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Sinh




Mathematica Notation

Traditional Notation









Elementary Functions > Sinh[z] > Integration > Indefinite integration > Involving functions of the direct function > Involving rational functions of the direct function > Involving (a+b sinh(c z))-n





http://functions.wolfram.com/01.19.21.1676.01









  


  








Input Form





Integrate[1/(I + Sinh[z])^2, z] == (Cosh[(3 z)/2] + 3 I Sinh[z/2])/ (3 (I Cosh[z/2] + Sinh[z/2])^3)








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[FractionBox["1", SuperscriptBox[RowBox[List["(", RowBox[List["\[ImaginaryI]", "+", RowBox[List["Sinh", "[", "z", "]"]]]], ")"]], "2"]], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", FractionBox[RowBox[List[RowBox[List["Cosh", "[", FractionBox[RowBox[List["3", " ", "z"]], "2"], "]"]], "+", RowBox[List["3", " ", "\[ImaginaryI]", " ", RowBox[List["Sinh", "[", FractionBox["z", "2"], "]"]]]]]], RowBox[List["3", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", RowBox[List["Cosh", "[", FractionBox["z", "2"], "]"]]]], "+", RowBox[List["Sinh", "[", FractionBox["z", "2"], "]"]]]], ")"]], "3"]]]]]]]]








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> <mrow> <mfrac> <mn> 1 </mn> <msup> <mrow> <mo> ( </mo> <mrow> <mi> &#8520; </mi> <mo> + </mo> <mrow> <mi> sinh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mfrac> <mo> &#8290; </mo> <mrow> <mo> &#8518; </mo> <mi> z </mi> </mrow> </mrow> </mrow> <mo> &#10869; </mo> <mfrac> <mrow> <mrow> <mi> cosh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mfrac> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mn> 2 </mn> </mfrac> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mrow> <mi> sinh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mfrac> <mi> z </mi> <mn> 2 </mn> </mfrac> <mo> ) </mo> </mrow> </mrow> </mrow> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mrow> <mi> cosh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mfrac> <mi> z </mi> <mn> 2 </mn> </mfrac> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mi> sinh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mfrac> <mi> z </mi> <mn> 2 </mn> </mfrac> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mn> 3 </mn> </msup> </mrow> </mfrac> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <int /> <bvar> <ci> z </ci> </bvar> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <power /> <apply> <plus /> <imaginaryi /> <apply> <sinh /> <ci> z </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <cosh /> <apply> <times /> <cn type='integer'> 3 </cn> <ci> z </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 3 </cn> <imaginaryi /> <apply> <sinh /> <apply> <times /> <ci> z </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 3 </cn> <apply> <power /> <apply> <plus /> <apply> <times /> <imaginaryi /> <apply> <cosh /> <apply> <times /> <ci> z </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <sinh /> <apply> <times /> <ci> z </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <cn type='integer'> 3 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[FractionBox["1", SuperscriptBox[RowBox[List["(", RowBox[List["\[ImaginaryI]", "+", RowBox[List["Sinh", "[", "z_", "]"]]]], ")"]], "2"]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["Cosh", "[", FractionBox[RowBox[List["3", " ", "z"]], "2"], "]"]], "+", RowBox[List["3", " ", "\[ImaginaryI]", " ", RowBox[List["Sinh", "[", FractionBox["z", "2"], "]"]]]]]], RowBox[List["3", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", RowBox[List["Cosh", "[", FractionBox["z", "2"], "]"]]]], "+", RowBox[List["Sinh", "[", FractionBox["z", "2"], "]"]]]], ")"]], "3"]]]]]]]]


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





2002-12-18