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Integrate[(Pi + ArcCos[x])^2/x, x] ==
(-I)*Pi*ArcCos[x]^2 - (I/3)*ArcCos[x]^3 + 2*Pi*ArcCos[x]*Log[1 + E^((2*I)*ArcCos[x])] + ArcCos[x]^2*Log[1 + E^((2*I)*ArcCos[x])] + Pi^2*Log[x] - I*(Pi + ArcCos[x])* PolyLog[2, -E^((2*I)*ArcCos[x])] + PolyLog[3, -E^((2*I)*ArcCos[x])]/2



                          2
          (Pi + ArcCos[x])
Integrate[-----------------, x] == 
                  x

               2   I          3
-I Pi ArcCos[x]  - - ArcCos[x]  + 
                   3
 
                          (2 I) ArcCos[x]
  2 Pi ArcCos[x] Log[1 + E               ] + 
 
           2          (2 I) ArcCos[x]      2
  ArcCos[x]  Log[1 + E               ] + Pi  Log[x] - 
 
                                  (2 I) ArcCos[x]
  I (Pi + ArcCos[x]) PolyLog[2, -E               ] + 
 
               (2 I) ArcCos[x]
  PolyLog[3, -E               ]
  -----------------------------
                2

Time to compute: 0.10 second

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