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 Cosh

 http://functions.wolfram.com/01.20.21.1260.01

 Input Form

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

 Standard Form

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

 MathML Form

 p z cos ( b z ) cosh ( c z ) z 1 8 ( 8 p z ( b cosh ( c z ) sin ( b z ) + c cos ( b z ) sinh ( c z ) ) b 2 + c 2 - p 2 4 c - 4 b p π erfi ( p - 2 ( c - b ) z 2 b - c ) ( b - c ) 3 / 2 - p 2 - 4 c - 4 b p π erfi ( 2 z ( c + b ) + p 2 c + b ) ( c + b ) 3 / 2 - p 2 4 c + 4 b p π erfi ( p - 2 ( c + b ) z 2 - c - b ) ( - c - b ) 3 / 2 - p 2 4 b - 4 c p π erfi ( 2 z ( c - b ) + p 2 c - b ) ( c - b ) 3 / 2 ) z p z 1 2 b z c z 1 8 8 p z 1 2 b c z b z c b z c z b 2 c 2 -1 -1 p 2 4 c -1 4 b -1 p 1 2 Erfi p -1 2 c -1 b z 1 2 2 b -1 c 1 2 -1 b -1 c 3 2 -1 -1 p 2 -4 c -1 4 b -1 p 1 2 Erfi 2 z 1 2 c b p 2 c b 1 2 -1 c b 3 2 -1 -1 p 2 4 c 4 b -1 p 1 2 Erfi p -1 2 c b z 1 2 2 -1 c -1 b 1 2 -1 -1 c -1 b 3 2 -1 -1 p 2 4 b -1 4 c -1 p 1 2 Erfi 2 z 1 2 c -1 b p 2 c -1 b 1 2 -1 c -1 b 3 2 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["p_", " ", SqrtBox["z_"]]]], " ", RowBox[List["Cos", "[", RowBox[List["b_", " ", "z_"]], "]"]], " ", RowBox[List["Cosh", "[", RowBox[List["c_", " ", "z_"]], "]"]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List[FractionBox[RowBox[List["8", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["p", " ", SqrtBox["z"]]]], " ", RowBox[List["(", RowBox[List[RowBox[List["b", " ", RowBox[List["Cosh", "[", RowBox[List["c", " ", "z"]], "]"]], " ", RowBox[List["Sin", "[", RowBox[List["b", " ", "z"]], "]"]]]], "+", RowBox[List["c", " ", RowBox[List["Cos", "[", RowBox[List["b", " ", "z"]], "]"]], " ", RowBox[List["Sinh", "[", RowBox[List["c", " ", "z"]], "]"]]]]]], ")"]]]], RowBox[List[SuperscriptBox["b", "2"], "+", SuperscriptBox["c", "2"]]]], "-", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", FractionBox[SuperscriptBox["p", "2"], RowBox[List[RowBox[List["4", " ", "c"]], "-", RowBox[List["4", " ", "\[ImaginaryI]", " ", "b"]]]]]], " ", "p", " ", SqrtBox["\[Pi]"], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List["p", "-", RowBox[List["2", " ", RowBox[List["(", RowBox[List["c", "-", RowBox[List["\[ImaginaryI]", " ", "b"]]]], ")"]], " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox[RowBox[List[RowBox[List["-", "c"]], "+", RowBox[List["\[ImaginaryI]", " ", "b"]]]]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "c"]], "+", RowBox[List["\[ImaginaryI]", " ", "b"]]]], ")"]], RowBox[List["3", "/", "2"]]]], "-", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", FractionBox[SuperscriptBox["p", "2"], RowBox[List[RowBox[List[RowBox[List["-", "4"]], " ", "c"]], "+", RowBox[List["4", " ", "\[ImaginaryI]", " ", "b"]]]]]], " ", "p", " ", SqrtBox["\[Pi]"], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List["p", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["c", "-", RowBox[List["\[ImaginaryI]", " ", "b"]]]], ")"]], " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox[RowBox[List["c", "-", RowBox[List["\[ImaginaryI]", " ", "b"]]]]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["c", "-", RowBox[List["\[ImaginaryI]", " ", "b"]]]], ")"]], RowBox[List["3", "/", "2"]]]], "-", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", FractionBox[SuperscriptBox["p", "2"], RowBox[List[RowBox[List["4", " ", "c"]], "+", RowBox[List["4", " ", "\[ImaginaryI]", " ", "b"]]]]]], " ", "p", " ", SqrtBox["\[Pi]"], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List["p", "-", RowBox[List["2", " ", RowBox[List["(", RowBox[List["c", "+", RowBox[List["\[ImaginaryI]", " ", "b"]]]], ")"]], " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox[RowBox[List[RowBox[List["-", "c"]], "-", RowBox[List["\[ImaginaryI]", " ", "b"]]]]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "c"]], "-", RowBox[List["\[ImaginaryI]", " ", "b"]]]], ")"]], RowBox[List["3", "/", "2"]]]], "-", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", FractionBox[SuperscriptBox["p", "2"], RowBox[List[RowBox[List[RowBox[List["-", "4"]], " ", "c"]], "-", RowBox[List["4", " ", "\[ImaginaryI]", " ", "b"]]]]]], " ", "p", " ", SqrtBox["\[Pi]"], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List["p", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["c", "+", RowBox[List["\[ImaginaryI]", " ", "b"]]]], ")"]], " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox[RowBox[List["c", "+", RowBox[List["\[ImaginaryI]", " ", "b"]]]]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["c", "+", RowBox[List["\[ImaginaryI]", " ", "b"]]]], ")"]], RowBox[List["3", "/", "2"]]]]]], ")"]]]]]]]]

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

 2002-12-18