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 Cosh

 http://functions.wolfram.com/01.20.21.0753.01

 Input Form

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

 Standard Form

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RowBox[List["4", " ", RowBox[List["(", RowBox[List["d", "+", RowBox[List["\[ImaginaryI]", " ", "f"]]]], ")"]]]]]]], "]"]], " ", RowBox[List["FresnelC", "[", FractionBox[RowBox[List["b", "+", 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[RowBox[List["(", RowBox[List["b", "+", RowBox[List["\[ImaginaryI]", " ", "c"]]]], ")"]], " ", SqrtBox[RowBox[List["2", " ", "\[Pi]"]]], " ", RowBox[List["FresnelS", "[", FractionBox[RowBox[List["b", "+", 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"]], "-", 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SqrtBox[RowBox[List[RowBox[List["-", "d"]], "+", RowBox[List["\[ImaginaryI]", " ", "f"]]]]], " ", RowBox[List["Sin", "[", RowBox[List["e", "-", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "b"]], "+", RowBox[List["\[ImaginaryI]", " ", "c"]]]], ")"]], " ", SqrtBox["z"]]], "-", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "d"]], "+", RowBox[List["\[ImaginaryI]", " ", "f"]]]], ")"]], " ", "z"]]]], "]"]]]]]], ")"]]]], ")"]]]]]]]]

 MathML Form

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

 Rule Form

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

 2002-12-18