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http://functions.wolfram.com/01.21.21.0137.01
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Integrate[((A + B Cosh[z]) Tanh[z])/(a + b Sinh[z]), z] ==
(-(1/(b (-a^2 - b^2)^(3/2)))) (2 A b^2 Sqrt[-a^2 - b^2] ArcTan[Tanh[z/2]] -
2 a (a^2 + b^2) B ArcTan[(b - a Tanh[z/2])/Sqrt[-a^2 - b^2]] +
Sqrt[-a^2 - b^2] ((a^2 + b^2) B z + a A b Log[Cosh[z]] -
a A b Log[a + b Sinh[z]]))
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2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <apply> <plus /> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> </apply> <ci> B </ci> <ci> z </ci> </apply> <apply> <times /> <ci> a </ci> <ci> A </ci> <ci> b </ci> <apply> <ln /> <apply> <cosh /> <ci> z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> a </ci> <ci> A </ci> <ci> b </ci> <apply> <ln /> <apply> <plus /> <ci> a </ci> <apply> <times /> <ci> b </ci> <apply> <sinh /> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> </apply> </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[RowBox[List["(", RowBox[List["A_", "+", RowBox[List["B_", " ", RowBox[List["Cosh", "[", "z_", "]"]]]]]], ")"]], " ", RowBox[List["Tanh", "[", "z_", "]"]]]], RowBox[List["a_", "+", RowBox[List["b_", " ", RowBox[List["Sinh", "[", "z_", "]"]]]]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List["-", FractionBox[RowBox[List[RowBox[List["2", " ", "A", " ", SuperscriptBox["b", "2"], " ", SqrtBox[RowBox[List[RowBox[List["-", SuperscriptBox["a", "2"]]], "-", SuperscriptBox["b", "2"]]]], " ", RowBox[List["ArcTan", "[", RowBox[List["Tanh", "[", FractionBox["z", "2"], "]"]], "]"]]]], "-", RowBox[List["2", " ", "a", " ", RowBox[List["(", RowBox[List[SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"]]], ")"]], " ", "B", " ", RowBox[List["ArcTan", "[", FractionBox[RowBox[List["b", "-", RowBox[List["a", " ", RowBox[List["Tanh", "[", FractionBox["z", "2"], "]"]]]]]], SqrtBox[RowBox[List[RowBox[List["-", SuperscriptBox["a", "2"]]], "-", SuperscriptBox["b", "2"]]]]], "]"]]]], "+", RowBox[List[SqrtBox[RowBox[List[RowBox[List["-", SuperscriptBox["a", "2"]]], "-", SuperscriptBox["b", "2"]]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"]]], ")"]], " ", "B", " ", "z"]], "+", RowBox[List["a", " ", "A", " ", "b", " ", RowBox[List["Log", "[", RowBox[List["Cosh", "[", "z", "]"]], "]"]]]], "-", RowBox[List["a", " ", "A", " ", "b", " ", RowBox[List["Log", "[", RowBox[List["a", "+", RowBox[List["b", " ", RowBox[List["Sinh", "[", "z", "]"]]]]]], "]"]]]]]], ")"]]]]]], RowBox[List["b", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", SuperscriptBox["a", "2"]]], "-", SuperscriptBox["b", "2"]]], ")"]], RowBox[List["3", "/", "2"]]]]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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){kind=small}
