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Cot






Mathematica Notation

Traditional Notation









Elementary Functions > Cot[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving trigonometric functions > Involving algebraic functions of sin > Involving (a+b sin(c z))beta





http://functions.wolfram.com/01.09.21.0063.01









  


  










Input Form





Integrate[Sqrt[a + a Sin[c z]] Cot[c z], z] == ((2 Cos[(c z)/2] + Log[-1 + Cos[(c z)/2] + Sin[(c z)/2]] - Log[1 + Cos[(c z)/2] + Sin[(c z)/2]] + 2 Sin[(c z)/2]) Sqrt[a (1 + Sin[c z])])/(c (Cos[(c z)/2] + Sin[(c z)/2]))










Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[RowBox[List[SqrtBox[RowBox[List["a_", "+", RowBox[List["a_", " ", RowBox[List["Sin", "[", RowBox[List["c_", " ", "z_"]], "]"]]]]]]], " ", RowBox[List["Cot", "[", RowBox[List["c_", " ", "z_"]], "]"]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["2", " ", RowBox[List["Cos", "[", FractionBox[RowBox[List["c", " ", "z"]], "2"], "]"]]]], "+", RowBox[List["Log", "[", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["Cos", "[", FractionBox[RowBox[List["c", " ", "z"]], "2"], "]"]], "+", RowBox[List["Sin", "[", FractionBox[RowBox[List["c", " ", "z"]], "2"], "]"]]]], "]"]], "-", RowBox[List["Log", "[", RowBox[List["1", "+", RowBox[List["Cos", "[", FractionBox[RowBox[List["c", " ", "z"]], "2"], "]"]], "+", RowBox[List["Sin", "[", FractionBox[RowBox[List["c", " ", "z"]], "2"], "]"]]]], "]"]], "+", RowBox[List["2", " ", RowBox[List["Sin", "[", FractionBox[RowBox[List["c", " ", "z"]], "2"], "]"]]]]]], ")"]], " ", SqrtBox[RowBox[List["a", " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["Sin", "[", RowBox[List["c", " ", "z"]], "]"]]]], ")"]]]]]]], RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["Cos", "[", FractionBox[RowBox[List["c", " ", "z"]], "2"], "]"]], "+", RowBox[List["Sin", "[", FractionBox[RowBox[List["c", " ", "z"]], "2"], "]"]]]], ")"]]]]]]]]]










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





2002-12-18