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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 powers of sinh and exp > Involving ep z sinhu(b z) tanh(c z)





http://functions.wolfram.com/01.21.21.0152.01









  


  










Input Form





Integrate[E^(p z) Sinh[c z]^\[Mu] Tanh[c z], z] == (-(1/(p - c \[Mu]))) ((E^(p z) AppellF1[(p - c \[Mu])/(2 c), -1 - \[Mu], 1, (1/2) (2 + p/c - \[Mu]), E^(2 c z), -E^(2 c z)] Sinh[c z]^\[Mu])/ (1 - E^(2 c z))^\[Mu])










Standard Form





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MathML Form







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</mo> <mi> z </mi> </mrow> </msup> </mrow> <mo> ) </mo> </mrow> <mrow> <mo> - </mo> <mi> &#956; </mi> </mrow> </msup> <mo> &#8290; </mo> <mrow> <msup> <mi> sinh </mi> <mi> &#956; </mi> </msup> <mo> ( </mo> <mrow> <mi> c </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mi> p </mi> <mo> - </mo> <mrow> <mi> c </mi> <mo> &#8290; </mo> <mi> &#956; </mi> </mrow> </mrow> </mfrac> </mrow> <mo> &#8290; </mo> <mrow> <semantics> <msub> <mi> F </mi> <mn> 1 </mn> </msub> <annotation-xml encoding='MathML-Content'> <ci> AppellF1 </ci> </annotation-xml> </semantics> <mo> ( </mo> <mrow> <mrow> <mfrac> <mrow> <mi> p </mi> <mo> - </mo> <mrow> <mi> c </mi> <mo> &#8290; </mo> <mi> &#956; </mi> </mrow> </mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> c </mi> </mrow> </mfrac> <mo> ; </mo> <mrow> <mrow> <mo> - </mo> <mi> &#956; </mi> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </mrow> <mo> , </mo> <mrow> <mn> 1 </mn> <mo> ; </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> &#8290; 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</ci> </apply> </apply> <apply> <power /> <apply> <sinh /> <apply> <times /> <ci> c </ci> <ci> z </ci> </apply> </apply> <ci> &#956; </ci> </apply> <apply> <power /> <apply> <plus /> <ci> p </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> c </ci> <ci> &#956; </ci> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <ci> AppellF1 </ci> <apply> <times /> <apply> <plus /> <ci> p </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> c </ci> <ci> &#956; </ci> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#956; </ci> </apply> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <plus /> <apply> <times /> <ci> p </ci> <apply> <power /> <ci> c </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#956; 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Rule Form





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





2002-12-18





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