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Tan




Mathematica Notation

Traditional Notation









Elementary Functions > Tan[z] > Integration > Indefinite integration > Involving functions of the direct function > Involving algebraic functions of the direct function > Involving ((a+b tan2(c z))n)beta





http://functions.wolfram.com/01.08.21.0125.01









  


  








Input Form





Integrate[Tan[c z]/Sqrt[(a + b Tan[c z]^2)^3], z] == ((a + b + (a - b) Cos[2 c z]) (a - b + (a - b) Cos[2 c z] - Sqrt[2] Sqrt[(a - b) Cos[c z]^2] Sqrt[a + b + (a - b) Cos[2 c z]] Log[Sqrt[2] Sqrt[(a - b) Cos[c z]^2] + Sqrt[a + b + (a - b) Cos[2 c z]]]) Sec[c z]^4)/ (4 (a - b)^2 c Sqrt[(a + b Tan[c z]^2)^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["Tan", "[", RowBox[List["c_", " ", "z_"]], "]"]], SqrtBox[SuperscriptBox[RowBox[List["(", RowBox[List["a_", "+", RowBox[List["b_", " ", SuperscriptBox[RowBox[List["Tan", "[", RowBox[List["c_", " ", "z_"]], "]"]], "2"]]]]], ")"]], "3"]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["a", "+", "b", "+", RowBox[List[RowBox[List["(", RowBox[List["a", "-", "b"]], ")"]], " ", RowBox[List["Cos", "[", RowBox[List["2", " ", "c", " ", "z"]], "]"]]]]]], ")"]], " ", RowBox[List["(", RowBox[List["a", "-", "b", "+", RowBox[List[RowBox[List["(", RowBox[List["a", "-", "b"]], ")"]], " ", RowBox[List["Cos", "[", RowBox[List["2", " ", "c", " ", "z"]], "]"]]]], "-", RowBox[List[SqrtBox["2"], " ", SqrtBox[RowBox[List[RowBox[List["(", RowBox[List["a", "-", "b"]], ")"]], " ", SuperscriptBox[RowBox[List["Cos", "[", RowBox[List["c", " ", "z"]], "]"]], "2"]]]], " ", SqrtBox[RowBox[List["a", "+", "b", "+", RowBox[List[RowBox[List["(", RowBox[List["a", "-", "b"]], ")"]], " ", RowBox[List["Cos", "[", RowBox[List["2", " ", "c", " ", "z"]], "]"]]]]]]], " ", RowBox[List["Log", "[", RowBox[List[RowBox[List[SqrtBox["2"], " ", SqrtBox[RowBox[List[RowBox[List["(", RowBox[List["a", "-", "b"]], ")"]], " ", SuperscriptBox[RowBox[List["Cos", "[", RowBox[List["c", " ", "z"]], "]"]], "2"]]]]]], "+", SqrtBox[RowBox[List["a", "+", "b", "+", RowBox[List[RowBox[List["(", RowBox[List["a", "-", "b"]], ")"]], " ", RowBox[List["Cos", "[", RowBox[List["2", " ", "c", " ", "z"]], "]"]]]]]]]]], "]"]]]]]], ")"]], " ", SuperscriptBox[RowBox[List["Sec", "[", RowBox[List["c", " ", "z"]], "]"]], "4"]]], RowBox[List["4", " ", SuperscriptBox[RowBox[List["(", RowBox[List["a", "-", "b"]], ")"]], "2"], " ", "c", " ", SqrtBox[SuperscriptBox[RowBox[List["(", RowBox[List["a", "+", RowBox[List["b", " ", SuperscriptBox[RowBox[List["Tan", "[", RowBox[List["c", " ", "z"]], "]"]], "2"]]]]], ")"]], "3"]]]]]]]]]


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





2002-12-18