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/01.20.21.0265.01

 Input Form

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

 Standard Form

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

 MathML Form

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

 Rule Form

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

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

 2002-12-18