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variants of this functions
UnitStep




Mathematica Notation

Traditional Notation









Generalized Functions > UnitStep[x1,x2,...] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving power function





http://functions.wolfram.com/14.02.21.0002.01









  


  








Input Form





Integrate[Subscript[x, 1]^(\[Alpha] - 1) UnitStep[Subscript[x, 1], Subscript[x, 2], \[Ellipsis]], Subscript[x, 1]] == (Subscript[x, 1]^\[Alpha]/\[Alpha]) UnitStep[Subscript[x, 1], Subscript[x, 2], \[Ellipsis]]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[RowBox[List[SubsuperscriptBox["x", "1", RowBox[List["\[Alpha]", "-", "1"]]], " ", RowBox[List["UnitStep", "[", RowBox[List[SubscriptBox["x", "1"], ",", SubscriptBox["x", "2"], ",", "\[Ellipsis]"]], "]"]]]], RowBox[List["\[DifferentialD]", SubscriptBox["x", "1"]]]]]]], "\[Equal]", RowBox[List[FractionBox[RowBox[List[SubsuperscriptBox["x", "1", "\[Alpha]"], " "]], "\[Alpha]"], RowBox[List["UnitStep", "[", RowBox[List[SubscriptBox["x", "1"], ",", SubscriptBox["x", "2"], ",", "\[Ellipsis]"]], "]"]]]]]]]]








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> <msubsup> <mi> x </mi> <mn> 1 </mn> <mrow> <mi> &#945; </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msubsup> <mo> &#8290; </mo> <mrow> <semantics> <mi> &#952; </mi> <annotation-xml encoding='MathML-Content'> <ci> UnitStep </ci> </annotation-xml> </semantics> <mo> ( </mo> <mrow> <msub> <mi> x </mi> <mn> 1 </mn> </msub> <mo> , </mo> <msub> <mi> x </mi> <mn> 2 </mn> </msub> <mo> , </mo> <mo> &#8230; </mo> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> &#8290; </mo> <mrow> <mo> &#8518; </mo> <msub> <mi> x </mi> <mn> 1 </mn> </msub> </mrow> </mrow> </mrow> <mo> &#10869; </mo> <mrow> <mfrac> <msubsup> <mi> x </mi> <mn> 1 </mn> <mi> &#945; </mi> </msubsup> <mi> &#945; </mi> </mfrac> <mo> &#8290; </mo> <mrow> <semantics> <mi> &#952; </mi> <annotation-xml encoding='MathML-Content'> <ci> UnitStep </ci> </annotation-xml> </semantics> <mo> ( </mo> <mrow> <msub> <mi> x </mi> <mn> 1 </mn> </msub> <mo> , </mo> <msub> <mi> x </mi> <mn> 2 </mn> </msub> <mo> , </mo> <mo> &#8230; </mo> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <int /> <bvar> <apply> <ci> Subscript </ci> <ci> x </ci> <cn type='integer'> 1 </cn> </apply> </bvar> <apply> <times /> <apply> <power /> <apply> <ci> Subscript </ci> <ci> x </ci> <cn type='integer'> 1 </cn> </apply> <apply> <plus /> <ci> &#945; </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> UnitStep </ci> <apply> <ci> Subscript </ci> <ci> x </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> x </ci> <cn type='integer'> 2 </cn> </apply> <ci> &#8230; </ci> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <apply> <power /> <apply> <ci> Subscript </ci> <ci> x </ci> <cn type='integer'> 1 </cn> </apply> <ci> &#945; </ci> </apply> <apply> <power /> <ci> &#945; </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> UnitStep </ci> <apply> <ci> Subscript </ci> <ci> x </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> x </ci> <cn type='integer'> 2 </cn> </apply> <ci> &#8230; </ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[RowBox[List[SubsuperscriptBox["x_", "1", RowBox[List["\[Alpha]_", "-", "1"]]], " ", RowBox[List["UnitStep", "[", RowBox[List[SubscriptBox["x_", "1"], ",", SubscriptBox["x_", "2"], ",", "\[Ellipsis]_"]], "]"]]]], RowBox[List["\[DifferentialD]", SubscriptBox["x_", "1"]]]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[SubsuperscriptBox["xx", "1", "\[Alpha]"], " ", RowBox[List["UnitStep", "[", RowBox[List[SubscriptBox["xx", "1"], ",", SubscriptBox["xx", "2"], ",", "\[Ellipsis]"]], "]"]]]], "\[Alpha]"]]]]]


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





2001-10-29