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Cos






Mathematica Notation

Traditional Notation









Elementary Functions > Cos[z] > Integration > Indefinite integration > Involving functions of the direct function and a power function > Involving powers of the direct function and a power function > Involving powers of sin and power > Involving zalpha-1 cosnu(a z+b)





http://functions.wolfram.com/01.07.21.1468.01









  


  










Input Form





Integrate[z^2 Cos[a z + b]^5, z] == (1/(54000 a^3)) (67500 a z Cos[b + a z] + 3750 a z Cos[3 (b + a z)] + 270 a z Cos[5 (b + a z)] - 67500 Sin[b + a z] + 33750 a^2 z^2 Sin[b + a z] - 1250 Sin[3 (b + a z)] + 5625 a^2 z^2 Sin[3 (b + a z)] - 54 Sin[5 (b + a z)] + 675 a^2 z^2 Sin[5 (b + a 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[RowBox[List[SuperscriptBox["z_", "2"], " ", SuperscriptBox[RowBox[List["Cos", "[", RowBox[List[RowBox[List["a_", " ", "z_"]], "+", "b_"]], "]"]], "5"]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["67500", " ", "a", " ", "z", " ", RowBox[List["Cos", "[", RowBox[List["b", "+", RowBox[List["a", " ", "z"]]]], "]"]]]], "+", RowBox[List["3750", " ", "a", " ", "z", " ", RowBox[List["Cos", "[", RowBox[List["3", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["a", " ", "z"]]]], ")"]]]], "]"]]]], "+", RowBox[List["270", " ", "a", " ", "z", " ", RowBox[List["Cos", "[", RowBox[List["5", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["a", " ", "z"]]]], ")"]]]], "]"]]]], "-", RowBox[List["67500", " ", RowBox[List["Sin", "[", RowBox[List["b", "+", RowBox[List["a", " ", "z"]]]], "]"]]]], "+", RowBox[List["33750", " ", SuperscriptBox["a", "2"], " ", SuperscriptBox["z", "2"], " ", RowBox[List["Sin", "[", RowBox[List["b", "+", RowBox[List["a", " ", "z"]]]], "]"]]]], "-", RowBox[List["1250", " ", RowBox[List["Sin", "[", RowBox[List["3", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["a", " ", "z"]]]], ")"]]]], "]"]]]], "+", RowBox[List["5625", " ", SuperscriptBox["a", "2"], " ", SuperscriptBox["z", "2"], " ", RowBox[List["Sin", "[", RowBox[List["3", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["a", " ", "z"]]]], ")"]]]], "]"]]]], "-", RowBox[List["54", " ", RowBox[List["Sin", "[", RowBox[List["5", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["a", " ", "z"]]]], ")"]]]], "]"]]]], "+", RowBox[List["675", " ", SuperscriptBox["a", "2"], " ", SuperscriptBox["z", "2"], " ", RowBox[List["Sin", "[", RowBox[List["5", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["a", " ", "z"]]]], ")"]]]], "]"]]]]]], RowBox[List["54000", " ", SuperscriptBox["a", "3"]]]]]]]]










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





2002-12-18