html, body, form { margin: 0; padding: 0; width: 100%; } #calculate { position: relative; width: 177px; height: 110px; background: transparent url(/images/alphabox/embed_functions_inside.gif) no-repeat scroll 0 0; } #i { position: relative; left: 18px; top: 44px; width: 133px; border: 0 none; outline: 0; font-size: 11px; } #eq { width: 9px; height: 10px; background: transparent; position: absolute; top: 47px; right: 18px; cursor: pointer; }

 Cosh

 http://functions.wolfram.com/01.20.21.1266.01

 Input Form

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

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

 MathML Form

 p z cos ( b z ) cosh ( c z ) z 1 8 ( - ( c - p ) 2 4 b ( c - p ) π erfi ( - c + p - 2 b z 2 - b ) ( - b ) 3 / 2 + - b - ( c + p ) 2 4 b ( c + p ) π erfi ( c + p - 2 b z 2 - b ) b 2 + 8 p z cosh ( c z ) sin ( b z ) b - b ( c - p ) 2 4 b ( c - p ) π erfi ( - c + p + 2 b z 2 b ) b 2 - ( c + p ) 2 4 b ( c + p ) π erfi ( c + p + 2 b z 2 b ) ( b ) 3 / 2 ) z p z 1 2 b z c z 1 2 1 8 -1 c -1 p 2 4 b -1 c -1 p 1 2 Erfi -1 c p -1 2 b z 1 2 2 -1 b 1 2 -1 -1 b 3 2 -1 -1 b 1 2 -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 b 2 -1 8 p z 1 2 c z 1 2 b z b -1 -1 b 1 2 c -1 p 2 4 b -1 c -1 p 1 2 Erfi -1 c p 2 b z 1 2 2 b 1 2 -1 b 2 -1 -1 c p 2 4 b -1 c p 1 2 Erfi c p 2 b z 1 2 2 b 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["Cos", "[", RowBox[List["b_", " ", "z_"]], "]"]], " ", RowBox[List["Cosh", "[", RowBox[List["c_", " ", SqrtBox["z_"]]], "]"]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List[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[RowBox[List["-", "c"]], "+", "p", "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "b"]]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "b"]], ")"]], RowBox[List["3", "/", "2"]]]], "+", FractionBox[RowBox[List[SqrtBox[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "b"]]], " ", 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"]]]]]], "]"]]]], SuperscriptBox["b", "2"]], "-", FractionBox[RowBox[List[SqrtBox[RowBox[List["\[ImaginaryI]", " ", "b"]]], " ", 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[RowBox[List["-", "c"]], "+", "p", "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox[RowBox[List["\[ImaginaryI]", " ", "b"]]]]]], "]"]]]], SuperscriptBox["b", "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"]]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["\[ImaginaryI]", " ", "b"]], ")"]], RowBox[List["3", "/", "2"]]]], "+", FractionBox[RowBox[List["8", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["p", " ", SqrtBox["z"]]]], " ", RowBox[List["Cosh", "[", RowBox[List["c", " ", SqrtBox["z"]]], "]"]], " ", RowBox[List["Sin", "[", RowBox[List["b", " ", "z"]], "]"]]]], "b"]]], ")"]]]]]]]]

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

 2002-12-18