html, body, form { margin: 0; padding: 0; width: 100%; } #calculate { position: relative; width: 177px; height: 110px; background: transparent url(/images/alphabox/embed_functions_inside.gif) no-repeat scroll 0 0; } #i { position: relative; left: 18px; top: 44px; width: 133px; border: 0 none; outline: 0; font-size: 11px; } #eq { width: 9px; height: 10px; background: transparent; position: absolute; top: 47px; right: 18px; cursor: pointer; }

 Log

 http://functions.wolfram.com/01.04.21.0010.01

 Input Form

 Integrate[Log[(a + b z)/(c + d z)]^2/z, z] == Log[-((b z)/a)] Log[a/b + z]^2 + Log[-((d z)/c)] Log[c/d + z]^2 + Log[z] (-Log[a/b + z] + Log[c/d + z] + Log[(a + b z)/(c + d z)])^2 + 2 (-Log[a/b + z] + Log[c/d + z] + Log[(a + b z)/(c + d z)]) (Log[z] (Log[a/b + z] - Log[c/d + z] - Log[1 + (b z)/a] + Log[1 + (d z)/c]) - PolyLog[2, -((b z)/a)] + PolyLog[2, -((d z)/c)]) + 2 Log[a/b + z] PolyLog[2, 1 + (b z)/a] + 2 Log[c/d + z] PolyLog[2, 1 + (d z)/c] - 2 PolyLog[3, 1 + (b z)/a] - 2 (Log[-((b z)/a)] Log[a/b + z] Log[c/d + z] + (1/2) Log[(a (c + d z))/(c (a + b z))]^2 (Log[-((b z)/a)] + Log[((-b) c + a d)/(d (a + b z))] - Log[(b c z - a d z)/(a c + b c z)]) + (-Log[-((b z)/a)] + Log[-((d z)/c)]) Log[(a (c + d z))/(c (a + b z))] Log[1 + (d z)/c] + (1/2) (Log[-((b z)/a)] - Log[-((d z)/c)]) Log[1 + (d z)/c] (-2 Log[a/b + z] + Log[1 + (d z)/c]) + (Log[c/d + z] - Log[(a (c + d z))/(c (a + b z))]) PolyLog[2, 1 + (b z)/a] + Log[(a (c + d z))/(c (a + b z))] (-PolyLog[2, (a (c + d z))/(c (a + b z))] + PolyLog[2, (b (c + d z))/(d (a + b z))]) + (Log[a/b + z] + Log[(a (c + d z))/(c (a + b z))]) PolyLog[2, 1 + (d z)/c] - PolyLog[3, 1 + (b z)/a] + PolyLog[3, (a (c + d z))/(c (a + b z))] - PolyLog[3, (b (c + d z))/(d (a + b z))] - PolyLog[3, 1 + (d z)/c]) - 2 PolyLog[3, 1 + (d z)/c]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[FractionBox[SuperscriptBox[RowBox[List["Log", "[", FractionBox[RowBox[List["a", "+", RowBox[List["b", " ", "z"]]]], RowBox[List["c", "+", RowBox[List["d", " ", "z"]]]]], "]"]], "2"], "z"], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[RowBox[List[RowBox[List["Log", "[", RowBox[List["-", FractionBox[RowBox[List["b", " ", "z"]], "a"]]], "]"]], " ", SuperscriptBox[RowBox[List["Log", "[", RowBox[List[FractionBox["a", "b"], "+", "z"]], "]"]], "2"]]], "+", RowBox[List[RowBox[List["Log", "[", RowBox[List["-", FractionBox[RowBox[List["d", " ", "z"]], "c"]]], "]"]], " ", SuperscriptBox[RowBox[List["Log", "[", RowBox[List[FractionBox["c", "d"], "+", "z"]], "]"]], "2"]]], "+", RowBox[List[RowBox[List["Log", "[", "z", "]"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", RowBox[List["Log", "[", RowBox[List[FractionBox["a", "b"], "+", "z"]], "]"]]]], "+", RowBox[List["Log", "[", RowBox[List[FractionBox["c", "d"], "+", "z"]], "]"]], "+", RowBox[List["Log", "[", FractionBox[RowBox[List["a", "+", RowBox[List["b", " ", "z"]]]], RowBox[List["c", "+", RowBox[List["d", " ", "z"]]]]], "]"]]]], ")"]], "2"]