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Sec






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/01.11.21.0095.01









  


  










Input Form





Integrate[Sec[c z]/Sqrt[(a + b Sec[c z])^3], z] == -(2 Cot[(c z)/2] Sqrt[(a + b Sec[c z])/(a + b)] ((b + a Cos[c z]) EllipticE[ArcSin[Sqrt[1 - Sec[c z]]/Sqrt[2]], (2 b)/(a + b)] Sqrt[1 - Sec[c z]] Sec[c z] + b (-1 + Sec[c z]) Sqrt[1 + Sec[c z]] Sqrt[(a + b Sec[c z])/(a + b)]))/ ((a - b) c Sqrt[1 + Sec[c z]] Sqrt[(a + b Sec[c z])^3])










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[FractionBox[RowBox[List["Sec", "[", RowBox[List["c_", " ", "z_"]], "]"]], SqrtBox[SuperscriptBox[RowBox[List["(", RowBox[List["a_", "+", RowBox[List["b_", " ", RowBox[List["Sec", "[", RowBox[List["c_", " ", "z_"]], "]"]]]]]], ")"]], "3"]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List["-", FractionBox[RowBox[List["2", " ", RowBox[List["Cot", "[", FractionBox[RowBox[List["c", " ", "z"]], "2"], "]"]], " ", SqrtBox[FractionBox[RowBox[List["a", "+", RowBox[List["b", " ", RowBox[List["Sec", "[", RowBox[List["c", " ", "z"]], "]"]]]]]], RowBox[List["a", "+", "b"]]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["b", "+", RowBox[List["a", " ", RowBox[List["Cos", "[", RowBox[List["c", " ", "z"]], "]"]]]]]], ")"]], " ", RowBox[List["EllipticE", "[", RowBox[List[RowBox[List["ArcSin", "[", FractionBox[SqrtBox[RowBox[List["1", "-", RowBox[List["Sec", "[", RowBox[List["c", " ", "z"]], "]"]]]]], SqrtBox["2"]], "]"]], ",", FractionBox[RowBox[List["2", " ", "b"]], RowBox[List["a", "+", "b"]]]]], "]"]], " ", SqrtBox[RowBox[List["1", "-", RowBox[List["Sec", "[", RowBox[List["c", " ", "z"]], "]"]]]]], " ", RowBox[List["Sec", "[", RowBox[List["c", " ", "z"]], "]"]]]], "+", RowBox[List["b", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["Sec", "[", RowBox[List["c", " ", "z"]], "]"]]]], ")"]], " ", SqrtBox[RowBox[List["1", "+", RowBox[List["Sec", "[", RowBox[List["c", " ", "z"]], "]"]]]]], " ", SqrtBox[FractionBox[RowBox[List["a", "+", RowBox[List["b", " ", RowBox[List["Sec", "[", RowBox[List["c", " ", "z"]], "]"]]]]]], RowBox[List["a", "+", "b"]]]]]]]], ")"]]]], RowBox[List[RowBox[List["(", RowBox[List["a", "-", "b"]], ")"]], " ", "c", " ", SqrtBox[RowBox[List["1", "+", RowBox[List["Sec", "[", RowBox[List["c", " ", "z"]], "]"]]]]], " ", SqrtBox[SuperscriptBox[RowBox[List["(", RowBox[List["a", "+", RowBox[List["b", " ", RowBox[List["Sec", "[", RowBox[List["c", " ", "z"]], "]"]]]]]], ")"]], "3"]]]]]]]]]]]










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





2002-10-15





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