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 Cosh

 http://functions.wolfram.com/01.20.21.1194.01

 Input Form

 Integrate[E^(p z) Sin[b Sqrt[z]] Cosh[c Sqrt[z]], z] == (-(1/8)) I ((1/p^(3/2)) ((b - I c) E^((b - I c)^2/(4 p)) Sqrt[Pi] (Erf[(b - I c - 2 I p Sqrt[z])/(2 Sqrt[p])] - Erf[(b - I c + 2 I p Sqrt[z])/(2 Sqrt[p])])) + (1/p^(3/2)) ((b + I c) E^((b + I c)^2/(4 p)) Sqrt[Pi] (Erf[(b + I c - 2 I p Sqrt[z])/(2 Sqrt[p])] - Erf[(b + I c + 2 I p Sqrt[z])/(2 Sqrt[p])])) + (8 I E^(p z) Cosh[c Sqrt[z]] Sin[b Sqrt[z]])/p)

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["p", " ", "z"]]], RowBox[List["Sin", "[", RowBox[List["b", " ", SqrtBox["z"]]], "]"]], RowBox[List["Cosh", "[", RowBox[List["c", " ", SqrtBox["z"]]], "]"]], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[RowBox[List["-", FractionBox["1", "8"]]], " ", "\[ImaginaryI]", " ", RowBox[List["(", RowBox[List[RowBox[List[FractionBox["1", SuperscriptBox["p", RowBox[List["3", "/", "2"]]]], RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["b", "-", RowBox[List["\[ImaginaryI]", " ", "c"]]]], ")"]], " ", SuperscriptBox["\[ExponentialE]", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["b", "-", RowBox[List["\[ImaginaryI]", " ", "c"]]]], ")"]], "2"], RowBox[List["4", " ", "p"]]]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["(", RowBox[List[RowBox[List["Erf", "[", FractionBox[RowBox[List["b", "-", RowBox[List["\[ImaginaryI]", " ", "c"]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "p", " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox["p"]]]], "]"]], "-", RowBox[List["Erf", "[", FractionBox[RowBox[List["b", "-", RowBox[List["\[ImaginaryI]", " ", "c"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "p", " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox["p"]]]], "]"]]]], ")"]]]], ")"]]]], "+", RowBox[List[FractionBox["1", SuperscriptBox["p", RowBox[List["3", "/", "2"]]]], RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["b", "+", RowBox[List["\[ImaginaryI]", " ", "c"]]]], ")"]], " ", SuperscriptBox["\[ExponentialE]", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["b", "+", RowBox[List["\[ImaginaryI]", " ", "c"]]]], ")"]], "2"], RowBox[List["4", " ", "p"]]]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["(", RowBox[List[RowBox[List["Erf", "[", FractionBox[RowBox[List["b", "+", RowBox[List["\[ImaginaryI]", " ", "c"]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "p", " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox["p"]]]], "]"]], "-", RowBox[List["Erf", "[", FractionBox[RowBox[List["b", "+", RowBox[List["\[ImaginaryI]", " ", "c"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "p", " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox["p"]]]], "]"]]]], ")"]]]], ")"]]]], "+", FractionBox[RowBox[List["8", " ", "\[ImaginaryI]", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["p", " ", "z"]]], " ", RowBox[List["Cosh", "[", RowBox[List["c", " ", SqrtBox["z"]]], "]"]], " ", RowBox[List["Sin", "[", RowBox[List["b", " ", SqrtBox["z"]]], "]"]]]], "p"]]], ")"]]]]]]]]

 MathML Form

 p z sin ( b z ) cosh ( c z ) z - 1 8 ( ( b + c ) ( b + c ) 2 4 p π ( erf ( b + c - 2 p z 2 p ) - erf ( b + c + 2 p z 2 p ) ) p 3 / 2 + ( b - c ) ( b - c ) 2 4 p π ( erf ( b - c - 2 p z 2 p ) - erf ( b - c + 2 p z 2 p ) ) p 3 / 2 + 8 p z cosh ( c z ) sin ( b z ) p ) z p z b z 1 2 c z 1 2 -1 1 8 b c b c 2 4 p -1 1 2 Erf b c -1 2 p z 1 2 2 p 1 2 -1 -1 Erf b c 2 p z 1 2 2 p 1 2 -1 p 3 2 -1 b -1 c b -1 c 2 4 p -1 1 2 Erf b -1 c -1 2 p z 1 2 2 p 1 2 -1 -1 Erf b -1 c 2 p z 1 2 2 p 1 2 -1 p 3 2 -1 8 p z c z 1 2 b z 1 2 p -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_", " ", SqrtBox["z_"]]], "]"]], " ", RowBox[List["Cosh", "[", RowBox[List["c_", " ", SqrtBox["z_"]]], "]"]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["-", FractionBox["1", "8"]]], " ", "\[ImaginaryI]", " ", RowBox[List["(", RowBox[List[FractionBox[RowBox[List[RowBox[List["(", RowBox[List["b", "-", RowBox[List["\[ImaginaryI]", " ", "c"]]]], ")"]], " ", SuperscriptBox["\[ExponentialE]", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["b", "-", RowBox[List["\[ImaginaryI]", " ", "c"]]]], ")"]], "2"], RowBox[List["4", " ", "p"]]]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["(", RowBox[List[RowBox[List["Erf", "[", FractionBox[RowBox[List["b", "-", RowBox[List["\[ImaginaryI]", " ", "c"]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "p", " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox["p"]]]], "]"]], "-", RowBox[List["Erf", "[", FractionBox[RowBox[List["b", "-", RowBox[List["\[ImaginaryI]", " ", "c"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "p", " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox["p"]]]], "]"]]]], ")"]]]], SuperscriptBox["p", RowBox[List["3", "/", "2"]]]], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["b", "+", RowBox[List["\[ImaginaryI]", " ", "c"]]]], ")"]], " ", SuperscriptBox["\[ExponentialE]", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["b", "+", RowBox[List["\[ImaginaryI]", " ", "c"]]]], ")"]], "2"], RowBox[List["4", " ", "p"]]]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["(", RowBox[List[RowBox[List["Erf", "[", FractionBox[RowBox[List["b", "+", RowBox[List["\[ImaginaryI]", " ", "c"]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "p", " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox["p"]]]], "]"]], "-", RowBox[List["Erf", "[", FractionBox[RowBox[List["b", "+", RowBox[List["\[ImaginaryI]", " ", "c"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "p", " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox["p"]]]], "]"]]]], ")"]]]], SuperscriptBox["p", RowBox[List["3", "/", "2"]]]], "+", FractionBox[RowBox[List["8", " ", "\[ImaginaryI]", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["p", " ", "z"]]], " ", RowBox[List["Cosh", "[", RowBox[List["c", " ", SqrtBox["z"]]], "]"]], " ", RowBox[List["Sin", "[", RowBox[List["b", " ", SqrtBox["z"]]], "]"]]]], "p"]]], ")"]]]]]]]]

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

 2002-12-18