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 Cosh

 http://functions.wolfram.com/01.20.21.1267.01

 Input Form

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

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

 MathML Form

 p z cos ( b z 2 ) cosh ( c z 2 ) z 1 8 π ( p 2 4 ( c + b ) erfi ( p - 2 b z - 2 c z 2 - c - b ) - c - b + p 2 4 ( c - b ) erfi ( p - 2 c z + 2 b z 2 b - c ) b - c + - p 2 4 ( c - b ) erfi ( p - 2 b z + 2 c z 2 c - b ) - b + c + - p 2 4 ( c + b ) erfi ( p + 2 c z + 2 b z 2 c + b ) c + b ) z p z b z 2 c z 2 1 8 1 2 p 2 4 c b -1 Erfi p -1 2 b z -1 2 c z 2 -1 c -1 b 1 2 -1 -1 c -1 b 1 2 -1 p 2 4 c -1 b -1 Erfi p -1 2 c z 2 b z 2 b -1 c 1 2 -1 b -1 c 1 2 -1 -1 p 2 4 c -1 b -1 Erfi p -1 2 b z 2 c z 2 c -1 b 1 2 -1 -1 b c 1 2 -1 -1 p 2 4 c b -1 Erfi p 2 c z 2 b z 2 c b 1 2 -1 c 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_", " ", SuperscriptBox["z_", "2"]]], "]"]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox["1", "8"], " ", SqrtBox["\[Pi]"], " ", RowBox[List["(", RowBox[List[FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", FractionBox[SuperscriptBox["p", "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "b"]], "+", "c"]], ")"]]]]]], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List["p", "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "z"]], "-", RowBox[List["2", " ", "c", " ", "z"]]]], RowBox[List["2", " ", SqrtBox[RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "b"]], "-", "c"]]]]]], "]"]]]], SqrtBox[RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "b"]], "-", "c"]]]], "+", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", FractionBox[SuperscriptBox["p", "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "b"]], "+", "c"]], ")"]]]]]], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List["p", "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "z"]], "-", RowBox[List["2", " ", "c", " ", "z"]]]], RowBox[List["2", " ", SqrtBox[RowBox[List[RowBox[List["\[ImaginaryI]", " ", "b"]], "-", "c"]]]]]], "]"]]]], SqrtBox[RowBox[List[RowBox[List["\[ImaginaryI]", " ", "b"]], "-", "c"]]]], "+", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[SuperscriptBox["p", "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "b"]], "+", "c"]], ")"]]]]]]]], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List["p", "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "z"]], "+", RowBox[List["2", " ", "c", " ", "z"]]]], RowBox[List["2", " ", SqrtBox[RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "b"]], "+", "c"]]]]]], "]"]]]], SqrtBox[RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "b"]], "+", "c"]]]], "+", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[SuperscriptBox["p", "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "b"]], "+", "c"]], ")"]]]]]]]], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List["p", "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "z"]], "+", RowBox[List["2", " ", "c", " ", "z"]]]], RowBox[List["2", " ", SqrtBox[RowBox[List[RowBox[List["\[ImaginaryI]", " ", "b"]], "+", "c"]]]]]], "]"]]]], SqrtBox[RowBox[List[RowBox[List["\[ImaginaryI]", " ", "b"]], "+", "c"]]]]]], ")"]]]]]]]]

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

 2002-12-18