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Cosh




Mathematica Notation

Traditional Notation









Elementary Functions > Cosh[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving trigonometric and exponential functions > Involving rational functions of cos and exp > Involving ep zcosh(c z)/a+b cos2(d z)





http://functions.wolfram.com/01.20.21.1317.01









  


  








Input Form





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