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http://functions.wolfram.com/01.07.21.0141.01
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Integrate[(1/z^4) Cos[a Sqrt[z] + b], z] ==
(1/(360 z^3)) (-120 Cos[b + a Sqrt[z]] + 6 a^2 z Cos[b + a Sqrt[z]] -
a^4 z^2 Cos[b + a Sqrt[z]] - a^6 z^3 Cos[b] CosIntegral[a Sqrt[z]] +
24 a Sqrt[z] Sin[b + a Sqrt[z]] - 2 a^3 z^(3/2) Sin[b + a Sqrt[z]] +
a^5 z^(5/2) Sin[b + a Sqrt[z]] + a^6 z^3 Sin[b] SinIntegral[a Sqrt[z]])
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Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[FractionBox["1", SuperscriptBox["z", "4"]], RowBox[List["Cos", "[", RowBox[List[RowBox[List["a", " ", SqrtBox["z"]]], "+", "b"]], "]"]], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["360", " ", SuperscriptBox["z", "3"]]]], RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "120"]], " ", RowBox[List["Cos", "[", RowBox[List["b", "+", RowBox[List["a", " ", SqrtBox["z"]]]]], "]"]]]], "+", RowBox[List["6", " ", SuperscriptBox["a", "2"], " ", "z", " ", RowBox[List["Cos", "[", RowBox[List["b", "+", RowBox[List["a", " ", SqrtBox["z"]]]]], "]"]]]], "-", RowBox[List[SuperscriptBox["a", "4"], " ", SuperscriptBox["z", "2"], " ", RowBox[List["Cos", "[", RowBox[List["b", "+", RowBox[List["a", " ", SqrtBox["z"]]]]], "]"]]]], "-", RowBox[List[SuperscriptBox["a", "6"], " ", SuperscriptBox["z", "3"], " ", RowBox[List["Cos", "[", "b", "]"]], " ", RowBox[List["CosIntegral", "[", RowBox[List["a", " ", SqrtBox["z"]]], "]"]]]], "+", RowBox[List["24", " ", "a", " ", SqrtBox["z"], " ", RowBox[List["Sin", "[", RowBox[List["b", "+", RowBox[List["a", " ", SqrtBox["z"]]]]], "]"]]]], "-", RowBox[List["2", " ", SuperscriptBox["a", "3"], " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]], " ", RowBox[List["Sin", "[", RowBox[List["b", "+", RowBox[List["a", " ", SqrtBox["z"]]]]], "]"]]]], "+", RowBox[List[SuperscriptBox["a", "5"], " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]], " ", RowBox[List["Sin", "[", RowBox[List["b", "+", RowBox[List["a", " ", SqrtBox["z"]]]]], "]"]]]], "+", RowBox[List[SuperscriptBox["a", "6"], " ", SuperscriptBox["z", "3"], " ", RowBox[List["Sin", "[", "b", "]"]], " ", RowBox[List["SinIntegral", "[", RowBox[List["a", " ", SqrtBox["z"]]], "]"]]]]]], ")"]]]]]]]]
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[FractionBox[RowBox[List["Cos", "[", RowBox[List[RowBox[List["a_", " ", SqrtBox["z_"]]], "+", "b_"]], "]"]], SuperscriptBox["z_", "4"]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List[RowBox[List["-", "120"]], " ", RowBox[List["Cos", "[", RowBox[List["b", "+", RowBox[List["a", " ", SqrtBox["z"]]]]], "]"]]]], "+", RowBox[List["6", " ", SuperscriptBox["a", "2"], " ", "z", " ", RowBox[List["Cos", "[", RowBox[List["b", "+", RowBox[List["a", " ", SqrtBox["z"]]]]], "]"]]]], "-", RowBox[List[SuperscriptBox["a", "4"], " ", SuperscriptBox["z", "2"], " ", RowBox[List["Cos", "[", RowBox[List["b", "+", RowBox[List["a", " ", SqrtBox["z"]]]]], "]"]]]], "-", RowBox[List[SuperscriptBox["a", "6"], " ", SuperscriptBox["z", "3"], " ", RowBox[List["Cos", "[", "b", "]"]], " ", RowBox[List["CosIntegral", "[", RowBox[List["a", " ", SqrtBox["z"]]], "]"]]]], "+", RowBox[List["24", " ", "a", " ", SqrtBox["z"], " ", RowBox[List["Sin", "[", RowBox[List["b", "+", RowBox[List["a", " ", SqrtBox["z"]]]]], "]"]]]], "-", RowBox[List["2", " ", SuperscriptBox["a", "3"], " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]], " ", RowBox[List["Sin", "[", RowBox[List["b", "+", RowBox[List["a", " ", SqrtBox["z"]]]]], "]"]]]], "+", RowBox[List[SuperscriptBox["a", "5"], " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]], " ", RowBox[List["Sin", "[", RowBox[List["b", "+", RowBox[List["a", " ", SqrtBox["z"]]]]], "]"]]]], "+", RowBox[List[SuperscriptBox["a", "6"], " ", SuperscriptBox["z", "3"], " ", RowBox[List["Sin", "[", "b", "]"]], " ", RowBox[List["SinIntegral", "[", RowBox[List["a", " ", SqrtBox["z"]]], "]"]]]]]], RowBox[List["360", " ", SuperscriptBox["z", "3"]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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