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 Exp

 http://functions.wolfram.com/01.03.21.0776.01

 Input Form

 Integrate[z^2/(a + b c^(d z))^2, z] == (d z Log[c] ((a + b c^(d z)) d^2 z^2 Log[c]^2 + 6 (a + b c^(d z)) Log[1 + (b c^(d z))/a] - 3 d z Log[c] (b c^(d z) + (a + b c^(d z)) Log[1 + (b c^(d z))/a])) - 6 (a + b c^(d z)) (-1 + d z Log[c]) PolyLog[2, -((b c^(d z))/a)] + 6 (a + b c^(d z)) PolyLog[3, -((b c^(d z))/a)])/ (3 a^2 (a + b c^(d z)) d^3 Log[c]^3)

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[FractionBox[SuperscriptBox["z", "2"], SuperscriptBox[RowBox[List["(", RowBox[List["a", "+", RowBox[List["b", " ", SuperscriptBox["c", RowBox[List["d", " ", "z"]]]]]]], ")"]], "2"]], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["d", " ", "z", " ", RowBox[List["Log", "[", "c", "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["a", "+", RowBox[List["b", " ", SuperscriptBox["c", RowBox[List["d", " ", "z"]]]]]]], ")"]], " ", SuperscriptBox["d", "2"], " ", SuperscriptBox["z", "2"], " ", SuperscriptBox[RowBox[List["Log", "[", "c", "]"]], "2"]]], "+", RowBox[List["6", " ", RowBox[List["(", RowBox[List["a", "+", RowBox[List["b", " ", SuperscriptBox["c", RowBox[List["d", " ", "z"]]]]]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List["1", "+", FractionBox[RowBox[List["b", " ", SuperscriptBox["c", RowBox[List["d", " ", "z"]]]]], "a"]]], "]"]]]], "-", RowBox[List["3", " ", "d", " ", "z", " ", RowBox[List["Log", "[", "c", "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["b", " ", SuperscriptBox["c", RowBox[List["d", " ", "z"]]]]], "+", RowBox[List[RowBox[List["(", RowBox[List["a", "+", RowBox[List["b", " ", SuperscriptBox["c", RowBox[List["d", " ", "z"]]]]]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List["1", "+", FractionBox[RowBox[List["b", " ", SuperscriptBox["c", RowBox[List["d", " ", "z"]]]]], "a"]]], "]"]]]]]], ")"]]]]]], ")"]]]], "-", RowBox[List["6", " ", RowBox[List["(", RowBox[List["a", "+", RowBox[List["b", " ", SuperscriptBox["c", RowBox[List["d", " ", "z"]]]]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["d", " ", "z", " ", RowBox[List["Log", "[", "c", "]"]]]]]], ")"]], " ", RowBox[List["PolyLog", "[", RowBox[List["2", ",", RowBox[List["-", FractionBox[RowBox[List["b", " ", SuperscriptBox["c", RowBox[List["d", " ", "z"]]]]], "a"]]]]], "]"]]]], "+", RowBox[List["6", " ", RowBox[List["(", RowBox[List["a", "+", RowBox[List["b", " ", SuperscriptBox["c", RowBox[List["d", " ", "z"]]]]]]], ")"]], " ", RowBox[List["PolyLog", "[", RowBox[List["3", ",", RowBox[List["-", FractionBox[RowBox[List["b", " ", SuperscriptBox["c", RowBox[List["d", " ", "z"]]]]], "a"]]]]], "]"]]]]]], ")"]], "/", RowBox[List["(", RowBox[List["3", " ", SuperscriptBox["a", "2"], " ", RowBox[List["(", RowBox[List["a", "+", RowBox[List["b", " ", SuperscriptBox["c", RowBox[List["d", " ", "z"]]]]]]], ")"]], " ", SuperscriptBox["d", "3"], " ", SuperscriptBox[RowBox[List["Log", "[", "c", "]"]], "3"]]], ")"]]]]]]]]

