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Cos




Mathematica Notation

Traditional Notation









Elementary Functions > Cos[z] > Integration > Indefinite integration > Involving functions of the direct function and trigonometric functions > Involving algebraic functions of the direct function and trigonometric functions > Involving algebraic functions of sin > Involving (a sin2(e z)+b cos2(e z))beta





http://functions.wolfram.com/01.07.21.2402.01









  


  








Input Form





Integrate[Cos[e z] Sqrt[a Sin[e z]^2 + b Cos[e z]^2], z] == (1/(4 Sqrt[2] (a - b) e)) (Csc[e z] ((a - b) Sqrt[a + b + (-a + b) Cos[2 e z]] - (a - b) Cos[2 e z] Sqrt[a + b + (-a + b) Cos[2 e z]] + 2 Sqrt[2] b Log[Sqrt[a + b + (-a + b) Cos[2 e z]] + Sqrt[2] Sqrt[(a - b) Sin[e z]^2]] Sqrt[(a - b) Sin[e z]^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[RowBox[List[RowBox[List["Cos", "[", RowBox[List["e_", " ", "z_"]], "]"]], " ", SqrtBox[RowBox[List[RowBox[List["a_", " ", SuperscriptBox[RowBox[List["Sin", "[", RowBox[List["e_", " ", "z_"]], "]"]], "2"]]], "+", RowBox[List["b_", " ", SuperscriptBox[RowBox[List["Cos", "[", RowBox[List["e_", " ", "z_"]], "]"]], "2"]]]]]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["Csc", "[", RowBox[List["e", " ", "z"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["a", "-", "b"]], ")"]], " ", SqrtBox[RowBox[List["a", "+", "b", "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "+", "b"]], ")"]], " ", RowBox[List["Cos", "[", RowBox[List["2", " ", "e", " ", "z"]], "]"]]]]]]]]], "-", RowBox[List[RowBox[List["(", RowBox[List["a", "-", "b"]], ")"]], " ", RowBox[List["Cos", "[", RowBox[List["2", " ", "e", " ", "z"]], "]"]], " ", SqrtBox[RowBox[List["a", "+", "b", "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "+", "b"]], ")"]], " ", RowBox[List["Cos", "[", RowBox[List["2", " ", "e", " ", "z"]], "]"]]]]]]]]], "+", RowBox[List["2", " ", SqrtBox["2"], " ", "b", " ", RowBox[List["Log", "[", RowBox[List[SqrtBox[RowBox[List["a", "+", "b", "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "+", "b"]], ")"]], " ", RowBox[List["Cos", "[", RowBox[List["2", " ", "e", " ", "z"]], "]"]]]]]]], "+", RowBox[List[SqrtBox["2"], " ", SqrtBox[RowBox[List[RowBox[List["(", RowBox[List["a", "-", "b"]], ")"]], " ", SuperscriptBox[RowBox[List["Sin", "[", RowBox[List["e", " ", "z"]], "]"]], "2"]]]]]]]], "]"]], " ", SqrtBox[RowBox[List[RowBox[List["(", RowBox[List["a", "-", "b"]], ")"]], " ", SuperscriptBox[RowBox[List["Sin", "[", RowBox[List["e", " ", "z"]], "]"]], "2"]]]]]]]], ")"]]]], RowBox[List["4", " ", SqrtBox["2"], " ", RowBox[List["(", RowBox[List["a", "-", "b"]], ")"]], " ", "e"]]]]]]]


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





2002-12-18