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Cosh




Mathematica Notation

Traditional Notation









Elementary Functions > Cosh[z] > Integration > Indefinite integration > Involving functions of the direct function and hyperbolic functions > Involving rational functions of the direct function and hyperbolic functions > Involving rational functions of sinh > Involving ep zcosh(d z)(a sinh2(e z)+b cosh2(e z))-n





http://functions.wolfram.com/01.20.21.4293.01









  


  








Input Form





Integrate[Cosh[d z]/(a Sinh[e z]^2 + b Cosh[e z]^2)^2, z] == (1/2) (-((I E^((-d + 2 e) z) ((Sqrt[a] + I Sqrt[b])^2 (a - b) Hypergeometric2F1[1 - d/(2 e), 1, 2 - d/(2 e), ((a + b) E^(2 e z))/ (Sqrt[a] - I Sqrt[b])^2] - (Sqrt[a] - I Sqrt[b])^2 (a - b) Hypergeometric2F1[1 - d/(2 e), 1, 2 - d/(2 e), ((a + b) E^(2 e z))/ (Sqrt[a] + I Sqrt[b])^2] - 2 I Sqrt[a] Sqrt[b] ((Sqrt[a] + I Sqrt[b])^2 Hypergeometric2F1[1 - d/(2 e), 2, 2 - d/(2 e), ((a + b) E^(2 e z))/(Sqrt[a] - I Sqrt[b])^2] + (Sqrt[a] - I Sqrt[b])^2 Hypergeometric2F1[1 - d/(2 e), 2, 2 - d/(2 e), ((a + b) E^(2 e z))/(Sqrt[a] + I Sqrt[b])^2])))/ (2 a^(3/2) b^(3/2) (a + b) (-d + 2 e))) - (I E^((d + 2 e) z) ((Sqrt[a] + I Sqrt[b])^2 (a - b) Hypergeometric2F1[1 + d/(2 e), 1, 2 + d/(2 e), ((a + b) E^(2 e z))/ (Sqrt[a] - I Sqrt[b])^2] - (Sqrt[a] - I Sqrt[b])^2 (a - b) Hypergeometric2F1[1 + d/(2 e), 1, 2 + d/(2 e), ((a + b) E^(2 e z))/ (Sqrt[a] + I Sqrt[b])^2] - 2 I Sqrt[a] Sqrt[b] ((Sqrt[a] + I Sqrt[b])^2 Hypergeometric2F1[1 + d/(2 e), 2, 2 + d/(2 e), ((a + b) E^(2 e z))/(Sqrt[a] - I Sqrt[b])^2] + (Sqrt[a] - I Sqrt[b])^2 Hypergeometric2F1[1 + d/(2 e), 2, 2 + d/(2 e), ((a + b) E^(2 e z))/(Sqrt[a] + I Sqrt[b])^2])))/ (2 a^(3/2) b^(3/2) (a + b) (d + 2 e)))








Standard Form





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MathML Form







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<ci> a </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <times /> <imaginaryi /> <apply> <power /> <ci> b </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2002-12-18