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Coth






Mathematica Notation

Traditional Notation









Elementary Functions > Coth[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving hyperbolic functions > Involving sinh and cosh > Other integrals





http://functions.wolfram.com/01.22.21.0154.01









  


  










Input Form





Integrate[Sqrt[Cosh[c z] Sinh[c z]] Coth[c z], z] == (-((2 Coth[c z] (Cosh[c z] Sinh[c z])^(3/2))/(5 c (-Sinh[c z]^2)^(1/4)))) Hypergeometric2F1[5/4, 3/4, 9/4, Cosh[c z]^2]










Standard Form





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MathML Form







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</mo> <mrow> <msup> <mi> cosh </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mrow> <mi> c </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox[&quot;\[InvisiblePrefixScriptBase]&quot;, FormBox[&quot;2&quot;, TraditionalForm]], SubscriptBox[&quot;F&quot;, FormBox[&quot;1&quot;, TraditionalForm]]]], &quot;\[InvisibleApplication]&quot;, RowBox[List[&quot;(&quot;, RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox[&quot;5&quot;, &quot;4&quot;], Hypergeometric2F1], &quot;,&quot;, TagBox[FractionBox[&quot;3&quot;, &quot;4&quot;], Hypergeometric2F1]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], &quot;;&quot;, TagBox[TagBox[TagBox[FractionBox[&quot;9&quot;, &quot;4&quot;], Hypergeometric2F1], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], &quot;;&quot;, TagBox[RowBox[List[SuperscriptBox[&quot;cosh&quot;, &quot;2&quot;], &quot;(&quot;, RowBox[List[&quot;c&quot;, &quot; 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Rule Form





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





2002-12-18