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-x + (b/a + x)*Log[b + a*x]

Integrate[Log[b + a*x], x] ==
-x + (b/a + x)*Log[b + a*x] 

Integrate[Log[b + a x], x] == 

      b
-x + (- + x) Log[b + a x]
      a
Time to compute: < 0.01 second
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