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variants of this functions
Log




Mathematica Notation

Traditional Notation









Elementary Functions > Log[z] > Integration > Definite integration > Involving related functions





http://functions.wolfram.com/01.04.21.0074.01









  


  








Input Form





Integrate[Exp[-t] Log[t], {t, 0, 1}] == -EulerGamma + ExpIntegralEi[-1]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[SubsuperscriptBox["\[Integral]", "0", "1"], RowBox[List[RowBox[List["Exp", "[", RowBox[List["-", "t"]], "]"]], RowBox[List["Log", "[", "t", "]"]], RowBox[List["\[DifferentialD]", "t"]]]]]], "\[Equal]", RowBox[List[RowBox[List["-", "EulerGamma"]], "+", RowBox[List["ExpIntegralEi", "[", RowBox[List["-", "1"]], "]"]]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <msubsup> <mo> &#8747; </mo> <mn> 0 </mn> <mn> 1 </mn> </msubsup> <mrow> <mrow> <msup> <mi> &#8519; </mi> <mrow> <mo> - </mo> <mi> t </mi> </mrow> </msup> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> t </mi> <mo> ) </mo> </mrow> </mrow> <mo> &#8290; </mo> <mrow> <mo> &#8518; </mo> <mi> t </mi> </mrow> </mrow> </mrow> <mo> &#10869; </mo> <mrow> <mrow> <mi> Ei </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> - </mo> <semantics> <mi> &#8509; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubledGamma]&quot;, Function[EulerGamma]] </annotation> </semantics> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <int /> <bvar> <ci> t </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <cn type='integer'> 1 </cn> </uplimit> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> t </ci> </apply> </apply> <apply> <ln /> <ci> t </ci> </apply> </apply> </apply> <apply> <plus /> <apply> <ci> ExpIntegralEi </ci> <cn type='integer'> -1 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <eulergamma /> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SubsuperscriptBox["\[Integral]", "0", "1"], RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["-", "t_"]]], " ", RowBox[List["Log", "[", "t_", "]"]]]], RowBox[List["\[DifferentialD]", "t_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["-", "EulerGamma"]], "+", RowBox[List["ExpIntegralEi", "[", RowBox[List["-", "1"]], "]"]]]]]]]]


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





2001-10-29