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 Cosh

 http://functions.wolfram.com/01.20.21.1262.01

 Input Form

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

 Standard Form

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

 MathML Form

 p z cos ( b z ) cosh ( c z ) z 1 8 ( 8 p z cos ( b z ) ( p cosh ( c z ) - c sinh ( c z ) ) p 2 - c 2 + b b 2 4 p - 4 c π erfi ( - b + 2 ( p - c ) z 2 p - c ) ( p - c ) 3 / 2 + b b 2 4 ( c + p ) π erfi ( - b + 2 ( c + p ) z 2 c + p ) ( c + p ) 3 / 2 - b b 2 4 p - 4 c π erfi ( b + 2 ( p - c ) z 2 p - c ) ( p - c ) 3 / 2 - b b 2 4 ( c + p ) π erfi ( b + 2 ( c + p ) z 2 c + p ) ( c + p ) 3 / 2 ) z p z b z 1 2 c z 1 8 8 p z b z 1 2 p c z -1 c c z p 2 -1 c 2 -1 b b 2 4 p -1 4 c -1 1 2 Erfi -1 b 2 p -1 c z 1 2 2 p -1 c 1 2 -1 p -1 c 3 2 -1 b b 2 4 c p -1 1 2 Erfi -1 b 2 c p z 1 2 2 c p 1 2 -1 c p 3 2 -1 -1 b b 2 4 p -1 4 c -1 1 2 Erfi b 2 p -1 c z 1 2 2 p -1 c 1 2 -1 p -1 c 3 2 -1 -1 b b 2 4 c p -1 1 2 Erfi b 2 c p z 1 2 2 c p 1 2 -1 c p 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_", " ", "z_"]]], " ", RowBox[List["Cos", "[", RowBox[List["b_", " ", SqrtBox["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", " ", "z"]]], " ", RowBox[List["Cos", "[", RowBox[List["b", " ", SqrtBox["z"]]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["p", " ", RowBox[List["Cosh", "[", RowBox[List["c", " ", "z"]], "]"]]]], "-", RowBox[List["c", " ", RowBox[List["Sinh", "[", RowBox[List["c", " ", "z"]], "]"]]]]]], ")"]]]], RowBox[List[RowBox[List["-", SuperscriptBox["c", "2"]]], "+", SuperscriptBox["p", "2"]]]], "+", FractionBox[RowBox[List["\[ImaginaryI]", " ", "b", " ", SuperscriptBox["\[ExponentialE]", FractionBox[SuperscriptBox["b", "2"], RowBox[List[RowBox[List[RowBox[List["-", "4"]], " ", "c"]], "+", RowBox[List["4", " ", "p"]]]]]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "b"]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "c"]], "+", "p"]], ")"]], " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox[RowBox[List[RowBox[List["-", "c"]], "+", "p"]]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "c"]], "+", "p"]], ")"]], RowBox[List["3", "/", "2"]]]], "-", FractionBox[RowBox[List["\[ImaginaryI]", " ", "b", " ", SuperscriptBox["\[ExponentialE]", FractionBox[SuperscriptBox["b", "2"], RowBox[List[RowBox[List[RowBox[List["-", "4"]], " ", "c"]], "+", RowBox[List["4", " ", "p"]]]]]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List[RowBox[List["\[ImaginaryI]", " ", "b"]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "c"]], "+", "p"]], ")"]], " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox[RowBox[List[RowBox[List["-", "c"]], "+", "p"]]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "c"]], "+", "p"]], ")"]], RowBox[List["3", "/", "2"]]]], "+", FractionBox[RowBox[List["\[ImaginaryI]", " ", "b", " ", SuperscriptBox["\[ExponentialE]", FractionBox[SuperscriptBox["b", "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["c", "+", "p"]], ")"]]]]]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "b"]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["c", "+", "p"]], ")"]], " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox[RowBox[List["c", "+", "p"]]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["c", "+", "p"]], ")"]], RowBox[List["3", "/", "2"]]]], "-", FractionBox[RowBox[List["\[ImaginaryI]", " ", "b", " ", SuperscriptBox["\[ExponentialE]", FractionBox[SuperscriptBox["b", "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["c", "+", "p"]], ")"]]]]]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List[RowBox[List["\[ImaginaryI]", " ", "b"]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["c", "+", "p"]], ")"]], " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox[RowBox[List["c", "+", "p"]]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["c", "+", "p"]], ")"]], RowBox[List["3", "/", "2"]]]]]], ")"]]]]]]]]

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

 2002-12-18