Hyperbolic sine: Integration (formula 01.19.21.0417)

Sinh

$Mathematica Notation$

Elementary Functions

Sinh[z]

Integration

Indefinite integration

Involving one direct function and elementary functions

Arguments involving exponential functions

http://functions.wolfram.com/01.19.21.0417.01

Input Form

Integrate[Sinh[E^z], z] == SinhIntegral[E^z]

Standard Form

Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[RowBox[List["Sinh", "[", SuperscriptBox["\[ExponentialE]", "z"], "]"]], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List["SinhIntegral", "[", SuperscriptBox["\[ExponentialE]", "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> ∫ </mo> <mrow> <mrow> <mi> sinh </mi> <mo> ⁡ </mo> <mo> ( </mo> <msup> <mi> ⅇ </mi> <mi> z </mi> </msup> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ⅆ </mo> <mi> z </mi> </mrow> </mrow> </mrow> <mo> ⩵ </mo> <mrow> <mi> Shi </mi> <mo> ⁡ </mo> <mo> ( </mo> <msup> <mi> ⅇ </mi> <mi> z </mi> </msup> <mo> ) </mo> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <int /> <bvar> <ci> z </ci> </bvar> <apply> <sinh /> <apply> <power /> <exponentiale /> <ci> z </ci> </apply> </apply> </apply> <apply> <ci> SinhIntegral </ci> <apply> <power /> <exponentiale /> <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["Sinh", "[", SuperscriptBox["\[ExponentialE]", "z_"], "]"]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List["SinhIntegral", "[", SuperscriptBox["\[ExponentialE]", "z"], "]"]]]]]]

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

2002-12-18