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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/01.20.21.4346.01









  


  










Input Form





Integrate[Sinh[c z]^2 Cosh[c z]^4 Sqrt[a + b Cosh[2 c z]], z] == (-8 I (4 a^4 - 3 a^3 b - 15 a^2 b^2 - 29 a b^3 - 21 b^4) Sqrt[(a + b Cosh[2 c z])/(a + b)] EllipticE[I c z, (2 b)/(a + b)] + 8 I (4 a^4 - 7 a^3 b - 9 a^2 b^2 + 7 a b^3 + 5 b^4) Sqrt[(a + b Cosh[2 c z])/(a + b)] EllipticF[I c z, (2 b)/(a + b)] + b (-16 a^3 + 28 a^2 b - 4 a b^2 + 42 b^3 + b (-4 a^2 + 112 a b + 5 b^2) Cosh[2 c z] + 6 b^2 (6 a + 7 b) Cosh[4 c z] + 15 b^3 Cosh[6 c z]) Sinh[2 c z])/(3360 b^3 c Sqrt[a + b Cosh[2 c z]])










Standard Form





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MathML Form







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( </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> c </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> / </mo> <mrow> <mo> ( </mo> <mrow> <mn> 3360 </mn> <mo> &#8290; </mo> <msup> <mi> b </mi> <mn> 3 </mn> </msup> <mo> &#8290; </mo> <mi> c </mi> <mo> &#8290; </mo> <msqrt> <mrow> <mi> a </mi> <mo> + </mo> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mrow> <mi> cosh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> c </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </msqrt> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <int /> <bvar> <ci> z </ci> </bvar> <apply> <times /> <apply> <power /> <apply> <sinh /> <apply> <times /> <ci> c </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <cosh /> <apply> <times /> <ci> c </ci> <ci> z </ci> </apply> </apply> <cn 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</semantics> </math>










Rule Form





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





2002-12-18