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variants of this functions
Log




Mathematica Notation

Traditional Notation









Elementary Functions > Log[z] > Integration > Indefinite integration > Involving the direct function





http://functions.wolfram.com/01.04.21.0025.01









  


  








Input Form





Integrate[Log[Cos[z]] Tan[z], z] == (-(1/2)) Log[Cos[z]]^2








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[RowBox[List["Log", "[", RowBox[List["Cos", "[", "z", "]"]], "]"]], RowBox[List["Tan", "[", "z", "]"]], RowBox[List["\[DifferentialD]", " ", "z"]]]]]], "\[Equal]", RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], " ", SuperscriptBox[RowBox[List["Log", "[", RowBox[List["Cos", "[", "z", "]"]], "]"]], "2"]]]]]]]








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> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> cos </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> tan </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> <mrow> <mo> - </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> &#8290; </mo> <mrow> <msup> <mi> log </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mrow> <mi> cos </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <int /> <bvar> <ci> z </ci> </bvar> <apply> <times /> <apply> <ln /> <apply> <cos /> <ci> z </ci> </apply> </apply> <apply> <tan /> <ci> z </ci> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <ln /> <apply> <cos /> <ci> z </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[RowBox[List[RowBox[List["Log", "[", RowBox[List["Cos", "[", "z_", "]"]], "]"]], " ", RowBox[List["Tan", "[", "z_", "]"]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], " ", SuperscriptBox[RowBox[List["Log", "[", RowBox[List["Cos", "[", "z", "]"]], "]"]], "2"]]]]]]]


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





2001-10-29