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(Log[1 + (2*x)/3]*Log[a*x] + PolyLog[2, (-2*x)/3])/2

Integrate[Log[a*x]/(3 + 2*x), x] ==
(Log[1 + (2*x)/3]*Log[a*x] + PolyLog[2, (-2*x)/3])/2 

          Log[a x]
Integrate[--------, x] == 
          3 + 2 x

        2 x                        -2 x
Log[1 + ---] Log[a x] + PolyLog[2, ----]
         3                          3
----------------------------------------
                   2
Time to compute: 0.02 second
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