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Cosh




Mathematica Notation

Traditional Notation









Elementary Functions > Cosh[z] > Integration > Indefinite integration > Involving functions of the direct function > Involving algebraic functions of the direct function > Involving (a+b cosh2(c z))beta coshnu(c z)





http://functions.wolfram.com/01.20.21.2421.01









  


  








Input Form





Integrate[Cosh[c z]^5/(a + b Cosh[c z]^2)^(3/2), z] == (1/(2 c)) (((-3 a + b) ArcTanh[(Sqrt[2] Sqrt[b] Sinh[c z])/ Sqrt[2 a + b + b Cosh[2 c z]]])/b^(5/2) + ((6 a^2 + 3 a b + b^2 + b (a + b) Cosh[2 c z]) Sinh[c z])/ (Sqrt[2] b^2 (a + b) Sqrt[2 a + b + b Cosh[2 c z]]))








Standard Form





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MathML Form







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</mo> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> + </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> <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> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> sinh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> c </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <msqrt> <mn> 2 </mn> </msqrt> <mo> &#8290; </mo> <msup> <mi> b </mi> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> + </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msqrt> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> a </mi> </mrow> <mo> + </mo> <mi> b </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> </mfrac> </mrow> <mrow> <mn> 2 </mn> <mo> &#8290; 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Rule Form





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





2002-12-18