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Coth




Mathematica Notation

Traditional Notation









Elementary Functions > Coth[z] > Integration > Definite integration > For the direct function itself





http://functions.wolfram.com/01.22.21.0009.01









  


  








Input Form





Integrate[Coth[t], {t, a, b}] == Log[Sinh[b]] - Log[Sinh[a]]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[SubsuperscriptBox["\[Integral]", "a", "b"], " ", RowBox[List[RowBox[List["Coth", "[", "t", "]"]], RowBox[List["\[DifferentialD]", "t"]]]]]], "\[Equal]", RowBox[List[RowBox[List["Log", "[", RowBox[List["Sinh", "[", "b", "]"]], "]"]], "-", RowBox[List["Log", "[", RowBox[List["Sinh", "[", "a", "]"]], "]"]]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <msubsup> <mo> &#8747; </mo> <mi> a </mi> <mi> b </mi> </msubsup> <mrow> <mrow> <mi> coth </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> t </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> &#8518; </mo> <mi> t </mi> </mrow> </mrow> </mrow> <mo> &#10869; </mo> <mrow> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> sinh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> b </mi> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> sinh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> a </mi> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <int /> <bvar> <ci> t </ci> </bvar> <lowlimit> <ci> a </ci> </lowlimit> <uplimit> <ci> b </ci> </uplimit> <apply> <coth /> <ci> t </ci> </apply> </apply> <apply> <plus /> <apply> <ln /> <apply> <sinh /> <ci> b </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ln /> <apply> <sinh /> <ci> a </ci> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SubsuperscriptBox["\[Integral]", "a_", "b_"], RowBox[List[RowBox[List["Coth", "[", "t_", "]"]], RowBox[List["\[DifferentialD]", "t_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["Log", "[", RowBox[List["Sinh", "[", "b", "]"]], "]"]], "-", RowBox[List["Log", "[", RowBox[List["Sinh", "[", "a", "]"]], "]"]]]]]]]]


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





2001-10-29