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 Cosh

 http://functions.wolfram.com/01.20.21.0763.01

 Input Form

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

 Standard Form

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"2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["d", "+", RowBox[List["\[ImaginaryI]", " ", "f"]]]], ")"]]]]]]], "+", RowBox[List["\[ImaginaryI]", " ", "g"]]]], "]"]]]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", SqrtBox[RowBox[List[RowBox[List["-", "d"]], "-", RowBox[List["\[ImaginaryI]", " ", "f"]]]]], " ", RowBox[List["Sinh", "[", RowBox[List["g", "-", RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["\[ImaginaryI]", " ", "c"]]]], ")"]], " ", SqrtBox["z"]]], "-", RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["d", "+", RowBox[List["\[ImaginaryI]", " ", "f"]]]], ")"]], " ", "z"]]]], "]"]]]]]], ")"]]]]]], ")"]]]]]]]]

 MathML Form

 cos ( z b + d z ) cosh ( z c + g + f z ) z 1 4 ( 1 ( f - d ) 3 / 2 ( ( b - c ) 2 π cos ( ( c - b ) 2 4 ( f - d ) - g ) 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 ) - g ) + 2 f - d sin ( z ( c - b ) + g + ( f - d ) z ) ) - 1 ( - d - f ) 3 / 2 ( ( b + c ) 2 π cos ( g - ( b + c ) 2 4 ( d + f ) ) 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 ( g - ( b + c ) 2 4 ( d + f ) ) + 2 - d - f sinh ( g - ( d + f ) z - ( b + c ) z ) ) ) z z 1 2 b d z z 1 2 c g f z 1 4 1 f -1 d 3 2 -1 b -1 c 2 1 2 c -1 b 2 4 f -1 d -1 -1 g 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 -1 g 2 f -1 d 1 2 z 1 2 c -1 b g f -1 d z -1 1 -1 d -1 f 3 2 -1 b c 2 1 2 g -1 b c 2 4 d f -1 FresnelC b c 2 d f z 1 2 -1 d -1 f 1 2 2 1 2 -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 g -1 b c 2 4 d f -1 2 -1 d -1 f 1 2 g -1 d f z -1 b c z 1 2 [/itex]

 Rule Form

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

 2002-12-18