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Sin






Mathematica Notation

Traditional Notation









Elementary Functions > Sin[z] > Integration > Indefinite integration > Involving functions of the direct function > Involving algebraic functions of the direct function > Involving (a+b sin2(c z))beta sinnu(c z)





http://functions.wolfram.com/01.06.21.0981.01









  


  










Input Form





Integrate[Sin[c z]^7/Sqrt[a + b Sin[c z]^2], z] == (1/(16 c)) (-((1/(3 Sqrt[2] b^3)) (Cos[c z] Sqrt[2 a + b - b Cos[2 c z]] (15 a^2 - 19 a b + 23 b^2 + (5 a - 9 b) b Cos[2 c z] + b^2 Cos[4 c z]))) + (1/(-b)^(7/2)) ((-a + b) (5 a^2 + 2 a b + 5 b^2) Log[Sqrt[2] Sqrt[-b] Cos[c z] + Sqrt[2 a + b - b Cos[2 c z]]]))










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[SuperscriptBox[RowBox[List["Sin", "[", RowBox[List["c_", " ", "z_"]], "]"]], "7"], SqrtBox[RowBox[List["a_", "+", RowBox[List["b_", " ", SuperscriptBox[RowBox[List["Sin", "[", RowBox[List["c_", " ", "z_"]], "]"]], "2"]]]]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["-", FractionBox[RowBox[List[RowBox[List["Cos", "[", RowBox[List["c", " ", "z"]], "]"]], " ", SqrtBox[RowBox[List[RowBox[List["2", " ", "a"]], "+", "b", "-", RowBox[List["b", " ", RowBox[List["Cos", "[", RowBox[List["2", " ", "c", " ", "z"]], "]"]]]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List["15", " ", SuperscriptBox["a", "2"]]], "-", RowBox[List["19", " ", "a", " ", "b"]], "+", RowBox[List["23", " ", SuperscriptBox["b", "2"]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["5", " ", "a"]], "-", RowBox[List["9", " ", "b"]]]], ")"]], " ", "b", " ", RowBox[List["Cos", "[", RowBox[List["2", " ", "c", " ", "z"]], "]"]]]], "+", RowBox[List[SuperscriptBox["b", "2"], " ", RowBox[List["Cos", "[", RowBox[List["4", " ", "c", " ", "z"]], "]"]]]]]], ")"]]]], RowBox[List["3", " ", SqrtBox["2"], " ", SuperscriptBox["b", "3"]]]]]], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "+", "b"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["5", " ", SuperscriptBox["a", "2"]]], "+", RowBox[List["2", " ", "a", " ", "b"]], "+", RowBox[List["5", " ", SuperscriptBox["b", "2"]]]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List[RowBox[List[SqrtBox["2"], " ", SqrtBox[RowBox[List["-", "b"]]], " ", RowBox[List["Cos", "[", RowBox[List["c", " ", "z"]], "]"]]]], "+", SqrtBox[RowBox[List[RowBox[List["2", " ", "a"]], "+", "b", "-", RowBox[List["b", " ", RowBox[List["Cos", "[", RowBox[List["2", " ", "c", " ", "z"]], "]"]]]]]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["-", "b"]], ")"]], RowBox[List["7", "/", "2"]]]]]], RowBox[List["16", " ", "c"]]]]]]]










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





2002-12-18