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Sech






Mathematica Notation

Traditional Notation









Elementary Functions > Sech[z] > Integration > Indefinite integration > Involving functions of the direct function and hyperbolic functions > Involving algebraic functions of the direct function and hyperbolic functions > Involving sinh, cosh and tanh





http://functions.wolfram.com/01.24.21.0477.01









  


  










Input Form





Integrate[((3 + Sinh[z]^2) Tanh[z]^3)/((-2 + Cosh[z]^2) Sqrt[(5 - 4 Sech[z]^2)^3]), z] == (Sech[z]^2 (21 - 35 Cosh[2 z] + (1/(15 Sqrt[1 + Cosh[2 z]])) ((-3 + 5 Cosh[2 z])^(3/2) (36 Sqrt[5] ArcSinh[Sqrt[-3 + 5 Cosh[2 z]]/ (2 Sqrt[2])] Cosh[z] - 5 Sqrt[3] (14 ArcTanh[(Sqrt[6] Cosh[z])/Sqrt[-3 + 5 Cosh[2 z]]] Sqrt[Cosh[z]^2] + 3 Cosh[z] (-Log[4 Sqrt[3] + 5 Sqrt[6] Sqrt[Cosh[z]^2] - 3 Sqrt[-3 + 5 Cosh[2 z]]] - Log[2 Sqrt[3] - Sqrt[-3 + 5 Cosh[2 z]]] + Log[2 Sqrt[3] + Sqrt[-3 + 5 Cosh[2 z]]] + Log[4 Sqrt[3] + 5 Sqrt[6] Sqrt[Cosh[z]^2] + 3 Sqrt[-3 + 5 Cosh[2 z]]]))) Sech[z])))/ (120 Sqrt[(5 - 4 Sech[z]^2)^3])










Standard Form





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MathML Form







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<times /> <cn type='integer'> 4 </cn> <apply> <power /> <cn type='integer'> 3 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ln /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <cn type='integer'> 3 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 5 </cn> <apply> <cosh /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> </apply> </apply> </apply> <cn type='integer'> -3 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <ln /> <apply> <plus /> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 5 </cn> <apply> <cosh /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> </apply> </apply> </apply> <cn type='integer'> -3 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <cn type='integer'> 3 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> <apply> <ln /> <apply> <plus /> <apply> <times /> <cn type='integer'> 5 </cn> <apply> <power /> <cn type='integer'> 6 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <power /> <apply> <cosh /> <ci> z </ci> </apply> <cn type='integer'> 2 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 3 </cn> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 5 </cn> <apply> <cosh /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> </apply> </apply> </apply> <cn type='integer'> -3 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <power /> <cn type='integer'> 3 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <sech /> <ci> z </ci> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 5 </cn> <apply> <cosh /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> </apply> </apply> </apply> <cn type='integer'> -3 </cn> </apply> <cn type='rational'> 3 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 35 </cn> <apply> <cosh /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> </apply> </apply> </apply> </apply> <cn type='integer'> 21 </cn> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 120 </cn> <apply> <power /> <apply> <power /> <apply> <plus /> <cn type='integer'> 5 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <power /> <apply> <sech /> <ci> z </ci> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> <cn type='integer'> 3 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2002-12-18





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