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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 algebraic functions of the direct function, hyperbolic and exponential functions > Involving algebraic functions of sinh and exp > Involving ep z cosh(d z) (a sinh2(e z)+b cosh2(e z))beta





http://functions.wolfram.com/01.20.21.4737.01









  


  










Input Form





Integrate[E^(p z) Cosh[d z] (a Sinh[e z]^2 + b Cosh[e z]^2)^\[Beta], z] == (1/2) (-((1/(d - p + 2 e \[Beta])) ((E^((-d + p) z) ((a (-1 + E^(2 e z))^2 + b (1 + E^(2 e z))^2)/ E^(2 e z))^\[Beta] AppellF1[(-d + p)/(2 e) - \[Beta], -\[Beta], -\[Beta], 1 + (-d + p)/(2 e) - \[Beta], -(((a + b) E^(2 e z))/(-a + b + 2 Sqrt[(-a) b])), ((a + b) E^(2 e z))/(a - b + 2 Sqrt[(-a) b])])/ (4^\[Beta] (1 - ((a + b) E^(2 e z))/(a - b + 2 Sqrt[(-a) b]))^\[Beta] (1 + ((a + b) E^(2 e z))/(-a + b + 2 Sqrt[(-a) b]))^\[Beta]))) - (1/(-d - p + 2 e \[Beta])) ((E^((d + p) z) ((a (-1 + E^(2 e z))^2 + b (1 + E^(2 e z))^2)/E^(2 e z))^ \[Beta] AppellF1[(d + p)/(2 e) - \[Beta], -\[Beta], -\[Beta], 1 + (d + p)/(2 e) - \[Beta], -(((a + b) E^(2 e z))/ (-a + b + 2 Sqrt[(-a) b])), ((a + b) E^(2 e z))/ (a - b + 2 Sqrt[(-a) b])])/(4^\[Beta] (1 - ((a + b) E^(2 e z))/(a - b + 2 Sqrt[(-a) b]))^\[Beta] (1 + ((a + b) E^(2 e z))/(-a + b + 2 Sqrt[(-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