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Coth






Mathematica Notation

Traditional Notation









Elementary Functions > Coth[z] > Integration > Indefinite integration > Involving functions of the direct function > Involving algebraic functions of the direct function > Involving ((a+b coth2(c z))n)beta





http://functions.wolfram.com/01.22.21.0281.01









  


  










Input Form





Integrate[Coth[c z]/Sqrt[(a + b Coth[c z]^2)^5], z] == ((-a + b + (a + b) Cosh[2 c z]) Csch[c z]^6 (-2 (a + b)^2 Cosh[4 c z] + (a + b) Cosh[2 c z] (8 a + 2 b + 3 Sqrt[2] Sqrt[-a + b + (a + b) Cosh[2 c z]] Log[Sqrt[-a + b + (a + b) Cosh[2 c z]] + Sqrt[2] Sqrt[(a + b) Sinh[c z]^2]] Sqrt[(a + b) Sinh[c z]^2]) - 3 (2 a (a + b) + Sqrt[2] (a - b) Sqrt[-a + b + (a + b) Cosh[2 c z]] Log[Sqrt[-a + b + (a + b) Cosh[2 c z]] + Sqrt[2] Sqrt[(a + b) Sinh[c z]^2]] Sqrt[(a + b) Sinh[c z]^2])))/ (24 (a + b)^3 c Sqrt[(a + b Coth[c z]^2)^5])










Standard Form





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MathML Form







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type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 24 </cn> <apply> <power /> <apply> <plus /> <ci> a </ci> <ci> b </ci> </apply> <cn type='integer'> 3 </cn> </apply> <ci> c </ci> <apply> <power /> <apply> <power /> <apply> <plus /> <apply> <times /> <ci> b </ci> <apply> <power /> <apply> <coth /> <apply> <times /> <ci> c </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <ci> a </ci> </apply> <cn type='integer'> 5 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2002-12-18