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 Cosh

 http://functions.wolfram.com/01.20.21.1274.01

 Input Form

 Integrate[E^(b Sqrt[z] + e) Cos[a Sqrt[z] + q] Cosh[c Sqrt[z] + g], z] == (1/2) ((E^(e - g - I q + ((-I) a + b - c) Sqrt[z]) (-1 + ((-I) a + b - c) Sqrt[z]))/((-I) a + b - c)^2 + (E^(e - g + I q + (I a + b - c) Sqrt[z]) (-1 + (I a + b - c) Sqrt[z]))/ (I a + b - c)^2 + (E^(e + g - I q + ((-I) a + b + c) Sqrt[z]) (-1 + ((-I) a + b + c) Sqrt[z]))/((-I) a + b + c)^2 + (E^(e + g + I q + (I a + b + c) Sqrt[z]) (-1 + (I a + b + c) Sqrt[z]))/ (I a + b + c)^2)

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["b", " ", SqrtBox["z"]]], "+", "e"]]], RowBox[List["Cos", "[", RowBox[List[RowBox[List["a", " ", SqrtBox["z"]]], "+", "q"]], "]"]], RowBox[List["Cosh", "[", RowBox[List[RowBox[List["c", " ", SqrtBox["z"]]], "+", "g"]], "]"]], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["e", "-", "g", "-", RowBox[List["\[ImaginaryI]", " ", "q"]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b", "-", "c"]], ")"]], " ", SqrtBox["z"]]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b", "-", "c"]], ")"]], " ", SqrtBox["z"]]]]], ")"]]]], SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b", "-", "c"]], ")"]], "2"]], "+", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["e", "-", "g", "+", RowBox[List["\[ImaginaryI]", " ", "q"]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b", "-", "c"]], ")"]], " ", SqrtBox["z"]]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b", "-", "c"]], ")"]], " ", SqrtBox["z"]]]]], ")"]]]], SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b", "-", "c"]], ")"]], "2"]], "+", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["e", "+", "g", "-", RowBox[List["\[ImaginaryI]", " ", "q"]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b", "+", "c"]], ")"]], " ", SqrtBox["z"]]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b", "+", "c"]], ")"]], " ", SqrtBox["z"]]]]], ")"]]]], SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b", "+", "c"]], ")"]], "2"]], "+", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["e", "+", "g", "+", RowBox[List["\[ImaginaryI]", " ", "q"]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b", "+", "c"]], ")"]], " ", SqrtBox["z"]]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b", "+", "c"]], ")"]], " ", SqrtBox["z"]]]]], ")"]]]], SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b", "+", "c"]], ")"]], "2"]]]], ")"]]]]]]]]

 MathML Form

 z b + e cos ( z a + q ) cosh ( z c + g ) z 1 2 ( z ( b - c - a ) + e - g - q ( ( b - c - a ) z - 1 ) ( b - c - a ) 2 + z ( b - c + a ) + e - g + q ( ( b - c + a ) z - 1 ) ( b - c + a ) 2 + z ( b + c - a ) + e + g - q ( ( b + c - a ) z - 1 ) ( b + c - a ) 2 + z ( b + c + a ) + e + g + q ( ( b + c + a ) z - 1 ) ( b + c + a ) 2 ) z z 1 2 b e z 1 2 a q z 1 2 c g 1 2 z 1 2 b -1 c -1 a e -1 g -1 q b -1 c -1 a z 1 2 -1 b -1 c -1 a 2 -1 z 1 2 b -1 c a e -1 g q b -1 c a z 1 2 -1 b -1 c a 2 -1 z 1 2 b c -1 a e g -1 q b c -1 a z 1 2 -1 b c -1 a 2 -1 z 1 2 b c a e g q b c a z 1 2 -1 b c a 2 -1 [/itex]

 Rule Form

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

 2002-12-18