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Sech




Mathematica Notation

Traditional Notation









Elementary Functions > Sech[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving hyperbolic functions > Involving algebraic functions of cosh and tanh





http://functions.wolfram.com/01.24.21.0147.01









  


  








Input Form





Integrate[Tanh[z] (Cosh[z] + Sech[z]), z] == Sinh[z] Tanh[z]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[RowBox[List["Tanh", "[", "z", "]"]], RowBox[List["(", RowBox[List[RowBox[List["Cosh", "[", "z", "]"]], "+", RowBox[List["Sech", "[", "z", "]"]]]], ")"]], " ", RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[RowBox[List["Sinh", "[", "z", "]"]], " ", RowBox[List["Tanh", "[", "z", "]"]]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mo> &#8747; </mo> <mtext> </mtext> <mrow> <mrow> <mi> tanh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> cosh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <mi> sech </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> &#8518; </mo> <mi> z </mi> </mrow> </mrow> </mrow> <mo> &#10869; </mo> <mrow> <mrow> <mi> sinh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> tanh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <int /> <bvar> <ci> z </ci> </bvar> <apply> <times /> <apply> <tanh /> <ci> z </ci> </apply> <apply> <plus /> <apply> <cosh /> <ci> z </ci> </apply> <apply> <sech /> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <sinh /> <ci> z </ci> </apply> <apply> <tanh /> <ci> z </ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[RowBox[List[RowBox[List["Tanh", "[", "z_", "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["Cosh", "[", "z_", "]"]], "+", RowBox[List["Sech", "[", "z_", "]"]]]], ")"]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["Sinh", "[", "z", "]"]], " ", RowBox[List["Tanh", "[", "z", "]"]]]]]]]]


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





2002-12-18