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Cos






Mathematica Notation

Traditional Notation









Elementary Functions > Cos[z] > Integration > Indefinite integration > Involving functions of the direct function and exponential function > Involving products of the direct function and exponential function > Involving products of several direct functions and exponential function > Involving ep zcos(a z) cos(b z) cos(c z)





http://functions.wolfram.com/01.07.21.1785.01









  


  










Input Form





Integrate[E^(p z) Cos[a z] Cos[b z] Cos[c z], z] == (1/4) E^(p z) ((p Cos[(a - b - c) z] + (a - b - c) Sin[(a - b - c) z])/ (a^2 + b^2 + 2 b c + c^2 - 2 a (b + c) + p^2) + (p Cos[(a + b - c) z] + (a + b - c) Sin[(a + b - c) z])/ ((a + b - c - I p) (a + b - c + I p)) + (p Cos[(a - b + c) z] + (a - b + c) Sin[(a - b + c) z])/ ((a - b + c - I p) (a - b + c + I p)) + (p Cos[(a + b + c) z] + (a + b + c) Sin[(a + b + c) z])/ ((a + b + c - I p) (a + b + c + I p)))










Standard Form





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MathML Form







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</annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["p_", " ", "z_"]]], " ", RowBox[List["Cos", "[", RowBox[List["a_", " ", "z_"]], "]"]], " ", RowBox[List["Cos", "[", RowBox[List["b_", " ", "z_"]], "]"]], " ", RowBox[List["Cos", "[", RowBox[List["c_", " ", "z_"]], "]"]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox["1", "4"], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["p", " ", "z"]]], " ", RowBox[List["(", RowBox[List[FractionBox[RowBox[List[RowBox[List["p", " ", RowBox[List["Cos", "[", RowBox[List[RowBox[List["(", RowBox[List["a", "-", "b", "-", "c"]], ")"]], " ", "z"]], "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List["a", "-", "b", "-", "c"]], ")"]], " ", RowBox[List["Sin", "[", RowBox[List[RowBox[List["(", RowBox[List["a", "-", "b", "-", "c"]], ")"]], " ", "z"]], "]"]]]]]], RowBox[List[SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"], "+", RowBox[List["2", " ", "b", " ", "c"]], "+", SuperscriptBox["c", "2"], "-", RowBox[List["2", " ", "a", " ", RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]]]], "+", SuperscriptBox["p", "2"]]]], "+", FractionBox[RowBox[List[RowBox[List["p", " ", RowBox[List["Cos", "[", RowBox[List[RowBox[List["(", RowBox[List["a", "+", "b", "-", "c"]], ")"]], " ", "z"]], "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List["a", "+", "b", "-", "c"]], ")"]], " ", RowBox[List["Sin", "[", RowBox[List[RowBox[List["(", RowBox[List["a", "+", "b", "-", "c"]], ")"]], " ", "z"]], "]"]]]]]], RowBox[List[RowBox[List["(", RowBox[List["a", "+", "b", "-", "c", "-", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]], " ", RowBox[List["(", RowBox[List["a", "+", "b", "-", "c", "+", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]]]]], "+", FractionBox[RowBox[List[RowBox[List["p", " ", RowBox[List["Cos", "[", RowBox[List[RowBox[List["(", RowBox[List["a", "-", "b", "+", "c"]], ")"]], " ", "z"]], "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List["a", "-", "b", "+", "c"]], ")"]], " ", RowBox[List["Sin", "[", RowBox[List[RowBox[List["(", RowBox[List["a", "-", "b", "+", "c"]], ")"]], " ", "z"]], "]"]]]]]], RowBox[List[RowBox[List["(", RowBox[List["a", "-", "b", "+", "c", "-", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]], " ", RowBox[List["(", RowBox[List["a", "-", "b", "+", "c", "+", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]]]]], "+", FractionBox[RowBox[List[RowBox[List["p", " ", RowBox[List["Cos", "[", RowBox[List[RowBox[List["(", RowBox[List["a", "+", "b", "+", "c"]], ")"]], " ", "z"]], "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List["a", "+", "b", "+", "c"]], ")"]], " ", RowBox[List["Sin", "[", RowBox[List[RowBox[List["(", RowBox[List["a", "+", "b", "+", "c"]], ")"]], " ", "z"]], "]"]]]]]], RowBox[List[RowBox[List["(", RowBox[List["a", "+", "b", "+", "c", "-", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]], " ", RowBox[List["(", RowBox[List["a", "+", "b", "+", "c", "+", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]]]]]]], ")"]]]]]]]]










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





2002-12-18