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 Cosh

 http://functions.wolfram.com/01.20.21.1191.01

 Input Form

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

 Standard Form

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 MathML Form

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

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

 2002-12-18