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 Cosh

 http://functions.wolfram.com/01.20.21.1265.01

 Input Form

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

 Standard Form

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

 MathML Form

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

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

 2002-12-18