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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 functions > Involving rational functions of sinh > Involving cosh(c z)/a+b sinh2(d z)





http://functions.wolfram.com/01.20.21.1634.01









  


  








Input Form





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