n)


Integrate[Log[a*x]^n, x] ==
(Gamma[1 + n, -Log[a*x]]*Log[a*x]^n)/(a*(-Log[a*x])^n)



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

                                n
Gamma[1 + n, -Log[a x]] Log[a x]
---------------------------------
                      n
         a (-Log[a x])

Time to compute: 0.04 second

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