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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))beta





http://functions.wolfram.com/01.11.21.0091.01









  


  










Input Form





Integrate[Sec[c z] Sqrt[a + b Sec[c z]], z] == -(2 I Cot[(c z)/2] (EllipticE[I ArcSinh[Sqrt[-(1/(a + b))] Sqrt[a + b Sec[c z]]], (a + b)/(a - b)] - EllipticF[ I ArcSinh[Sqrt[-(1/(a + b))] Sqrt[a + b Sec[c z]]], (a + b)/(a - b)]) Sqrt[(b - b Sec[c z])/(a + b)])/(Sqrt[-(1/(a + b))] c Sqrt[(b (1 + Sec[c z]))/(-a + b)])










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










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





2002-10-15