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 Log

 http://functions.wolfram.com/01.04.21.0017.01

 Input Form

 Integrate[(Log[z]^2 Log[1 - z])/(1 - z), z] == (1/12) (-Log[-1 + 1/z]^4 - 6 Log[-1 + 1/z]^2 Log[1 - z]^2 - Log[1 - z]^4 + 4 Log[-1 + 1/z]^3 (Log[1 - z] + Log[1/z]) - 6 Log[1 - z]^2 Log[z]^2 + 4 Log[1 - z]^2 Log[z] (-2 Log[1 - z] + 3 Log[z]) + 4 Log[-1 + 1/z] Log[1 - z]^2 (Log[1 - z] + 3 Log[z]) - 12 Log[1 - z] (-2 Log[-1 + 1/z] + Log[1 - z] - 2 Log[z]) PolyLog[2, 1 - z] + 12 Log[-1 + 1/z]^2 PolyLog[2, (-1 + z)/z] - 12 (Log[-1 + 1/z] - Log[1 - z])^2 PolyLog[2, z] - 24 (Log[-1 + 1/z] + Log[z]) PolyLog[3, 1 - z] - 24 Log[-1 + 1/z] PolyLog[3, (-1 + z)/z] + 24 (-Log[-1 + 1/z] + Log[1 - z]) PolyLog[3, z] + 24 (PolyLog[4, 1 - z] + PolyLog[4, (-1 + z)/z] - PolyLog[4, z]))

 Standard Form

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 MathML Form

 log 2 ( z ) log ( 1 - z ) 1 - z z 1 12 ( - log 4 ( 1 z - 1 ) + 4 ( log ( 1 - z ) + log ( 1 z ) ) log 3 ( 1 z - 1 ) - 6 log 2 ( 1 - z ) log 2 ( 1 z - 1 ) + 12 Li PolyLog 2 ( z - 1 z ) log 2 ( 1 z - 1 ) + 4 log 2 ( 1 - z ) ( log ( 1 - z ) + 3 log ( z ) ) log ( 1 z - 1 ) - 24 Li PolyLog 3 ( z - 1 z ) log ( 1 z - 1 ) - log 4 ( 1 - z ) - 6 log 2 ( 1 - z ) log 2 ( z ) + 4 log 2 ( 1 - z ) log ( z ) ( 3 log ( z ) - 2 log ( 1 - z ) ) - 12 log ( 1 - z ) ( - 2 log ( 1 z - 1 ) + log ( 1 - z ) - 2 log ( z ) ) Li PolyLog 2 ( 1 - z ) - 12 ( log ( 1 z - 1 ) - log ( 1 - z ) ) 2 Li PolyLog 2 ( z ) - 24 ( log ( 1 z - 1 ) + log ( z ) ) Li PolyLog 3 ( 1 - z ) + 24 ( log ( 1 - z ) - log ( 1 z - 1 ) ) Li PolyLog 3 ( z ) + 24 ( Li PolyLog 4 ( 1 - z ) + Li PolyLog 4 ( z - 1 z ) - Li PolyLog 4 ( z ) ) ) z z 2 1 -1 z 1 -1 z -1 1 12 -1 1 z -1 -1 4 4 1 -1 z 1 z -1 1 z -1 -1 3 -1 6 1 -1 z 2 1 z -1 -1 2 12 PolyLog 2 z -1 z -1 1 z -1 -1 2 4 1 -1 z 2 1 -1 z 3 z 1 z -1 -1 -1 24 PolyLog 3 z -1 z -1 1 z -1 -1 -1 1 -1 z 4 -1 6 1 -1 z 2 z 2 4 1 -1 z 2 z 3 z -1 2 1 -1 z -1 12 1 -1 z -2 1 z -1 -1 1 -1 z -1 2 z PolyLog 2 1 -1 z -1 12 1 z -1 -1 -1 1 -1 z 2 PolyLog 2 z -1 24 1 z -1 -1 z PolyLog 3 1 -1 z 24 1 -1 z -1 1 z -1 -1 PolyLog 3 z 24 PolyLog 4 1 -1 z PolyLog 4 z -1 z -1 -1 PolyLog 4 z [/itex]

 Rule Form

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 Date Added to functions.wolfram.com (modification date)

 2001-10-29