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 Cosh

 http://functions.wolfram.com/01.20.21.1261.01

 Input Form

 Integrate[E^(p z) Cos[b z^2] Cosh[c z], z] == (-(1/(8 b))) (I Sqrt[Pi] (((-Sqrt[(-I) b]) Erfi[(-c + p - 2 I b z)/(2 Sqrt[(-I) b])])/ E^((I (-c + p)^2)/(4 b)) - (Sqrt[(-I) b] Erfi[(c + p - 2 I b z)/(2 Sqrt[(-I) b])])/ E^((I (c + p)^2)/(4 b)) + Sqrt[I b] E^((I (-c + p)^2)/(4 b)) Erfi[(-c + p + 2 I b z)/(2 Sqrt[I b])] + Sqrt[I b] E^((I (c + p)^2)/(4 b)) Erfi[(c + p + 2 I b z)/(2 Sqrt[I b])]))

 Standard Form

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

 MathML Form

 p z cos ( b z 2 ) cosh ( c z ) z - 1 8 b ( π ( - - b - ( p - c ) 2 4 b erfi ( - c + p - 2 b z 2 - b ) - - b - ( c + p ) 2 4 b erfi ( c + p - 2 b z 2 - b ) + b ( p - c ) 2 4 b erfi ( - c + p + 2 b z 2 b ) + b ( c + p ) 2 4 b erfi ( c + p + 2 b z 2 b ) ) ) z p z b z 2 c z -1 1 8 b -1 1 2 -1 -1 b 1 2 -1 p -1 c 2 4 b -1 Erfi -1 c p -1 2 b z 2 -1 b 1 2 -1 -1 -1 b 1 2 -1 c p 2 4 b -1 Erfi c p -1 2 b z 2 -1 b 1 2 -1 b 1 2 p -1 c 2 4 b -1 Erfi -1 c p 2 b z 2 b 1 2 -1 b 1 2 c p 2 4 b -1 Erfi c p 2 b z 2 b 1 2 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["p_", " ", "z_"]]], " ", RowBox[List["Cos", "[", RowBox[List["b_", " ", SuperscriptBox["z_", "2"]]], "]"]], " ", RowBox[List["Cosh", "[", RowBox[List["c_", " ", "z_"]], "]"]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", " ", SqrtBox["\[Pi]"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", SqrtBox[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "b"]]]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "c"]], "+", "p"]], ")"]], "2"]]], RowBox[List["4", " ", "b"]]]]]], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List[RowBox[List["-", "c"]], "+", "p", "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "z"]]]], RowBox[List["2", " ", SqrtBox[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "b"]]]]]], "]"]]]], "-", RowBox[List[SqrtBox[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "b"]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox[RowBox[List["(", RowBox[List["c", "+", "p"]], ")"]], "2"]]], RowBox[List["4", " ", "b"]]]]]], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List["c", "+", "p", "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "z"]]]], RowBox[List["2", " ", SqrtBox[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "b"]]]]]], "]"]]]], "+", RowBox[List[SqrtBox[RowBox[List["\[ImaginaryI]", " ", "b"]]], " ", SuperscriptBox["\[ExponentialE]", FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "c"]], "+", "p"]], ")"]], "2"]]], RowBox[List["4", " ", "b"]]]], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List[RowBox[List["-", "c"]], "+", "p", "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "z"]]]], RowBox[List["2", " ", SqrtBox[RowBox[List["\[ImaginaryI]", " ", "b"]]]]]], "]"]]]], "+", RowBox[List[SqrtBox[RowBox[List["\[ImaginaryI]", " ", "b"]]], " ", SuperscriptBox["\[ExponentialE]", FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox[RowBox[List["(", RowBox[List["c", "+", "p"]], ")"]], "2"]]], RowBox[List["4", " ", "b"]]]], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List["c", "+", "p", "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "z"]]]], RowBox[List["2", " ", SqrtBox[RowBox[List["\[ImaginaryI]", " ", "b"]]]]]], "]"]]]]]], ")"]]]], RowBox[List["8", " ", "b"]]]]]]]]]

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

 2002-12-18