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Cosh




Mathematica Notation

Traditional Notation









Elementary Functions > Cosh[z] > Integration > Indefinite integration > Involving functions of the direct function and hyperbolic functions > Involving rational functions of the direct function and hyperbolic functions > Involving rational functions of sinh > Involving (a sinh2(e z)+b sinh(2 e z)+c cosh2(e z))-n





http://functions.wolfram.com/01.20.21.4302.01









  


  








Input Form





Integrate[(A Sinh[z]^2 + B Sinh[2 z] + C Cosh[z]^2 + \[Delta])/ (a Sinh[z]^2 + b Sinh[2 z] + c Cosh[z]^2), z] == ((-4 b B + a (A + C) + c (A + C)) z + (1/Sqrt[-b^2 + a c]) ((2 b B c + A (2 b^2 - c (a + c)) - 2 b^2 C - 4 b^2 \[Delta] + c^2 \[Delta] + a^2 (C + \[Delta]) + a (-2 b B + c C + 2 c \[Delta])) ArcTan[(b + a Tanh[z])/Sqrt[-b^2 + a c]]) + ((-A) b + a B + B c - b C) Log[-a + c + (a + c) Cosh[2 z] + 2 b Sinh[2 z]])/ ((a - 2 b + c) (a + 2 b + c))








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