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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 zsinh(d z)(a+b sinh(e z)+c cosh(e z))-n





http://functions.wolfram.com/01.20.21.4703.01









  


  








Input Form





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