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Cosh




Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/01.20.21.4707.01









  


  








Input Form





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








Standard Form





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MathML Form







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Rule Form





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





2002-12-18