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["-", RowBox[List["Log", "[", RowBox[List[FractionBox["a", "b"], "+", "z"]], "]"]]]], "+", RowBox[List["Log", "[", RowBox[List[FractionBox["c", "d"], "+", "z"]], "]"]], "+", RowBox[List["Log", "[", FractionBox[RowBox[List["a", "+", RowBox[List["b", " ", "z"]]]], RowBox[List["c", "+", RowBox[List["d", " ", "z"]]]]], "]"]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["Log", "[", "z", "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["Log", "[", RowBox[List[FractionBox["a", "b"], "+", "z"]], "]"]], "-", RowBox[List["Log", "[", RowBox[List[FractionBox["c", "d"], "+", "z"]], "]"]], "-", RowBox[List["Log", "[", RowBox[List["1", "+", FractionBox[RowBox[List["b", " ", "z"]], "a"]]], "]"]], "+", RowBox[List["Log", "[", RowBox[List["1", "+", FractionBox[RowBox[List["d", " ", "z"]], "c"]]], "]"]]]], ")"]]]], "-", RowBox[List["PolyLog", "[", RowBox[List["2", ",", RowBox[List["-", FractionBox[RowBox[List["b", " ", "z"]], "a"]]]]], "]"]], "+", RowBox[List["PolyLog", "[", RowBox[List["2", ",", RowBox[List["-", FractionBox[RowBox[List["d", " ", "z"]], "c"]]]]], "]"]]]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["Log", "[", RowBox[List[FractionBox["a", "b"], "+", "z"]], "]"]], " ", RowBox[List["PolyLog", "[", RowBox[List["2", ",", RowBox[List["1", "+", FractionBox[RowBox[List["b", " ", "z"]], "a"]]]]], "]"]]]], "+", RowBox[List["2", " ", RowBox[List["Log", "[", RowBox[List[FractionBox["c", "d"], "+", "z"]], "]"]], " ", RowBox[List["PolyLog", "[", RowBox[List["2", ",", RowBox[List["1", "+", FractionBox[RowBox[List["d", " ", "z"]], "c"]]]]], "]"]]]], "-", RowBox[List["2", " ", RowBox[List["PolyLog", "[", RowBox[List["3", ",", RowBox[List["1", "+", FractionBox[RowBox[List["b", " ", "z"]], "a"]]]]], "]"]]]], "-", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["Log", "[", RowBox[List["-", FractionBox[RowBox[List["b", " ", "z"]], "a"]]], "]"]], " ", RowBox[List["Log", "[", RowBox[List[FractionBox["a", "b"], "+", "z"]], "]"]], " ", RowBox[List["Log", "[", RowBox[List[FractionBox["c", "d"], "+", "z"]], "]"]]]], "+", RowBox[List[FractionBox["1", "2"], " ", SuperscriptBox[RowBox[List["Log", "[", FractionBox[RowBox[List["a", " ", RowBox[List["(", RowBox[List["c", "+", RowBox[List["d", " ", "z"]]]], ")"]]]], RowBox[List["c", " ", RowBox[List["(", RowBox[List["a", "+", RowBox[List["b", " ", "z"]]]], ")"]]]]], "]"]], "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["Log", "[", RowBox[List["-", FractionBox[RowBox[List["b", " ", "z"]], "a"]]], "]"]], "+", RowBox[List["Log", "[", FractionBox[RowBox[List[RowBox[List[RowBox[List["-", "b"]], " ", "c"]], "+", RowBox[List["a", " ", "d"]]]], RowBox[List["d", " ", RowBox[List["(", RowBox[List["a", "+", RowBox[List["b", " ", "z"]]]], ")"]]]]], "]"]], "-", RowBox[List["Log", "[", FractionBox[RowBox[List[RowBox[List["b", " ", "c", " ", "z"]], "-", RowBox[List["a", " ", "d", " ", "z"]]]], RowBox[List[RowBox[List["a", " ", "c"]], "+", RowBox[List["