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


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



          Log[1 + x]
Integrate[----------, x] == 
            1 - x

          -1 - x                           1 + x
-(Log[1 + ------] Log[1 + x]) - PolyLog[2, -----]
            2                                2

Time to compute: 0.01 second

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