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Tan






Mathematica Notation

Traditional Notation









Elementary Functions > Tan[z] > Integration > Indefinite integration > Involving functions of the direct function and trigonometric functions > Involving powers of the direct function and trigonometric functions > Involving sin and cos





http://functions.wolfram.com/01.08.21.0197.01









  


  










Input Form





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










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










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





2002-12-18





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