b", " ", "c", " ", "z"]]]]], "]"]]]], ")"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", RowBox[List["Log", "[", RowBox[List["-", FractionBox[RowBox[List["b", " ", "z"]], "a"]]], "]"]]]], "+", RowBox[List["Log", "[", RowBox[List["-", FractionBox[RowBox[List["d", " ", "z"]], "c"]]], "]"]]]], ")"]], " ", RowBox[List["Log", "[", FractionBox[RowBox[List["a", " ", RowBox[List["(", RowBox[List["c", "+", RowBox[List["d", " ", "z"]]]], ")"]]]], RowBox[List["c", " ", RowBox[List["(", RowBox[List["a", "+", RowBox[List["b", " ", "z"]]]], ")"]]]]], "]"]], " ", RowBox[List["Log", "[", RowBox[List["1", "+", FractionBox[RowBox[List["d", " ", "z"]], "c"]]], "]"]]]], "+", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["Log", "[", RowBox[List["-", FractionBox[RowBox[List["b", " ", "z"]], "a"]]], "]"]], "-", RowBox[List["Log", "[", RowBox[List["-", FractionBox[RowBox[List["d", " ", "z"]], "c"]]], "]"]]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List["1", "+", FractionBox[RowBox[List["d", " ", "z"]], "c"]]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", RowBox[List["Log", "[", RowBox[List[FractionBox["a", "b"], "+", "z"]], "]"]]]], "+", RowBox[List["Log", "[", RowBox[List["1", "+", FractionBox[RowBox[List["d", " ", "z"]], "c"]]], "]"]]]], ")"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["Log", "[", RowBox[List[FractionBox["c", "d"], "+", "z"]], "]"]], "-", RowBox[List["Log", "[", FractionBox[RowBox[List["a", " ", RowBox[List["(", RowBox[List["c", "+", RowBox[List["d", " ", "z"]]]], ")"]]]], RowBox[List["c", " ", RowBox[List["(", RowBox[List["a", "+", RowBox[List["b", " ", "z"]]]], ")"]]]]], "]"]]]], ")"]], " ", RowBox[List["PolyLog", "[", RowBox[List["2", ",", RowBox[List["1", "+", FractionBox[RowBox[List["b", " ", "z"]], "a"]]]]], "]"]]]], "+", RowBox[List[RowBox[List["Log", "[", FractionBox[RowBox[List["a", " ", RowBox[List["(", RowBox[List["c", "+", RowBox[List["d", " ", "z"]]]], ")"]]]], RowBox[List["c", " ", RowBox[List["(", RowBox[List["a", "+", RowBox[List["b", " ", "z"]]]], ")"]]]]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", RowBox[List["PolyLog", "[", RowBox[List["2", ",", FractionBox[RowBox[List["a", " ", RowBox[List["(", RowBox[List["c", "+", RowBox[List["d", " ", "z"]]]], ")"]]]], RowBox[List["c", " ", RowBox[List["(", RowBox[List["a", "+", RowBox[List["b", " ", "z"]]]], ")"]]]]]]], "]"]]]], "+", RowBox[List["PolyLog", "[", RowBox[List["2", ",", FractionBox[RowBox[List["b", " ", RowBox[List["(", RowBox[List["c", "+", RowBox[List["d", " ", "z"]]]], ")"]]]], RowBox[List["d", " ", RowBox[List["(", RowBox[List["a", "+", RowBox[List["b", " ", "z"]]]], ")"]]]]]]], "]"]]]], ")"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["Log", "[", RowBox[List[FractionBox["a", "b"], "+", "z"]], "]"]], "+", RowBox[List["Log", "[", FractionBox[RowBox[List["a", " ", RowBox[List["(", RowBox[List["c", "+", RowBox[List["d", " ", "z"]]]], ")"]]]], RowBox[List["c", " ", RowBox[List["(", RowBox[List["a", "+", RowBox[List["b", " ", "z"]]]], ")"]]]]], "]"]]]], ")"]], " ", RowBox[List["PolyLog", "[", RowBox[List["2", ",", RowBox[List["1", "+", FractionBox[RowBox[List["d", " ", "z"]], "c"]]]]], "]"]]]], "-", RowBox[List["PolyLog", "[", RowBox[List["3", ",", RowBox[List["1", "+", FractionBox[RowBox[List["b", " ", "z"]], "a"]]]]], "]"]], "+", RowBox[List["PolyLog", "[", RowBox[List["3", ",", FractionBox[RowBox[List["a", " ", RowBox[List["(", RowBox[List["c", "+", RowBox[List["d", " ", "z"]]]], ")"]]]], RowBox[List["c", " ", RowBox[List["(", RowBox[List["a", "+", RowBox[List["b", " ", "z"]]]], ")"]]]]]]], "]"]], "-", RowBox[List["PolyLog", "[", RowBox[List["3", ",", FractionBox[RowBox[List["b", " ", RowBox[List["(", RowBox[List["c", "+", RowBox[List["d", " ", "z"]]]], ")"]]]], RowBox[List["d", " ", RowBox[List["(", RowBox[List["a", "+", RowBox[List["b", " ", "z"]]]], ")"]]]]]]], "]"]], "-", RowBox[List["PolyLog", "[", RowBox[List["3", ",", RowBox[List["1", "+", FractionBox[RowBox[List["d", " ", "z"]], "c"]]]]], "]"]]]], ")"]]]], "-", RowBox[List["2", " ", RowBox[List["PolyLog", "[", RowBox[List["3", ",", RowBox[List["1", "+", FractionBox[RowBox[List["d", " ", "z"]], "c"]]]]], "]"]]]]]]]]]]

 MathML Form

 1 z log 2 ( a + b z c + d z ) z log ( - b z a ) log 2 ( a b + z ) + 2 Li PolyLog 2 ( b z a + 1 ) log ( a b + z ) + log ( - d z c ) log 2 ( c d + z ) + log ( z ) ( - log ( a b + z ) + log ( c d + z ) + log ( a + b z c + d z ) ) 2 + 2 log ( c d + z ) Li PolyLog 2 ( d z c + 1 ) + 2 ( - log ( a b + z ) + log ( c d + z ) + log ( a + b z c + d z ) ) ( ( - log ( b z a + 1 ) + log ( d z c + 1 ) + log ( a b + z ) - log ( c d + z ) ) log ( z ) - Li PolyLog 2 ( - b z a ) + Li PolyLog 2 ( - d z c ) ) - 2 Li PolyLog 3 ( b z a + 1 ) - 2 ( 1 2 ( log ( - b z a ) + log ( a d - b c d ( a + b z ) ) - log ( b c z - a d z a c + b z c ) ) log 2 ( a ( c + d z ) c ( a + b z ) ) + log ( d z c + 1 ) ( log ( - d z c ) - log ( - b z a ) ) log ( a ( c + d z ) c ( a + b z ) ) + ( Li PolyLog 2 ( b ( c + d z ) d ( a + b z ) ) - Li PolyLog 2 ( a ( c + d z ) c ( a + b z ) ) ) log ( a ( c + d z ) c ( a + b z ) ) + 1 2 log ( d z c + 1 ) ( log ( d z c + 1 ) - 2 log ( a b + z ) ) ( log ( - b z a ) - log ( - d z c ) ) + log ( - b z a ) log ( a b + z ) log ( c d + z ) + ( log ( c d + z ) - log ( a ( c + d z ) c ( a + b z ) ) ) Li PolyLog 2 ( b z a + 1 ) + ( log ( a b + z ) + log ( a ( c + d z ) c ( a + b z ) ) ) Li PolyLog 2 ( d z c + 1 ) - Li PolyLog 3 ( b z a + 1 ) - Li PolyLog 3 ( d z c + 1 ) + Li PolyLog 3 ( a ( c + d z ) c ( a + b z ) ) - Li PolyLog 3 ( b ( c + d z ) d ( a + b z ) ) ) - 2 Li PolyLog 3 ( d z c + 1 ) z 1 z -1 a b z c d z -1 2 -1 b z a -1 a b -1 z 2 2 PolyLog 2 b z a -1 1 a b -1 z -1 d z c -1 c d -1 z 2 z -1 a b -1 z c d -1 z a b z c d z -1 2 2 c d -1 z PolyLog 2 d z c -1 1 2 -1 a b -1 z c d -1 z a b z c d z -1 -1 b z a -1 1 d z c -1 1 a b -1 z -1 c d -1 z z -1 PolyLog 2 -1 b z a -1 PolyLog 2 -1 d z c -1 -1 2 PolyLog 3 b z a -1 1 -1 2 1 2 -1 b z a -1 