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 Coth

 http://functions.wolfram.com/01.22.21.0036.01

 Input Form

 Integrate[Coth[ArcSech[z]], z] == Sqrt[1/(1 + z)] Sqrt[1 + z] ArcTan[z/Sqrt[1 - z^2]]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[RowBox[List["Coth", "[", RowBox[List["ArcSech", "[", "z", "]"]], "]"]], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[SqrtBox[FractionBox["1", RowBox[List["1", "+", "z"]]]], " ", SqrtBox[RowBox[List["1", "+", "z"]]], " ", RowBox[List["ArcTan", "[", FractionBox["z", SqrtBox[RowBox[List["1", "-", SuperscriptBox["z", "2"]]]]], "]"]]]]]]]]

 MathML Form

 coth ( sech - 1 ( z ) ) z 1 z + 1 z + 1 tan - 1 ( z 1 - z 2 ) z z 1 z 1 -1 1 2 z 1 1 2 z 1 -1 z 2 1 2 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[RowBox[List["Coth", "[", RowBox[List["ArcSech", "[", "z_", "]"]], "]"]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[SqrtBox[FractionBox["1", RowBox[List["1", "+", "z"]]]], " ", SqrtBox[RowBox[List["1", "+", "z"]]], " ", RowBox[List["ArcTan", "[", FractionBox["z", SqrtBox[RowBox[List["1", "-", SuperscriptBox["z", "2"]]]]], "]"]]]]]]]]

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

 2002-12-18