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Tanh






Mathematica Notation

Traditional Notation









Elementary Functions > Tanh[z] > Integration > Indefinite integration > Involving functions of the direct function and hyperbolic functions > Involving algebraic functions of the direct function and hyperbolic functions > Involving cosh > Involving cosh(c z)(a+b tanh(c z))beta





http://functions.wolfram.com/01.21.21.0361.01









  


  










Input Form





Integrate[Cosh[c z] Sqrt[a + b Tanh[c z]], z] == (1/(2 c)) (Sech[c z] ((2 b)/Sqrt[a + b Tanh[c z]] + Sinh[2 c z] Sqrt[a + b Tanh[c z]] + (2 I a^2 Cosh[c z] (EllipticE[I ArcSinh[Sqrt[-a - b]/Sqrt[a + b Tanh[c z]]], (a - b)/(a + b)] - EllipticF[ I ArcSinh[Sqrt[-a - b]/Sqrt[a + b Tanh[c z]]], (a - b)/(a + b)]) (a Cosh[c z] + b Sinh[c z]) Sqrt[(b (1 + Tanh[c z]))/(a + b Tanh[c z])] Sqrt[1 - (a + b)/(a + b Tanh[c z])])/(Sqrt[-a - b] (a - b) b) + (1/(Sqrt[-a - b] b)) (2 I a Cosh[c z] EllipticF[I ArcSinh[Sqrt[-a - b]/Sqrt[a + b Tanh[c z]]], (a - b)/(a + b)] (a Cosh[c z] + b Sinh[c z]) Sqrt[(b (1 + Tanh[c z]))/(a + b Tanh[c z])] Sqrt[1 - (a + b)/(a + b Tanh[c z])]) - (2 I b Cosh[c z] (EllipticE[I ArcSinh[Sqrt[-a - b]/ Sqrt[a + b Tanh[c z]]], -1 + (2 a)/(a + b)] - EllipticF[I ArcSinh[Sqrt[-a - b]/Sqrt[a + b Tanh[c z]]], -1 + (2 a)/(a + b)]) (a Cosh[c z] + b Sinh[c z]) Sqrt[(b (1 + Tanh[c z]))/(a + b Tanh[c z])] Sqrt[1 - (a + b)/(a + b Tanh[c z])])/(Sqrt[-a - b] (a - b))))










Standard Form





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MathML Form







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










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





2002-12-18





© 1998- Wolfram Research, Inc.