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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 sec2(c z))beta





http://functions.wolfram.com/01.11.21.0097.01









  


  










Input Form





Integrate[Sqrt[a + b Sec[c z]^2], z] == (Sqrt[2] Cos[c z] (Sqrt[b] ArcTanh[(Sqrt[2] Sqrt[b] Sin[c z])/ Sqrt[a + 2 b + a Cos[2 c z]]] (a + 2 b + a Cos[2 c z]) + Sqrt[a] Sqrt[a + b] ArcSin[(Sqrt[a] Sin[c z])/Sqrt[a + b]] Sqrt[a + 2 b + a Cos[2 c z]] Sqrt[(a + 2 b + a Cos[2 c z])/(a + b)]) Sqrt[a + b Sec[c z]^2])/(c (a + 2 b + a Cos[2 c z])^(3/2))










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










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





2002-10-15





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