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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 powers of the direct function and hyperbolic functions > Involving cosh and tanh





http://functions.wolfram.com/01.24.21.0444.01









  


  








Input Form





Integrate[((-Cosh[2 z] + 2 Tanh[z]^2) Sech[z]^2)/Sqrt[Tanh[z]^3 Tanh[2 z]^3], z] == (Cosh[z]^4 (Cosh[2 z] - 2 Tanh[z]^2) (-24 AppellF1[1/2, 1, -(1/2), 3/2, Coth[z]^2, -Coth[z]^2] Cosh[2 z] Csch[z] Sech[z]^3 + Sqrt[1 + Coth[z]^2] (3 Coth[z] + 28 Cosh[z] Sinh[z] - Tanh[z] (6 + Tanh[z]^2 - 8 Tanh[z]^4 + 4 Tanh[z]^6 - 15 Log[Tanh[z]] Sech[z]^2 Sqrt[1 + Tanh[z]^2] + 15 Log[1 + Sqrt[1 + Tanh[z]^2]] Sech[z]^2 Sqrt[1 + Tanh[z]^2] + Sinh[z]^2 (26 + 32 Tanh[z]^2 - 30 Tanh[z]^4)))) Tanh[2 z]^2)/ (12 Sqrt[2] (5 - 2 Cosh[2 z] + Cosh[4 z]) Sqrt[1 + Coth[z]^2] Sqrt[Sech[2 z]^3 Sinh[z]^6])








Standard Form





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MathML Form







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type='integer'> 2 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 3 </cn> </apply> <apply> <power /> <apply> <sinh /> <ci> z </ci> </apply> <cn type='integer'> 6 </cn> </apply> </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