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Sinh




Mathematica Notation

Traditional Notation









Elementary Functions > Sinh[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving trigonometric functions > Involving powers of sin > Involving sinmu(c z)sinh(a z)





http://functions.wolfram.com/01.19.21.0604.01









  


  








Input Form





Integrate[Sin[z]^3 Sinh[z], z] == (1/40) ((-Cosh[z]) (-15 Sin[z] + Sin[3 z]) + 3 (-5 Cos[z] + Cos[3 z]) Sinh[z])








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[SuperscriptBox[RowBox[List["Sin", "[", "z", "]"]], "3"], " ", RowBox[List["Sinh", "[", "z", "]"]], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[FractionBox["1", "40"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", RowBox[List["Cosh", "[", "z", "]"]]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "15"]], " ", RowBox[List["Sin", "[", "z", "]"]]]], "+", RowBox[List["Sin", "[", RowBox[List["3", " ", "z"]], "]"]]]], ")"]]]], "+", RowBox[List["3", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "5"]], " ", RowBox[List["Cos", "[", "z", "]"]]]], "+", RowBox[List["Cos", "[", RowBox[List["3", " ", "z"]], "]"]]]], ")"]], " ", RowBox[List["Sinh", "[", "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> <mrow> <mrow> <mrow> <msup> <mi> sin </mi> <mn> 3 </mn> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> sinh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> &#8290; </mo> <mrow> <mo> &#8518; </mo> <mi> z </mi> </mrow> </mrow> </mrow> <mo> &#10869; </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 40 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> cos </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <mn> 5 </mn> <mo> &#8290; </mo> <mrow> <mi> cos </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> sinh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mrow> <mi> cosh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <mn> 15 </mn> <mo> &#8290; </mo> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <int /> <bvar> <ci> z </ci> </bvar> <apply> <times /> <apply> <power /> <apply> <sin /> <ci> z </ci> </apply> <cn type='integer'> 3 </cn> </apply> <apply> <sinh /> <ci> z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 40 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 3 </cn> <apply> <plus /> <apply> <cos /> <apply> <times /> <cn type='integer'> 3 </cn> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 5 </cn> <apply> <cos /> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <sinh /> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <cosh /> <ci> z </ci> </apply> <apply> <plus /> <apply> <sin /> <apply> <times /> <cn type='integer'> 3 </cn> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 15 </cn> <apply> <sin /> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["Sin", "[", "z_", "]"]], "3"], " ", RowBox[List["Sinh", "[", "z_", "]"]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox["1", "40"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", RowBox[List["Cosh", "[", "z", "]"]]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "15"]], " ", RowBox[List["Sin", "[", "z", "]"]]]], "+", RowBox[List["Sin", "[", RowBox[List["3", " ", "z"]], "]"]]]], ")"]]]], "+", RowBox[List["3", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "5"]], " ", RowBox[List["Cos", "[", "z", "]"]]]], "+", RowBox[List["Cos", "[", RowBox[List["3", " ", "z"]], "]"]]]], ")"]], " ", RowBox[List["Sinh", "[", "z", "]"]]]]]], ")"]]]]]]]]


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





2002-12-18