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Tanh




Mathematica Notation

Traditional Notation









Elementary Functions > Tanh[z] > Integration > Indefinite integration > Involving functions of the direct function > Involving algebraic functions of the direct function > Involving (a+b tanh1/2(c z))beta





http://functions.wolfram.com/01.21.21.0258.01









  


  








Input Form





Integrate[Tanh[c z] (a + b Sqrt[Tanh[c z]])^\[Beta], z] == (((a^3 + a^2 b + a b^2 + b^3) Hypergeometric2F1[1 + \[Beta], 1, 2 + \[Beta], (a + b Sqrt[Tanh[c z]])/(a - b)] + (a - b) ((a^2 + (1 + I) a b + I b^2) Hypergeometric2F1[1 + \[Beta], 1, 2 + \[Beta], (a + b Sqrt[Tanh[c z]])/(a - I b)] + (a - I b) ((a + b) Hypergeometric2F1[1 + \[Beta], 1, 2 + \[Beta], (a + b Sqrt[Tanh[c z]])/(a + I b)] + (a + I b) Hypergeometric2F1[1 + \[Beta], 1, 2 + \[Beta], (a + b Sqrt[Tanh[c z]])/(a + b)]))) (a + b Sqrt[Tanh[c z]])^ (1 + \[Beta]))/(2 c (a^4 - b^4) (1 + \[Beta]))








Standard Form





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MathML Form







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</ci> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> <apply> <plus /> <apply> <power /> <ci> a </ci> <cn type='integer'> 4 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> b </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <plus /> <ci> &#946; </ci> <cn type='integer'> 1 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <apply> <plus /> <apply> <power /> <ci> a </ci> <cn type='integer'> 3 </cn> </apply> <apply> <times /> <ci> b </ci> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <ci> a </ci> </apply> <apply> <power /> <ci> b </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <ci> Hypergeometric2F1 </ci> <apply> <plus /> <ci> &#946; 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</ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 1 </cn> <apply> <plus /> <ci> &#946; </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <apply> <plus /> <ci> a </ci> <apply> <times /> <ci> b </ci> <apply> <power /> <apply> <tanh /> <apply> <times /> <ci> c </ci> <ci> z </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <ci> a </ci> <ci> b </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <plus /> <ci> a </ci> <ci> b </ci> </apply> <apply> <ci> Hypergeometric2F1 </ci> <apply> <plus /> <ci> &#946; </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 1 </cn> <apply> <plus /> <ci> &#946; </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <apply> <plus /> <ci> a </ci> <apply> <times /> <ci> b </ci> <apply> <power /> <apply> <tanh /> <apply> <times /> <ci> c </ci> <ci> z </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <ci> a </ci> <apply> <times /> <imaginaryi /> <ci> b </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <ci> b </ci> <apply> <plus /> <cn type='integer'> 1 </cn> <imaginaryi /> </apply> <ci> a </ci> </apply> <apply> <times /> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <imaginaryi /> </apply> </apply> <apply> <ci> Hypergeometric2F1 </ci> <apply> <plus /> <ci> &#946; </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 1 </cn> <apply> <plus /> <ci> &#946; </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <apply> <plus /> <ci> a </ci> <apply> <times /> <ci> b </ci> <apply> <power /> <apply> <tanh /> <apply> <times /> <ci> c </ci> <ci> z </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <ci> a </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> b </ci> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <ci> a </ci> <apply> <times /> <ci> b </ci> <apply> <power /> <apply> <tanh /> <apply> <times /> <ci> c </ci> <ci> z </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <plus /> <ci> &#946; </ci> <cn type='integer'> 1 </cn> </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