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

Integrate[Log[(a + x)/(-a + x)]/x^2, x] ==
(2*Log[x])/a - Log[-a + x]/a - Log[a + x]/a - Log[(a + x)/(-a + x)]/x 

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

                                          a + x
                                      Log[------]
2 Log[x]   Log[-a + x]   Log[a + x]       -a + x
-------- - ----------- - ---------- - -----------
   a            a            a             x
Time to compute: 0.02 second
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