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variants of this functions
ProductLog




Mathematica Notation

Traditional Notation









Elementary Functions > ProductLog[z] > Integration > Indefinite integration > Involving only one direct function





http://functions.wolfram.com/01.31.21.0001.01









  


  








Input Form





Integrate[ProductLog[z], z] == (z (1 - ProductLog[z] + ProductLog[z]^2))/ ProductLog[z]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[RowBox[List["ProductLog", "[", "z", "]"]], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", FractionBox[RowBox[List["z", " ", RowBox[List["(", RowBox[List["1", "-", RowBox[List["ProductLog", "[", "z", "]"]], "+", SuperscriptBox[RowBox[List["ProductLog", "[", "z", "]"]], "2"]]], ")"]]]], RowBox[List["ProductLog", "[", "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> <mi> W </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> &#8518; </mo> <mi> z </mi> </mrow> </mrow> </mrow> <mo> &#10869; </mo> <mfrac> <mrow> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mrow> <mi> W </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mo> - </mo> <mrow> <mi> W </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mi> W </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mfrac> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <int /> <bvar> <ci> z </ci> </bvar> <apply> <ci> W </ci> <ci> z </ci> </apply> </apply> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <power /> <apply> <ci> W </ci> <ci> z </ci> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> W </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <apply> <ci> W </ci> <ci> z </ci> </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[RowBox[List["ProductLog", "[", "z_", "]"]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["z", " ", RowBox[List["(", RowBox[List["1", "-", RowBox[List["ProductLog", "[", "z", "]"]], "+", SuperscriptBox[RowBox[List["ProductLog", "[", "z", "]"]], "2"]]], ")"]]]], RowBox[List["ProductLog", "[", "z", "]"]]]]]]]


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





2001-10-29