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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+b sinh(e z)+c cosh(e z))beta





http://functions.wolfram.com/01.20.21.4734.01









  


  








Input Form





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








Standard Form





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MathML Form







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





2002-12-18