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/01.20.21.1464.01

 Input Form

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

 Standard Form

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

 MathML Form

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

 Rule Form

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

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

 2002-12-18