a d -1 b c d a b z -1 -1 b c z -1 a d z a c b z c -1 a c d z c a b z -1 2 d z c -1 1 -1 d z c -1 -1 -1 b z a -1 a c d z c a b z -1 PolyLog 2 b c d z d a b z -1 -1 PolyLog 2 a c d z c a b z -1 a c d z c a b z -1 1 2 d z c -1 1 d z c -1 1 -1 2 a b -1 z -1 b z a -1 -1 -1 d z c -1 -1 b z a -1 a b -1 z c d -1 z c d -1 z -1 a c d z c a b z -1 PolyLog 2 b z a -1 1 a b -1 z a c d z c a b z -1 PolyLog 2 d z c -1 1 -1 PolyLog 3 b z a -1 1 -1 PolyLog 3 d z c -1 1 PolyLog 3 a c d z c a b z -1 -1 PolyLog 3 b c d z d a b z -1 -1 2 PolyLog 3 d z c -1 1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[FractionBox[SuperscriptBox[RowBox[List["Log", "[", FractionBox[RowBox[List["a_", "+", RowBox[List["b_", " ", "z_"]]]], RowBox[List["c_", "+", RowBox[List["d_", " ", "z_"]]]]], "]"]], "2"], "z_"], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["Log", "[", RowBox[List["-", FractionBox[RowBox[List["b", " ", "z"]], "a"]]], "]"]], " ", SuperscriptBox[RowBox[List["Log", "[", RowBox[List[FractionBox["a", "b"], "+", "z"]], "]"]], "2"]]], "+", RowBox[List[RowBox[List["Log", "[", RowBox[List["-", FractionBox[RowBox[List["d", " ", "z"]], "c"]]], "]"]], " ", SuperscriptBox[RowBox[List["Log", "[", RowBox[List[FractionBox["c", "d"], "+", "z"]], "]"]], "2"]]], "+", RowBox[List[RowBox[List["Log", "[", "z", "]"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", RowBox[List["Log", "[", RowBox[List[FractionBox["a", "b"], "+", "z"]], "]"]]]], "+", RowBox[List["Log", "[", RowBox[List[FractionBox["c", "d"], "+", "z"]], "]"]], "+", RowBox[List["Log", "[", FractionBox[RowBox[List["a", "+", RowBox[List["b", " ", "z"]]]], RowBox[List["c", "+", RowBox[List["d", " ", "z"]]]]], "]"]]]], ")"]], "2"]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["-", RowBox[List["Log", "[", RowBox[List[FractionBox["a", "b"], "+", "z"]], "]"]]]], "+", RowBox[List["Log", "[", RowBox[List[FractionBox["c", "d"], "+", "z"]], "]"]], "+", RowBox[List["Log", "[", FractionBox[RowBox[List["a", "+", RowBox[List["b", " ", "z"]]]], RowBox[List["c", "+", RowBox[List["d", " ", "z"]]]]], "]"]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["Log", "[", "z", "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["Log", "[", RowBox[List[FractionBox["a", "b"], "+", "z"]], "]"]], "-", RowBox[List["Log", "[", RowBox[List[FractionBox["c", "d"], "+", "z"]], "]"]], "-", RowBox[List["Log", "[", RowBox[List["1", "+", FractionBox[RowBox[List["b", " ", "z"]], "a"]]], "]"]], "+", RowBox[List["Log", "[", RowBox[List["1", "+", FractionBox[RowBox[List["d", " ", "z"]], "c"]]], "]"]]]], ")"]]]], "-", RowBox[List["PolyLog", "[", RowBox[List["2", ",", RowBox[List["-", FractionBox[RowBox[List["b", " ", "z"]], "a"]]]]], "]"]], "+", RowBox[List["PolyLog", "[", RowBox[List["2", ",", RowBox[List["-", FractionBox[RowBox[List["d", " ", "z"]], "c"]]]]], "]"]]]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["Log", "[", RowBox[List[FractionBox["a", "b"], "+", "z"]], "]"]], " ", RowBox[List["PolyLog", "[