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Cosh






Mathematica Notation

Traditional Notation









Elementary Functions > Cosh[z] > Integration > Indefinite integration > Involving functions of the direct function > Involving rational functions of the direct function > Involving coshm(c z)/a+b coshn(c z)





http://functions.wolfram.com/01.20.21.2287.01









  


  










Input Form





Integrate[Cosh[c z]^2/(a + b Cosh[c z]^4), z] == -((I (ArcTanh[(Sqrt[a] Tanh[c z])/Sqrt[a - I Sqrt[a] Sqrt[b]]]/ Sqrt[a - I Sqrt[a] Sqrt[b]] - ArcTanh[(Sqrt[a] Tanh[c z])/Sqrt[a + I Sqrt[a] Sqrt[b]]]/ Sqrt[a + I Sqrt[a] Sqrt[b]]))/(2 Sqrt[b] c))










Standard Form





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MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mo> &#8747; </mo> <mrow> <mfrac> <mrow> <msup> <mi> cosh </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mrow> <mi> c </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mi> a </mi> <mo> + </mo> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mrow> <msup> <mi> cosh </mi> <mn> 4 </mn> </msup> <mo> ( </mo> <mrow> <mi> c </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mfrac> <mo> &#8290; </mo> <mrow> <mo> &#8518; </mo> <mi> z </mi> </mrow> </mrow> </mrow> <mo> &#10869; </mo> <mrow> <mrow> <mo> - </mo> <mfrac> <mrow> <mi> &#8520; </mi> <mtext> </mtext> </mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msqrt> <mi> b </mi> </msqrt> <mo> &#8290; </mo> <mi> c </mi> </mrow> </mfrac> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mfrac> <mrow> <msup> <mi> tanh </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mfrac> <mrow> <msqrt> <mi> a </mi> </msqrt> <mo> &#8290; 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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[FractionBox[SuperscriptBox[RowBox[List["Cosh", "[", RowBox[List["c_", " ", "z_"]], "]"]], "2"], RowBox[List["a_", "+", RowBox[List["b_", " ", SuperscriptBox[RowBox[List["Cosh", "[", RowBox[List["c_", " ", "z_"]], "]"]], "4"]]]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List[FractionBox[RowBox[List["ArcTanh", "[", FractionBox[RowBox[List[SqrtBox["a"], " ", RowBox[List["Tanh", "[", RowBox[List["c", " ", "z"]], "]"]]]], SqrtBox[RowBox[List["a", "-", RowBox[List["\[ImaginaryI]", " ", SqrtBox["a"], " ", SqrtBox["b"]]]]]]], "]"]], SqrtBox[RowBox[List["a", "-", RowBox[List["\[ImaginaryI]", " ", SqrtBox["a"], " ", SqrtBox["b"]]]]]]], "-", FractionBox[RowBox[List["ArcTanh", "[", FractionBox[RowBox[List[SqrtBox["a"], " ", RowBox[List["Tanh", "[", RowBox[List["c", " ", "z"]], "]"]]]], SqrtBox[RowBox[List["a", "+", RowBox[List["\[ImaginaryI]", " ", SqrtBox["a"], " ", SqrtBox["b"]]]]]]], "]"]], SqrtBox[RowBox[List["a", "+", RowBox[List["\[ImaginaryI]", " ", SqrtBox["a"], " ", SqrtBox["b"]]]]]]]]], ")"]]]], RowBox[List["2", " ", SqrtBox["b"], " ", "c"]]]]]]]]]










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





2002-12-18