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Tanh






Mathematica Notation

Traditional Notation









Elementary Functions > Tanh[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving hyperbolic and exponential functions > Involving cosh and exp > Involving ep zcosh(b z) tanh( c z)





http://functions.wolfram.com/01.21.21.0153.01









  


  










Input Form





Integrate[E^(p z) Cosh[b z] Tanh[c z], z] == (1/2) ((E^((-b + p) z) Hypergeometric2F1[(-b + p)/(2 c), 1, 1 + (-b + p)/(2 c), -E^(2 c z)])/(b - p) - (E^((b + p) z) Hypergeometric2F1[(b + p)/(2 c), 1, 1 + (b + p)/(2 c), -E^(2 c z)])/(b + p) - (E^((-b + p + 2 c) z) Hypergeometric2F1[(-b + p + 2 c)/(2 c), 1, (-b + p + 4 c)/(2 c), -E^(2 c z)])/(b - p - 2 c) + (E^((b + p + 2 c) z) Hypergeometric2F1[(b + p + 2 c)/(2 c), 1, (b + p + 4 c)/(2 c), -E^(2 c z)])/(b + p + 2 c))










Standard Form





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MathML Form







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<apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> <ci> p </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> </apply> </apply> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <plus /> <ci> b </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> p </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> Hypergeometric2F1 </ci> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> <ci> p </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 1 </cn> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> <ci> p </ci> <apply> <times /> <cn type='integer'> 4 </cn> <ci> c </ci> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> <ci> z </ci> </apply> </apply> </apply> </apply> </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





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