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Tan




Mathematica Notation

Traditional Notation









Elementary Functions > Tan[z] > Integration > Definite integration > Involving the direct function





http://functions.wolfram.com/01.08.21.0011.01









  


  








Input Form





Integrate[Tan[t]^n, {t, 0, Pi/2}] == (1/2) Pi Sec[(n Pi)/2] /; Abs[Re[n]] < 1








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[SubsuperscriptBox["\[Integral]", "0", FractionBox["\[Pi]", "2"]], RowBox[List[SuperscriptBox[RowBox[List["Tan", "[", "t", "]"]], "n"], RowBox[List["\[DifferentialD]", "t"]]]]]], "\[Equal]", RowBox[List[FractionBox["1", "2"], " ", "\[Pi]", " ", RowBox[List["Sec", "[", FractionBox[RowBox[List["n", " ", "\[Pi]"]], "2"], "]"]]]]]], "/;", RowBox[List[RowBox[List["Abs", "[", RowBox[List["Re", "[", "n", "]"]], "]"]], "<", "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> <mrow> <msubsup> <mo> &#8747; </mo> <mn> 0 </mn> <mfrac> <mi> &#960; </mi> <mn> 2 </mn> </mfrac> </msubsup> <mrow> <mrow> <msup> <mi> tan </mi> <mi> n </mi> </msup> <mo> ( </mo> <mi> t </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> &#8518; </mo> <mi> t </mi> </mrow> </mrow> </mrow> <mo> &#10869; </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> &#8290; </mo> <mi> &#960; </mi> <mo> &#8290; </mo> <mrow> <mi> sec </mi> <mo> &#8289; </mo> <mo> ( </mo> <mfrac> <mrow> <mi> n </mi> <mo> &#8290; </mo> <mi> &#960; </mi> </mrow> <mn> 2 </mn> </mfrac> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <semantics> <mo> &#10072; </mo> <annotation encoding='Mathematica'> &quot;\[LeftBracketingBar]&quot; </annotation> </semantics> <mrow> <mi> Re </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> n </mi> <mo> ) </mo> </mrow> <semantics> <mo> &#10072; </mo> <annotation encoding='Mathematica'> &quot;\[RightBracketingBar]&quot; </annotation> </semantics> </mrow> <mo> &lt; </mo> <mn> 1 </mn> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <int /> <bvar> <ci> t </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <apply> <times /> <pi /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </uplimit> <apply> <power /> <apply> <tan /> <ci> t </ci> </apply> <ci> n </ci> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <pi /> <apply> <sec /> <apply> <times /> <ci> n </ci> <pi /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <lt /> <apply> <abs /> <apply> <real /> <ci> n </ci> </apply> </apply> <cn type='integer'> 1 </cn> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SubsuperscriptBox["\[Integral]", "0", FractionBox["\[Pi]", "2"]], RowBox[List[SuperscriptBox[RowBox[List["Tan", "[", "t_", "]"]], "n_"], RowBox[List["\[DifferentialD]", "t_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", "\[Pi]", " ", RowBox[List["Sec", "[", FractionBox[RowBox[List["n", " ", "\[Pi]"]], "2"], "]"]]]], "/;", RowBox[List[RowBox[List["Abs", "[", RowBox[List["Re", "[", "n", "]"]], "]"]], "<", "1"]]]]]]]]


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





2001-10-29