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

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

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

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