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Csc






Mathematica Notation

Traditional Notation









Elementary Functions > Csc[z] > Integration > Indefinite integration > Involving functions of the direct function > Involving algebraic functions of the direct function > Involving ((a+b csc(c z))n)beta





http://functions.wolfram.com/01.10.21.0095.01









  


  










Input Form





Integrate[Csc[c z] ((a + b Csc[c z])^n)^\[Beta], z] == (-(1/(b c (1 + n \[Beta])))) (AppellF1[1 + n \[Beta], 1/2, 1/2, 2 + n \[Beta], (a + b Csc[c z])/(a + b), (a + b Csc[c z])/(a - b)] Sqrt[(b (1 + Csc[c z]))/(-a + b)] Sqrt[(b - b Csc[c z])/(a + b)] ((a + b Csc[c z])^n)^\[Beta] Sec[c z] (b + a Sin[c z]))










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[RowBox[List["Csc", "[", RowBox[List["c_", " ", "z_"]], "]"]], " ", SuperscriptBox[RowBox[List["(", SuperscriptBox[RowBox[List["(", RowBox[List["a_", "+", RowBox[List["b_", " ", RowBox[List["Csc", "[", RowBox[List["c_", " ", "z_"]], "]"]]]]]], ")"]], "n_"], ")"]], "\[Beta]_"]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List["-", FractionBox[RowBox[List[RowBox[List["AppellF1", "[", RowBox[List[RowBox[List["1", "+", RowBox[List["n", " ", "\[Beta]"]]]], ",", FractionBox["1", "2"], ",", FractionBox["1", "2"], ",", RowBox[List["2", "+", RowBox[List["n", " ", "\[Beta]"]]]], ",", FractionBox[RowBox[List["a", "+", RowBox[List["b", " ", RowBox[List["Csc", "[", RowBox[List["c", " ", "z"]], "]"]]]]]], RowBox[List["a", "+", "b"]]], ",", FractionBox[RowBox[List["a", "+", RowBox[List["b", " ", RowBox[List["Csc", "[", RowBox[List["c", " ", "z"]], "]"]]]]]], RowBox[List["a", "-", "b"]]]]], "]"]], " ", SqrtBox[FractionBox[RowBox[List["b", " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["Csc", "[", RowBox[List["c", " ", "z"]], "]"]]]], ")"]]]], RowBox[List[RowBox[List["-", "a"]], "+", "b"]]]], " ", SqrtBox[FractionBox[RowBox[List["b", "-", RowBox[List["b", " ", RowBox[List["Csc", "[", RowBox[List["c", " ", "z"]], "]"]]]]]], RowBox[List["a", "+", "b"]]]], " ", SuperscriptBox[RowBox[List["(", SuperscriptBox[RowBox[List["(", RowBox[List["a", "+", RowBox[List["b", " ", RowBox[List["Csc", "[", RowBox[List["c", " ", "z"]], "]"]]]]]], ")"]], "n"], ")"]], "\[Beta]"], " ", RowBox[List["Sec", "[", RowBox[List["c", " ", "z"]], "]"]], " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["a", " ", RowBox[List["Sin", "[", RowBox[List["c", " ", "z"]], "]"]]]]]], ")"]]]], RowBox[List["b", " ", "c", " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["n", " ", "\[Beta]"]]]], ")"]]]]]]]]]]]










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





2002-12-18





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