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Sinh






Mathematica Notation

Traditional Notation









Elementary Functions > Sinh[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving trigonometric functions > Involving cos > Involving cos(d z+e) sinh(c zr)





http://functions.wolfram.com/01.19.21.0718.01









  


  










Input Form





Integrate[Cos[d z + e] Sinh[c Sqrt[z]], z] == (1/4) I ((1/(-d)^(3/2)) (2 Sqrt[-d] Cos[e - I c Sqrt[z] + d z] + I c Sqrt[2 Pi] Cos[c^2/(4 d) + e] FresnelS[(I c - 2 d Sqrt[z])/ (Sqrt[-d] Sqrt[2 Pi])] - I c Sqrt[2 Pi] FresnelC[(I c - 2 d Sqrt[z])/(Sqrt[-d] Sqrt[2 Pi])] Sin[c^2/(4 d) + e]) + (1/(-d)^(3/2)) (-2 Sqrt[-d] Cos[e + I c Sqrt[z] + d z] - I c Sqrt[2 Pi] Cos[c^2/(4 d) + e] FresnelS[(I c + 2 d Sqrt[z])/ (Sqrt[-d] Sqrt[2 Pi])] + I c Sqrt[2 Pi] FresnelC[(I c + 2 d Sqrt[z])/(Sqrt[-d] Sqrt[2 Pi])] Sin[c^2/(4 d) + e]))










Standard Form





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MathML Form







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










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[RowBox[List[RowBox[List["Cos", "[", RowBox[List[RowBox[List["d_", " ", "z_"]], "+", "e_"]], "]"]], " ", RowBox[List["Sinh", "[", RowBox[List["c_", " ", SqrtBox["z_"]]], "]"]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox["1", "4"], " ", "\[ImaginaryI]", " ", RowBox[List["(", RowBox[List[FractionBox[RowBox[List[RowBox[List["2", " ", SqrtBox[RowBox[List["-", "d"]]], " ", RowBox[List["Cos", "[", RowBox[List["e", "-", RowBox[List["\[ImaginaryI]", " ", "c", " ", SqrtBox["z"]]], "+", RowBox[List["d", " ", "z"]]]], "]"]]]], "+", RowBox[List["\[ImaginaryI]", " ", "c", " ", SqrtBox[RowBox[List["2", " ", "\[Pi]"]]], " ", RowBox[List["Cos", "[", RowBox[List[FractionBox[SuperscriptBox["c", "2"], RowBox[List["4", " ", "d"]]], "+", "e"]], "]"]], " ", RowBox[List["FresnelS", "[", FractionBox[RowBox[List[RowBox[List["\[ImaginaryI]", " ", "c"]], "-", RowBox[List["2", " ", "d", " ", SqrtBox["z"]]]]], RowBox[List[SqrtBox[RowBox[List["-", "d"]]], " ", SqrtBox[RowBox[List["2", " ", "\[Pi]"]]]]]], "]"]]]], "-", RowBox[List["\[ImaginaryI]", " ", "c", " ", SqrtBox[RowBox[List["2", " ", "\[Pi]"]]], " ", RowBox[List["FresnelC", "[", FractionBox[RowBox[List[RowBox[List["\[ImaginaryI]", " ", "c"]], "-", RowBox[List["2", " ", "d", " ", SqrtBox["z"]]]]], RowBox[List[SqrtBox[RowBox[List["-", "d"]]], " ", SqrtBox[RowBox[List["2", " ", "\[Pi]"]]]]]], "]"]], " ", RowBox[List["Sin", "[", RowBox[List[FractionBox[SuperscriptBox["c", "2"], RowBox[List["4", " ", "d"]]], "+", "e"]], "]"]]]]]], SuperscriptBox[RowBox[List["(", RowBox[List["-", "d"]], ")"]], RowBox[List["3", "/", "2"]]]], "+", FractionBox[RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", SqrtBox[RowBox[List["-", "d"]]], " ", RowBox[List["Cos", "[", RowBox[List["e", "+", RowBox[List["\[ImaginaryI]", " ", "c", " ", SqrtBox["z"]]], "+", RowBox[List["d", " ", "z"]]]], "]"]]]], "-", RowBox[List["\[ImaginaryI]", " ", "c", " ", SqrtBox[RowBox[List["2", " ", "\[Pi]"]]], " ", RowBox[List["Cos", "[", RowBox[List[FractionBox[SuperscriptBox["c", "2"], RowBox[List["4", " ", "d"]]], "+", "e"]], "]"]], " ", RowBox[List["FresnelS", "[", FractionBox[RowBox[List[RowBox[List["\[ImaginaryI]", " ", "c"]], "+", RowBox[List["2", " ", "d", " ", SqrtBox["z"]]]]], RowBox[List[SqrtBox[RowBox[List["-", "d"]]], " ", SqrtBox[RowBox[List["2", " ", "\[Pi]"]]]]]], "]"]]]], "+", RowBox[List["\[ImaginaryI]", " ", "c", " ", SqrtBox[RowBox[List["2", " ", "\[Pi]"]]], " ", RowBox[List["FresnelC", "[", FractionBox[RowBox[List[RowBox[List["\[ImaginaryI]", " ", "c"]], "+", RowBox[List["2", " ", "d", " ", SqrtBox["z"]]]]], RowBox[List[SqrtBox[RowBox[List["-", "d"]]], " ", SqrtBox[RowBox[List["2", " ", "\[Pi]"]]]]]], "]"]], " ", RowBox[List["Sin", "[", RowBox[List[FractionBox[SuperscriptBox["c", "2"], RowBox[List["4", " ", "d"]]], "+", "e"]], "]"]]]]]], SuperscriptBox[RowBox[List["(", RowBox[List["-", "d"]], ")"]], RowBox[List["3", "/", "2"]]]]]], ")"]]]]]]]]










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





2002-12-18