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Tan






Mathematica Notation

Traditional Notation









Elementary Functions > Tan[z] > Integration > Indefinite integration > Involving functions of the direct function and trigonometric functions > Involving powers of the direct function and trigonometric functions > Involving sin and cos





http://functions.wolfram.com/01.08.21.0194.01









  


  










Input Form





Integrate[Sin[c z] (a + b Cos[2 c z])^\[Beta] Tan[c z]^\[Nu], z] == ((1/(c (2 + \[Nu]))) (a + b Cos[2 c z])^\[Beta] Sec[c z] (Sec[c z]^2)^(-(1/2) + \[Beta]) Tan[c z]^(2 + \[Nu]) AppellF1[(2 + \[Nu])/2, 3/2 + \[Beta], -\[Beta], (4 + \[Nu])/2, -Tan[c z]^2, -(((a - b) Tan[c z]^2)/(a + b))])/ (1 - ((-a + b) Tan[c z]^2)/(a + b))^\[Beta]










Standard Form





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MathML Form







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</ci> </apply> <apply> <power /> <apply> <tan /> <apply> <times /> <ci> c </ci> <ci> z </ci> </apply> </apply> <ci> &#957; </ci> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <ci> c </ci> <apply> <plus /> <ci> &#957; </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <apply> <plus /> <ci> a </ci> <apply> <times /> <ci> b </ci> <apply> <cos /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> <ci> z </ci> </apply> </apply> </apply> </apply> <ci> &#946; </ci> </apply> <apply> <sec /> <apply> <times /> <ci> c </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <power /> <apply> <sec /> <apply> <times /> <ci> c </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <plus /> <ci> &#946; </ci> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <tan /> <apply> <times /> <ci> c </ci> <ci> z </ci> </apply> </apply> <apply> <plus /> <ci> &#957; 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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[RowBox[List[RowBox[List["Sin", "[", RowBox[List["c_", " ", "z_"]], "]"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["a_", "+", RowBox[List["b_", " ", RowBox[List["Cos", "[", RowBox[List["2", " ", "c_", " ", "z_"]], "]"]]]]]], ")"]], "\[Beta]_"], " ", SuperscriptBox[RowBox[List["Tan", "[", RowBox[List["c_", " ", "z_"]], "]"]], "\[Nu]_"]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["a", "+", RowBox[List["b", " ", RowBox[List["Cos", "[", RowBox[List["2", " ", "c", " ", "z"]], "]"]]]]]], ")"]], "\[Beta]"], " ", RowBox[List["Sec", "[", RowBox[List["c", " ", "z"]], "]"]], " ", SuperscriptBox[RowBox[List["(", SuperscriptBox[RowBox[List["Sec", "[", RowBox[List["c", " ", "z"]], "]"]], "2"], ")"]], RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], "+", "\[Beta]"]]], " ", SuperscriptBox[RowBox[List["Tan", "[", RowBox[List["c", " ", "z"]], "]"]], RowBox[List["2", "+", "\[Nu]"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "+", "b"]], ")"]], " ", SuperscriptBox[RowBox[List["Tan", "[", RowBox[List["c", " ", "z"]], "]"]], "2"]]], RowBox[List["a", "+", "b"]]]]], ")"]], RowBox[List["-", "\[Beta]"]]], " ", RowBox[List["AppellF1", "[", RowBox[List[FractionBox[RowBox[List["2", "+", "\[Nu]"]], "2"], ",", RowBox[List[FractionBox["3", "2"], "+", "\[Beta]"]], ",", RowBox[List["-", "\[Beta]"]], ",", FractionBox[RowBox[List["4", "+", "\[Nu]"]], "2"], ",", RowBox[List["-", SuperscriptBox[RowBox[List["Tan", "[", RowBox[List["c", " ", "z"]], "]"]], "2"]]], ",", RowBox[List["-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["a", "-", "b"]], ")"]], " ", SuperscriptBox[RowBox[List["Tan", "[", RowBox[List["c", " ", "z"]], "]"]], "2"]]], RowBox[List["a", "+", "b"]]]]]]], "]"]]]], RowBox[List["c", " ", RowBox[List["(", RowBox[List["2", "+", "\[Nu]"]], ")"]]]]]]]]]










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





2002-12-18





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