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 Cosh

 http://functions.wolfram.com/01.20.21.0767.01

 Input Form

 Integrate[Cos[b Sqrt[z] + d z + e] Cosh[c Sqrt[z] + f z + g], z] == (1/8) (-(((I b + c) E^((-I) e + (I b + c)^2/(4 (I d + f)) - g) Sqrt[Pi] Erfi[(I b + c + 2 (I d + f) Sqrt[z])/(2 Sqrt[(-I) d - f])])/ ((-I) d - f)^(3/2)) - ((I b - c) E^(I e - (I b - c)^2/(4 (I d - f)) - g) Sqrt[Pi] Erfi[(I b - c + 2 (I d - f) Sqrt[z])/(2 Sqrt[I d - f])])/ (I d - f)^(3/2) - (((-I) b + c) E^((-I) e - ((-I) b + c)^2/(4 ((-I) d + f)) + g) Sqrt[Pi] Erfi[((-I) b + c + 2 ((-I) d + f) Sqrt[z])/(2 Sqrt[(-I) d + f])])/ ((-I) d + f)^(3/2) - ((I b + c) E^(I e - (I b + c)^2/(4 (I d + f)) + g) Sqrt[Pi] Erfi[(I b + c + 2 (I d + f) Sqrt[z])/(2 Sqrt[I d + f])])/ (I d + f)^(3/2) + (4 I Sin[e - I g - I (I b + c) Sqrt[z] - I (I d + f) z])/(I d + f) + (4 I Sin[e + I g - I (I b - c) Sqrt[z] - I (I d - f) z])/(I d - f))

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[RowBox[List["Cos", "[", RowBox[List[RowBox[List["b", " ", SqrtBox["z"]]], "+", RowBox[List["d", " ", "z"]], "+", "e"]], "]"]], " ", RowBox[List["Cosh", "[", RowBox[List[RowBox[List["c", " ", SqrtBox["z"]]], "+", RowBox[List["f", " ", "z"]], "+", "g"]], "]"]], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "b"]], "+", "c"]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "e"]], "+", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "b"]], "+", "c"]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "d"]], "+", "f"]], ")"]]]]], "-", "g"]]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["Erfi", "[", 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"d"]], "+", "f"]], ")"]], " ", "z"]]]], "]"]]]], RowBox[List[RowBox[List["\[ImaginaryI]", " ", "d"]], "+", "f"]]], "+", FractionBox[RowBox[List["4", " ", "\[ImaginaryI]", " ", RowBox[List["Sin", "[", RowBox[List["e", "+", RowBox[List["\[ImaginaryI]", " ", "g"]], "-", RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "b"]], "-", "c"]], ")"]], " ", SqrtBox["z"]]], "-", RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "d"]], "-", "f"]], ")"]], " ", "z"]]]], "]"]]]], RowBox[List[RowBox[List["\[ImaginaryI]", " ", "d"]], "-", "f"]]]]], ")"]]]]]]]]

 MathML Form

 cos ( z b + e + d z ) cosh ( z c + g + f z ) z 1 8 ( - ( c + b ) ( c + b ) 2 4 ( f + d ) - g - e π erfi ( c + b + 2 ( f + d ) z 2 - f - d ) ( - f - d ) 3 / 2 + 4 sin ( e + g - ( d - f ) z - ( b - c ) z ) d - f + 4 sin ( e - g - ( f + d ) z - ( c + b ) z ) f + d - ( b - c ) - ( b - c ) 2 4 ( d - f ) - g + e π erfi ( - c + b + 2 ( d - f ) z 2 d - f ) ( d - f ) 3 / 2 - ( c - b ) - ( c - b ) 2 4 ( f - d ) + g - e π erfi ( c - b + 2 ( f - d ) z 2 f - d ) ( f - d ) 3 / 2 - ( c + b ) - ( c + b ) 2 4 ( f + d ) + g + e π erfi ( c + b + 2 ( f + d ) z 2 f + d ) ( f + d ) 3 / 2 ) z z 1 2 b e d z z 1 2 c g f z 1 8 -1 c b c b 2 4 f d -1 -1 g -1 e 1 2 Erfi c b 2 f d z 1 2 2 -1 f -1 d 1 2 -1 -1 f -1 d 3 2 -1 4 e g -1 d -1 f z -1 b -1 c z 1 2 d -1 f -1 4 e -1 g -1 f d z -1 c b z 1 2 f d -1 -1 b -1 c -1 b -1 c 2 4 d -1 f -1 -1 g e 1 2 Erfi -1 c b 2 d -1 f z 1 2 2 d -1 f 1 2 -1 d -1 f 3 2 -1 -1 c -1 b -1 c -1 b 2 4 f -1 d -1 g -1 e 1 2 Erfi c -1 b 2 f -1 d z 1 2 2 f -1 d 1 2 -1 f -1 d 3 2 -1 -1 c b -1 c b 2 4 f d -1 g e 1 2 Erfi c b 2 f d z 1 2 2 f d 1 2 -1 f d 3 2 -1 [/itex]

 Rule Form

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

 2002-12-18