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http://functions.wolfram.com/01.27.21.0003.01
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Integrate[ArcTanh[z]/Sqrt[z], z] == 2 ArcTan[Sqrt[z]] + Log[Sqrt[z] - 1] -
Log[Sqrt[z] + 1] + 2 ArcTanh[z] Sqrt[z]
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Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[FractionBox[RowBox[List["ArcTanh", "[", "z", "]"]], SqrtBox["z"]], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[RowBox[List["2", " ", RowBox[List["ArcTan", "[", SqrtBox["z"], "]"]]]], "+", RowBox[List["Log", "[", RowBox[List[SqrtBox["z"], "-", "1"]], "]"]], "-", RowBox[List["Log", "[", RowBox[List[SqrtBox["z"], "+", "1"]], "]"]], "+", RowBox[List["2", " ", RowBox[List["ArcTanh", "[", "z", "]"]], " ", SqrtBox["z"]]]]]]]]]
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<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mo> ∫ </mo> <mrow> <mfrac> <mrow> <msup> <mi> tanh </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <msqrt> <mi> z </mi> </msqrt> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ⅆ </mo> <mi> z </mi> </mrow> </mrow> </mrow> <mo> ⩵ </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mrow> <msup> <mi> tan </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <msqrt> <mi> z </mi> </msqrt> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msqrt> <mi> z </mi> </msqrt> <mo> ⁢ </mo> <mrow> <msup> <mi> tanh </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <msqrt> <mi> z </mi> </msqrt> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <msqrt> <mi> z </mi> </msqrt> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <int /> <bvar> <ci> z </ci> </bvar> <apply> <times /> <apply> <arctanh /> <ci> z </ci> </apply> <apply> <power /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <arctan /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <arctanh /> <ci> z </ci> </apply> </apply> <apply> <ln /> <apply> <plus /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ln /> <apply> <plus /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> 1 </cn> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[FractionBox[RowBox[List["ArcTanh", "[", "z_", "]"]], SqrtBox["z_"]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["2", " ", RowBox[List["ArcTan", "[", SqrtBox["z"], "]"]]]], "+", RowBox[List["Log", "[", RowBox[List[SqrtBox["z"], "-", "1"]], "]"]], "-", RowBox[List["Log", "[", RowBox[List[SqrtBox["z"], "+", "1"]], "]"]], "+", RowBox[List["2", " ", RowBox[List["ArcTanh", "[", "z", "]"]], " ", SqrtBox["z"]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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