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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 sinh(d z))-n





http://functions.wolfram.com/01.20.21.1633.01









  


  










Input Form





Integrate[(A + B Cosh[c z] + C Cosh[c z]^2)/(a + b Sinh[c z])^3, z] == (1/(2 (a^2 + b^2)^2 c)) ((2 (b^2 (-A + C) + a^2 (2 A + C)) ArcTan[(b - a Tanh[(c z)/2])/ Sqrt[-a^2 - b^2]])/Sqrt[-a^2 - b^2] - ((a^2 + b^2) ((a^2 + b^2) B + (A b^2 + (a^2 + b^2) C) Cosh[c z]))/ (b (a + b Sinh[c z])^2) + (a (-3 A b^2 + (a^2 + b^2) C) Cosh[c z])/ (b (a + b Sinh[c z])))










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