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Cosh




Mathematica Notation

Traditional Notation









Elementary Functions > Cosh[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving hyperbolic and exponential functions > Involving rational functions of sinh and exp > Involving ep zcosh(c z)/a+b sinh2(d z)





http://functions.wolfram.com/01.20.21.1878.01









  


  








Input Form





Integrate[(E^(p z) Cosh[c z])/(a + b Sinh[c z]^2), z] == (1/(2 Sqrt[a] Sqrt[a - b] b)) ((1/(-c + p)) (E^((-c + p) z) ((-2 a + 2 Sqrt[a] Sqrt[a - b] + b) Hypergeometric2F1[(c - p)/(2 c), 1, 3/2 - p/(2 c), b/(E^(2 c z) (-2 a - 2 Sqrt[a] Sqrt[a - b] + b))] + (2 a + 2 Sqrt[a] Sqrt[a - b] - b) Hypergeometric2F1[(c - p)/(2 c), 1, 3/2 - p/(2 c), b/(E^(2 c z) (-2 a + 2 Sqrt[a] Sqrt[a - b] + b))])) + (1/(-3 c + p)) (E^((-3 c + p) z) ((-2 a + 2 Sqrt[a] Sqrt[a - b] + b) Hypergeometric2F1[3/2 - p/(2 c), 1, 5/2 - p/(2 c), b/(E^(2 c z) (-2 a - 2 Sqrt[a] Sqrt[a - b] + b))] + (2 a + 2 Sqrt[a] Sqrt[a - b] - b) Hypergeometric2F1[3/2 - p/(2 c), 1, 5/2 - p/(2 c), b/(E^(2 c z) (-2 a + 2 Sqrt[a] Sqrt[a - b] + b))])))








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