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 Cosh

 http://functions.wolfram.com/01.20.21.1189.01

 Input Form

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

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["p", " ", "z"]]], " ", RowBox[List["Sin", "[", 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", " ", "c"]]]]], RowBox[List["(", RowBox[List[SqrtBox["\[Pi]"], " ", RowBox[List["(", RowBox[List[RowBox[List[SqrtBox[RowBox[List["-", "c"]]], " ", SuperscriptBox["\[ExponentialE]", FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "b"]], "+", "p"]], ")"]], "2"], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "c", " ", "\[Pi]"]]]], RowBox[List["4", " ", "c"]]]], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "b"]], "+", "p", "-", RowBox[List["2", " ", "c", " ", "z"]]]], RowBox[List["2", " ", SqrtBox[RowBox[List["-", "c"]]]]]], "]"]]]], "+", RowBox[List[SqrtBox[RowBox[List["-", "c"]]], " ", SuperscriptBox["\[ExponentialE]", FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "b"]], "+", "p"]], ")"]], "2"], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "c", " ", "\[Pi]"]]]], RowBox[List["4", " ", "c"]]]], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List[RowBox[List["\[ImaginaryI]", " ", "b"]], "+", "p", "-", RowBox[List["2", " ", "c", " ", "z"]]]], RowBox[List["2", " ", SqrtBox[RowBox[List["-", "c"]]]]]], "]"]]]], "-", RowBox[List[SqrtBox["c"], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "b"]], "+", "p"]], ")"]], "2"], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "c", " ", "\[Pi]"]]]], RowBox[List["4", " ", "c"]]]]]], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "b"]], "+", "p", "+", RowBox[List["2", " ", "c", " ", "z"]]]], RowBox[List["2", " ", SqrtBox["c"]]]], "]"]]]], "-", RowBox[List[SqrtBox["c"], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "b"]], "+", "p"]], ")"]], "2"], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "c", " ", "\[Pi]"]]]], RowBox[List["4", " ", "c"]]]]]], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List[RowBox[List["\[ImaginaryI]", " ", "b"]], "+", "p", "+", RowBox[List["2", " ", "c", " ", "z"]]]], RowBox[List["2", " ", SqrtBox["c"]]]], "]"]]]]]], ")"]]]], ")"]]]]]]]]

 MathML Form

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

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

 2002-12-18