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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 algebraic functions of the direct function and hyperbolic functions > Involving sinh > Involving sinhm(c z)coshm(c z)(a+b cosh(2c z))beta





http://functions.wolfram.com/01.20.21.4360.01









  


  










Input Form





Integrate[(Sinh[c z]^3 Cosh[c z]^4)/Sqrt[a + b Cosh[2 c z]], z] == (1/(768 b^(7/2) c)) (-2 Sqrt[b] (-15 a^2 + 9 a b + 22 b^2) Cosh[c z] Sqrt[a + b Cosh[2 c z]] - 2 (5 a - 3 b) b^(3/2) Sqrt[a + b Cosh[2 c z]] Cosh[3 c z] + 4 b^(5/2) Sqrt[a + b Cosh[2 c z]] Cosh[5 c z] - 15 Sqrt[2] a^3 Log[Sqrt[2] Sqrt[b] Cosh[c z] + Sqrt[a + b Cosh[2 c z]]] + 9 Sqrt[2] a^2 b Log[Sqrt[2] Sqrt[b] Cosh[c z] + Sqrt[a + b Cosh[2 c z]]] + 27 Sqrt[2] a b^2 Log[Sqrt[2] Sqrt[b] Cosh[c z] + Sqrt[a + b Cosh[2 c z]]] - 21 Sqrt[2] b^3 Log[Sqrt[2] Sqrt[b] Cosh[c z] + Sqrt[a + b Cosh[2 c z]]])










Standard Form





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MathML Form







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z </ci> </apply> </apply> <apply> <power /> <apply> <plus /> <ci> a </ci> <apply> <times /> <ci> b </ci> <apply> <cosh /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> <ci> z </ci> </apply> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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Date Added to functions.wolfram.com (modification date)





2002-12-18