", RowBox[List["2", ",", RowBox[List["1", "+", FractionBox[RowBox[List["b", " ", "z"]], "a"]]]]], "]"]]]], "+", RowBox[List["2", " ", RowBox[List["Log", "[", RowBox[List[FractionBox["c", "d"], "+", "z"]], "]"]], " ", RowBox[List["PolyLog", "[", RowBox[List["2", ",", RowBox[List["1", "+", FractionBox[RowBox[List["d", " ", "z"]], "c"]]]]], "]"]]]], "-", RowBox[List["2", " ", RowBox[List["PolyLog", "[", RowBox[List["3", ",", RowBox[List["1", "+", FractionBox[RowBox[List["b", " ", "z"]], "a"]]]]], "]"]]]], "-", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["Log", "[", RowBox[List["-", FractionBox[RowBox[List["b", " ", "z"]], "a"]]], "]"]], " ", RowBox[List["Log", "[", RowBox[List[FractionBox["a", "b"], "+", "z"]], "]"]], " ", RowBox[List["Log", "[", RowBox[List[FractionBox["c", "d"], "+", "z"]], "]"]]]], "+", RowBox[List[FractionBox["1", "2"], " ", SuperscriptBox[RowBox[List["Log", "[", FractionBox[RowBox[List["a", " ", RowBox[List["(", RowBox[List["c", "+", RowBox[List["d", " ", "z"]]]], ")"]]]], RowBox[List["c", " ", RowBox[List["(", RowBox[List["a", "+", RowBox[List["b", " ", "z"]]]], ")"]]]]], "]"]], "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["Log", "[", RowBox[List["-", FractionBox[RowBox[List["b", " ", "z"]], "a"]]], "]"]], "+", RowBox[List["Log", "[", FractionBox[RowBox[List[RowBox[List[RowBox[List["-", "b"]], " ", "c"]], "+", RowBox[List["a", " ", "d"]]]], RowBox[List["d", " ", RowBox[List["(", RowBox[List["a", "+", RowBox[List["b", " ", "z"]]]], ")"]]]]], "]"]], "-", RowBox[List["Log", "[", FractionBox[RowBox[List[RowBox[List["b", " ", "c", " ", "z"]], "-", RowBox[List["a", " ", "d", " ", "z"]]]], RowBox[List[RowBox[List["a", " ", "c"]], "+", RowBox[List["b", " ", "c", " ", "z"]]]]], "]"]]]], ")"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", RowBox[List["Log", "[", RowBox[List["-", FractionBox[RowBox[List["b", " ", "z"]], "a"]]], "]"]]]], "+", RowBox[List["Log", "[", RowBox[List["-", FractionBox[RowBox[List["d", " ", "z"]], "c"]]], "]"]]]], ")"]], " ", RowBox[List["Log", "[", FractionBox[RowBox[List["a", " ", RowBox[List["(", RowBox[List["c", "+", RowBox[List["d", " ", "z"]]]], ")"]]]], RowBox[List["c", " ", RowBox[List["(", RowBox[List["a", "+", RowBox[List["b", " ", "z"]]]], ")"]]]]], "]"]], " ", RowBox[List["Log", "[", RowBox[List["1", "+", FractionBox[RowBox[List["d", " ", "z"]], "c"]]], "]"]]]], "+", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["Log", "[", RowBox[List["-", FractionBox[RowBox[List["b", " ", "z"]], "a"]]], "]"]], "-", RowBox[List["Log", "[", RowBox[List["-", FractionBox[RowBox[List["d", " ", "z"]], "c"]]], "]"]]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List["1", "+", FractionBox[RowBox[List["d", " ", "z"]], "c"]]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", RowBox[List["Log", "[", RowBox[List[FractionBox["a", "b"], "+", "z"]], "]"]]]], "+", RowBox[List["Log", "[", RowBox[List["1", "+", FractionBox[RowBox[List["d", " ", "z"]], "c"]]], "]"]]]], ")"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["Log", "[", RowBox[List[FractionBox["c", "d"], "+", "z"]], "]"]], "-", RowBox[List["Log", "[", FractionBox[RowBox[List["a", " ", RowBox[List["(", RowBox[List["c", "+", RowBox[List["d", " ", "z"]]]], ")"]]]], RowBox[List["c", " ", RowBox[List["(", RowBox[List["a", "+", RowBox[List["b", " ", "z"]]]], ")"]]]]], "]"]]]], ")"]], " ", RowBox[List["PolyLog", "[", RowBox[List["2", ",", RowBox[List["1", "+", FractionBox[RowBox[List["b", " ", "z"]], "a"]]]]], "]"]]]], "+", RowBox[List[RowBox[List["Log", "[", FractionBox[RowBox[List["a", " ", RowBox[List["(", RowBox[List["c", "+", RowBox[List["d", " ", "z"]]]], ")"]]]], RowBox[List["c", " ", RowBox[List["(", RowBox[List["a", "+", RowBox[List["b", " ", "z"]]]], ")"]]]]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", RowBox[List["PolyLog", "[", RowBox[List["2", ",", FractionBox[RowBox[List["a", " ", RowBox[List["(", RowBox[List["c", "+", RowBox[List["d", " ", "z"]]]], ")"]]]], RowBox[List["c", " ", RowBox[List["(", RowBox[List["a", "+", RowBox[List["b", " ", "z"]]]], ")"]]]]]]], "]"]]]], "+", RowBox[List["PolyLog", "[", RowBox[List["2", ",", FractionBox[RowBox[List["b", " ", RowBox[List["(", RowBox[List["c", "+", RowBox[List["d", " ", "z"]]]], ")"]]]], RowBox[List["d", " ", RowBox[List["(", RowBox[List["a", "+", RowBox[List["b", " ", "z"]]]], ")"]]]]]]], "]"]]]], ")"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["Log", "[", RowBox[List[FractionBox["a", "b"], "+", "z"]], "]"]], "+", RowBox[List["Log", "[", FractionBox[RowBox[List["a", " ", RowBox[List["(", RowBox[List["c", "+", RowBox[List["d", " ", "z"]]]], ")"]]]], RowBox[List["c", " ", RowBox[List["(", RowBox[List["a", "+", RowBox[List["b", " ", "z"]]]], ")"]]]]], "]"]]]], ")"]], " ", RowBox[List["PolyLog", "[", RowBox[List["2", ",", RowBox[List["1", "+", FractionBox[RowBox[List["d", " ", "z"]], "c"]]]]], "]"]]]], "-", RowBox[List["PolyLog", "[", RowBox[List["3", ",", RowBox[List["1", "+", FractionBox[RowBox[List["b", " ", "z"]], "a"]]]]], "]"]], "+", RowBox[List["PolyLog", "[", RowBox[List["3", ",", FractionBox[RowBox[List["a", " ", RowBox[List["(", RowBox[List["c", "+", RowBox[List["d", " ", "z"]]]], ")"]]]], RowBox[List["c", " ", RowBox[List["(", RowBox[List["a", "+", RowBox[List["b", " ", "z"]]]], ")"]]]]]]], "]"]], "-", RowBox[List["PolyLog", "[", RowBox[List["3", ",", FractionBox[RowBox[List["b", " ", RowBox[List["(", RowBox[List["c", "+", RowBox[List["d", " ", "z"]]]], ")"]]]], RowBox[List["d", " ", RowBox[List["(", RowBox[List["a", "+", RowBox[List["b", " ", "z"]]]], ")"]]]]]]], "]"]], "-", RowBox[List["PolyLog", "[", RowBox[List["3", ",", RowBox[List["1", "+", FractionBox[RowBox[List["d", " ", "z"]], "c"]]]]], "]"]]]], ")"]]]], "-", RowBox[List["2", " ", RowBox[List["PolyLog", "[", RowBox[List["3", ",", RowBox[List["1", "+", FractionBox[RowBox[List["d", " ", "z"]], "c"]]]]], "]"]]]]]]]]]]

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

 2001-10-29