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Cosh




Mathematica Notation

Traditional Notation









Elementary Functions > Cosh[z] > Integration > Indefinite integration > Involving functions of the direct function, hyperbolic and trigonometric functions > Involving algebraic functions of the direct function, hyperbolic and trigonometric functions > Involving cos, algebraic functions of sinh and exp > Involving cos(d z)(a sinh(e z)+b cosh(e z))beta





http://functions.wolfram.com/01.20.21.4795.01









  


  








Input Form





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








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