 MathML Form

 z 2 ( a + b c d z ) 2 z 1 3 a 2 ( b c d z + a ) d 3 log 3 ( c ) ( d z ( ( b c d z + a ) d 2 z 2 log 2 ( c ) - 3 d z ( b c d z + ( b c d z + a ) log ( b c d z a + 1 ) ) log ( c ) + 6 ( b c d z + a ) log ( b c d z a + 1 ) ) log ( c ) - 6 ( b c d z + a ) ( d z log ( c ) - 1 ) Li PolyLog 2 ( - b c d z a ) + 6 ( b c d z + a ) Li PolyLog 3 ( - b c d z a ) ) z z 2 a b c d z 2 -1 1 3 a 2 b c d z a d 3 c 3 -1 d z b c d z a d 2 z 2 c 2 -1 3 d z b c d z b c d z a b c d z a -1 1 c 6 b c d z a b c d z a -1 1 c -1 6 b c d z a d z c -1 PolyLog 2 -1 b c d z a -1 6 b c d z a PolyLog 3 -1 b c d z a -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[FractionBox[SuperscriptBox["z_", "2"], SuperscriptBox[RowBox[List["(", RowBox[List["a_", "+", RowBox[List["b_", " ", SuperscriptBox["c_", RowBox[List["d_", " ", "z_"]]]]]]], ")"]], "2"]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["d", " ", "z", " ", RowBox[List["Log", "[", "c", "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["a", "+", RowBox[List["b", " ", SuperscriptBox["c", RowBox[List["d", " ", "z"]]]]]]], ")"]], " ", SuperscriptBox["d", "2"], " ", SuperscriptBox["z", "2"], " ", SuperscriptBox[RowBox[List["Log", "[", "c", "]"]], "2"]]], "+", RowBox[List["6", " ", RowBox[List["(", RowBox[List["a", "+", RowBox[List["b", " ", SuperscriptBox["c", RowBox[List["d", " ", "z"]]]]]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List["1", "+", FractionBox[RowBox[List["b", " ", SuperscriptBox["c", RowBox[List["d", " ", "z"]]]]], "a"]]], "]"]]]], "-", RowBox[List["3", " ", "d", " ", "z", " ", RowBox[List["Log", "[", "c", "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["b", " ", SuperscriptBox["c", RowBox[List["d", " ", "z"]]]]], "+", RowBox[List[RowBox[List["(", RowBox[List["a", "+", RowBox[List["b", " ", SuperscriptBox["c", RowBox[List["d", " ", "z"]]]]]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List["1", "+", FractionBox[RowBox[List["b", " ", SuperscriptBox["c", RowBox[List["d", " ", "z"]]]]], "a"]]], "]"]]]]]], ")"]]]]]], ")"]]]], "-", RowBox[List["6", " ", RowBox[List["(", RowBox[List["a", "+", RowBox[List["b", " ", SuperscriptBox["c", RowBox[List["d", " ", "z"]]]]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["d", " ", "z", " ", RowBox[List["Log", "[", "c", "]"]]]]]], ")"]], " ", RowBox[List["PolyLog", "[", RowBox[List["2", ",", RowBox[List["-", FractionBox[RowBox[List["b", " ", SuperscriptBox["c", RowBox[List["d", " ", "z"]]]]], "a"]]]]], "]"]]]], "+", RowBox[List["6", " ", RowBox[List["(", RowBox[List["a", "+", RowBox[List["b", " ", SuperscriptBox["c", RowBox[List["d", " ", "z"]]]]]]], ")"]], " ", RowBox[List["PolyLog", "[", RowBox[List["3", ",", RowBox[List["-", FractionBox[RowBox[List["b", " ", SuperscriptBox["c", RowBox[List["d", " ", "z"]]]]], "a"]]]]], "]"]]]]]], RowBox[List["3", " ", SuperscriptBox["a", "2"], " ", RowBox[List["(", RowBox[List["a", "+", RowBox[List["b", " ", SuperscriptBox["c", RowBox[List["d", " ", "z"]]]]]]], ")"]], " ", SuperscriptBox["d", "3"], " ", SuperscriptBox[RowBox[List["Log", "[", "c", "]"]], "3"]]]]]]]]

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

 2002-12-18