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Cell[CellGroupData[{ Cell["New technology: General oscillatory integration", "Section", CellChangeTimes->{ 3.464895527404437*^9, {3.4649070392435055`*^9, 3.4649070413367147`*^9}, { 3.464974784018016*^9, 3.464974785961998*^9}, {3.465077426509364*^9, 3.465077428004531*^9}}], Cell["\<\ Integrals of highly oscillatory functions are very expensive to compute with \ traditional quadrature rules.\ \>", "Text", CellChangeTimes->{{3.4650778463805847`*^9, 3.465077897564612*^9}, { 3.4650781753249197`*^9, 3.46507818558074*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"NIntegrate", "[", RowBox[{ RowBox[{ FractionBox["1", RowBox[{"1", "+", RowBox[{"x", "^", "3"}]}]], RowBox[{"Sin", "[", "x", "]"}]}], ",", RowBox[{"{", RowBox[{"x", ",", "0", ",", "\[Infinity]"}], "}"}], ",", RowBox[{"Method", "\[Rule]", "\"\\""}]}], "]"}]], "Input", CellChangeTimes->{{3.4650775184471893`*^9, 3.465077554157711*^9}, { 3.465077590299583*^9, 3.465077590374626*^9}, {3.465077907647419*^9, 3.465077911655223*^9}}], 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