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 Cosh

 http://functions.wolfram.com/01.20.21.0755.01

 Input Form

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

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[RowBox[List["Cos", "[", RowBox[List["d", " ", "z"]], "]"]], RowBox[List["Cosh", "[", RowBox[List[RowBox[List["c", " ", SqrtBox["z"]]], "+", RowBox[List["f", " ", "z"]], "+", "g"]], "]"]], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", FractionBox["1", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "d"]], "-", RowBox[List["\[ImaginaryI]", " ", "f"]]]], ")"]], RowBox[List["3", "/", "2"]]]]]], RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "c", " ", SqrtBox[RowBox[List["2", " ", "\[Pi]"]]], " ", RowBox[List["Cos", "[", RowBox[List[FractionBox[SuperscriptBox["c", "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["d", "+", RowBox[List["\[ImaginaryI]", " ", "f"]]]], ")"]]]]], "+", RowBox[List["\[ImaginaryI]", " ", "g"]]]], "]"]], " ", RowBox[List["FresnelC", "[", FractionBox[RowBox[List[RowBox[List["\[ImaginaryI]", " ", "c"]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "+", RowBox[List["\[ImaginaryI]", " ", "f"]]]], ")"]], " ", SqrtBox["z"]]]]], RowBox[List[SqrtBox[RowBox[List[RowBox[List["-", "d"]], "-", RowBox[List["\[ImaginaryI]", " ", "f"]]]]], " ", SqrtBox[RowBox[List["2", " ", "\[Pi]"]]]]]], "]"]]]], "+", RowBox[List["\[ImaginaryI]", " ", "c", " ", SqrtBox[RowBox[List["2", " ", "\[Pi]"]]], " ", RowBox[List["FresnelS", "[", FractionBox[RowBox[List[RowBox[List["\[ImaginaryI]", " ", "c"]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "+", RowBox[List["\[ImaginaryI]", " ", "f"]]]], ")"]], " ", SqrtBox["z"]]]]], RowBox[List[SqrtBox[RowBox[List[RowBox[List["-", "d"]], "-", RowBox[List["\[ImaginaryI]", " ", "f"]]]]], " ", SqrtBox[RowBox[List["2", " ", "\[Pi]"]]]]]], "]"]], " ", RowBox[List["Sin", "[", RowBox[List[FractionBox[SuperscriptBox["c", "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["d", "+", RowBox[List["\[ImaginaryI]", " ", "f"]]]], ")"]]]]], "+", RowBox[List["\[ImaginaryI]", " ", "g"]]]], "]"]]]], "+", RowBox[List["2", " ", SqrtBox[RowBox[List[RowBox[List["-", "d"]], "-", RowBox[List["\[ImaginaryI]", " ", "f"]]]]], " ", RowBox[List["Sin", "[", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "g"]], "+", RowBox[List["\[ImaginaryI]", " ", "c", " ", SqrtBox["z"]]], "+", RowBox[List[RowBox[List["(", RowBox[List["d", "+", RowBox[List["\[ImaginaryI]", " ", "f"]]]], ")"]], " ", "z"]]]], "]"]]]]]], ")"]]]], "+", RowBox[List[FractionBox["1", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "d"]], "+", RowBox[List["\[ImaginaryI]", " ", "f"]]]], ")"]], RowBox[List["3", "/", "2"]]]], RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "c", " ", SqrtBox[RowBox[List["2", " ", "\[Pi]"]]], " ", RowBox[List["Cos", "[", RowBox[List[FractionBox[SuperscriptBox["c", "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "d"]], "+", RowBox[List["\[ImaginaryI]", " ", "f"]]]], ")"]]]]], "+", RowBox[List["\[ImaginaryI]", " ", "g"]]]], "]"]], " ", RowBox[List["FresnelC", "[", FractionBox[RowBox[List[RowBox[List["\[ImaginaryI]", " ", "c"]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "d"]], "+", RowBox[List["\[ImaginaryI]", " ", "f"]]]], ")"]], " ", SqrtBox["z"]]]]], RowBox[List[SqrtBox[RowBox[List[RowBox[List["-", "d"]], "+", RowBox[List["\[ImaginaryI]", " ", "f"]]]]], " ", SqrtBox[RowBox[List["2", " ", "\[Pi]"]]]]]], "]"]]]], "+", RowBox[List["\[ImaginaryI]", " ", "c", " ", SqrtBox[RowBox[List["2", " ", "\[Pi]"]]], " ", RowBox[List["FresnelS", "[", FractionBox[RowBox[List[RowBox[List["\[ImaginaryI]", " ", "c"]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "d"]], "+", RowBox[List["\[ImaginaryI]", " ", "f"]]]], ")"]], " ", SqrtBox["z"]]]]], RowBox[List[SqrtBox[RowBox[List[RowBox[List["-", "d"]], "+", RowBox[List["\[ImaginaryI]", " ", "f"]]]]], " ", SqrtBox[RowBox[List["2", " ", "\[Pi]"]]]]]], "]"]], " ", RowBox[List["Sin", "[", RowBox[List[FractionBox[SuperscriptBox["c", "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "d"]], "+", RowBox[List["\[ImaginaryI]", " ", "f"]]]], ")"]]]]], "+", RowBox[List["\[ImaginaryI]", " ", "g"]]]], "]"]]]], "+", RowBox[List["2", " ", SqrtBox[RowBox[List[RowBox[List["-", "d"]], "+", RowBox[List["\[ImaginaryI]", " ", "f"]]]]], " ", RowBox[List["Sin", "[", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "g"]], "+", RowBox[List["\[ImaginaryI]", " ", "c", " ", SqrtBox["z"]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "d"]], "+", RowBox[List["\[ImaginaryI]", " ", "f"]]]], ")"]], " ", "z"]]]], "]"]]]]]], ")"]]]]]], ")"]]]]]]]]

