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 Cosh

 http://functions.wolfram.com/01.20.21.1192.01

 Input Form

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

 Standard Form

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

 MathML Form

 p z sin ( b z ) cosh ( c z ) z 1 4 ( 2 ( p - c ) z ( 1 + 2 c z ) cos ( b z ) b + ( p - c ) 2 4 b ( p - c ) π erfi ( - c + p + 2 b z 2 b ) 2 ( b ) 3 / 2 + ( c + p ) 2 4 b ( c + p ) π erfi ( c + p + 2 b z 2 b ) 2 ( b ) 3 / 2 - - ( p - c ) 2 4 b ( p - c ) π erfi ( - c + p - 2 b z 2 - b ) 2 ( - b ) 3 / 2 - - ( c + p ) 2 4 b ( c + p ) π erfi ( c + p - 2 b z 2 - b ) 2 ( - b ) 3 / 2 ) z p z 1 2 b z c z 1 2 1 4 2 p -1 c z 1 2 1 2 c z 1 2 b z b -1 p -1 c 2 4 b -1 p -1 c 1 2 Erfi -1 c p 2 b z 1 2 2 b 1 2 -1 2 b 3 2 -1 c p 2 4 b -1 c p 1 2 Erfi c p 2 b z 1 2 2 b 1 2 -1 2 b 3 2 -1 -1 -1 p -1 c 2 4 b -1 p -1 c 1 2 Erfi -1 c p -1 2 b z 1 2 2 -1 b 1 2 -1 2 -1 b 3 2 -1 -1 -1 c p 2 4 b -1 c p 1 2 Erfi c p -1 2 b z 1 2 2 -1 b 1 2 -1 2 -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["Sin", "[", RowBox[List["b_", " ", "z_"]], "]"]], " ", RowBox[List["Cosh", "[", RowBox[List["c_", " ", SqrtBox["z_"]]], "]"]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox["1", "4"], " ", "\[ImaginaryI]", " ", RowBox[List["(", RowBox[List[FractionBox[RowBox[List["2", " ", "\[ImaginaryI]", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "c"]], "+", "p"]], ")"]], " ", SqrtBox["z"]]]], " ", RowBox[List["(", RowBox[List["1", "+", SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "c", " ", SqrtBox["z"]]]]]], ")"]], " ", RowBox[List["Cos", "[", RowBox[List["b", " ", "z"]], "]"]]]], "b"], "-", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "c"]], "+", "p"]], ")"]], "2"]]], RowBox[List["4", " ", "b"]]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "c"]], "+", "p"]], ")"]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List[RowBox[List["-", "c"]], "+", "p", "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "b"]]]]]], "]"]]]], RowBox[List["2", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "b"]], ")"]], RowBox[List["3", "/", "2"]]]]]], "-", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox[RowBox[List["(", RowBox[List["c", "+", "p"]], ")"]], "2"]]], RowBox[List["4", " ", "b"]]]]]], " ", RowBox[List["(", RowBox[List["c", "+", "p"]], ")"]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List["c", "+", "p", "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "b"]]]]]], "]"]]]], RowBox[List["2", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "b"]], ")"]], RowBox[List["3", "/", "2"]]]]]], "+", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "c"]], "+", "p"]], ")"]], "2"]]], RowBox[List["4", " ", "b"]]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "c"]], "+", "p"]], ")"]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List[RowBox[List["-", "c"]], "+", "p", "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox[RowBox[List["\[ImaginaryI]", " ", "b"]]]]]], "]"]]]], RowBox[List["2", " ", SuperscriptBox[RowBox[List["(", RowBox[List["\[ImaginaryI]", " ", "b"]], ")"]], RowBox[List["3", "/", "2"]]]]]], "+", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox[RowBox[List["(", RowBox[List["c", "+", "p"]], ")"]], "2"]]], RowBox[List["4", " ", "b"]]]], " ", RowBox[List["(", RowBox[List["c", "+", "p"]], ")"]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List["c", "+", "p", "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox[RowBox[List["\[ImaginaryI]", " ", "b"]]]]]], "]"]]]], RowBox[List["2", " ", SuperscriptBox[RowBox[List["(", RowBox[List["\[ImaginaryI]", " ", "b"]], ")"]], RowBox[List["3", "/", "2"]]]]]]]], ")"]]]]]]]]

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

 2002-12-18