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


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



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

                                     a + x
a Log[-a + x] + a Log[a + x] + x Log[------]
                                     -a + x

Time to compute: < 0.01 second

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