 MathML Form

 cos ( d z ) cosh ( z c + g + f z ) z 1 4 ( 1 ( f - d ) 3 / 2 ( - c 2 π cos ( c 2 4 ( f - d ) + g ) C TagBox["C", FresnelC] ( 2 z ( f - d ) + c f - d 2 π ) + c 2 π S TagBox["S", FresnelS] ( 2 z ( f - d ) + c f - d 2 π ) sin ( c 2 4 ( f - d ) + g ) + 2 f - d sin ( g + c z + ( f - d ) z ) ) - 1 ( - d - f ) 3 / 2 ( c 2 π cos ( c 2 4 ( d + f ) + g ) C TagBox["C", FresnelC] ( 2 z ( d + f ) + c - d - f 2 π ) + c 2 π S TagBox["S", FresnelS] ( 2 z ( d + f ) + c - d - f 2 π ) sin ( c 2 4 ( d + f ) + g ) + 2 - d - f sin ( g + c z + ( d + f ) z ) ) ) z d z z 1 2 c g f z 1 4 1 f -1 d 3 2 -1 -1 c 2 1 2 c 2 4 f -1 d -1 g FresnelC 2 z 1 2 f -1 d c f -1 d 1 2 2 1 2 -1 c 2 1 2 FresnelS 2 z 1 2 f -1 d c f -1 d 1 2 2 1 2 -1 c 2 4 f -1 d -1 g 2 f -1 d 1 2 g c z 1 2 f -1 d z -1 1 -1 d -1 f 3 2 -1 c 2 1 2 c 2 4 d f -1 g FresnelC 2 z 1 2 d f c -1 d -1 f 1 2 2 1 2 -1 c 2 1 2 FresnelS 2 z 1 2 d f c -1 d -1 f 1 2 2 1 2 -1 c 2 4 d f -1 g 2 -1 d -1 f 1 2 g c z 1 2 d f z [/itex]

 Rule Form

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

 2002-12-18