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/01.20.21.0207.01

 Input Form

 Integrate[E^(b Sqrt[z] + d z) Cosh[f z + g], z] == ((1/4) (-2 E^(b Sqrt[z]) (E^((d - f) z)/(-d + f) - E^(2 g + (d + f) z)/ (d + f)) - (b E^(b^2/(-4 d + 4 f)) Sqrt[Pi] Erfi[(b + 2 (d - f) Sqrt[z])/(2 Sqrt[d - f])])/(d - f)^(3/2) - (b E^(-(b^2/(4 (d + f))) + 2 g) Sqrt[Pi] Erfi[(b + 2 (d + f) Sqrt[z])/(2 Sqrt[d + f])])/(d + f)^(3/2)))/E^g

 Standard Form

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

 MathML Form

 z b + d z cosh ( g + f z ) z 1 4 - g ( - 2 b z ( ( d - f ) z f - d - 2 g + ( d + f ) z d + f ) - b b 2 4 f - 4 d π erfi ( b + 2 ( d - f ) z 2 d - f ) ( d - f ) 3 / 2 - b 2 g - b 2 4 ( d + f ) π erfi ( b + 2 ( d + f ) z 2 d + f ) ( d + f ) 3 / 2 ) z z 1 2 b d z g f z 1 4 -1 g -2 b z 1 2 d -1 f z f -1 d -1 -1 2 g d f z d f -1 -1 b b 2 4 f -1 4 d -1 1 2 Erfi b 2 d -1 f z 1 2 2 d -1 f 1 2 -1 d -1 f 3 2 -1 -1 b 2 g -1 b 2 4 d f -1 1 2 Erfi b 2 d f z 1 2 2 d f 1 2 -1 d f 3 2 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["b_", " ", SqrtBox["z_"]]], "+", RowBox[List["d_", " ", "z_"]]]]], " ", RowBox[List["Cosh", "[", RowBox[List[RowBox[List["f_", " ", "z_"]], "+", "g_"]], "]"]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox["1", "4"], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["-", "g"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["b", " ", SqrtBox["z"]]]], " ", RowBox[List["(", RowBox[List[FractionBox[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["(", RowBox[List["d", "-", "f"]], ")"]], " ", "z"]]], RowBox[List[RowBox[List["-", "d"]], "+", "f"]]], "-", FractionBox[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["2", " ", "g"]], "+", RowBox[List[RowBox[List["(", RowBox[List["d", "+", "f"]], ")"]], " ", "z"]]]]], RowBox[List["d", "+", "f"]]]]], ")"]]]], "-", FractionBox[RowBox[List["b", " ", SuperscriptBox["\[ExponentialE]", FractionBox[SuperscriptBox["b", "2"], RowBox[List[RowBox[List[RowBox[List["-", "4"]], " ", "d"]], "+", RowBox[List["4", " ", "f"]]]]]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List["b", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "-", "f"]], ")"]], " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox[RowBox[List["d", "-", "f"]]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["d", "-", "f"]], ")"]], RowBox[List["3", "/", "2"]]]], "-", FractionBox[RowBox[List["b", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", FractionBox[SuperscriptBox["b", "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["d", "+", "f"]], ")"]]]]]]], "+", RowBox[List["2", " ", "g"]]]]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List["b", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "+", "f"]], ")"]], " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox[RowBox[List["d", "+", "f"]]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", "f"]], ")"]], RowBox[List["3", "/", "2"]]]]]], ")"]]]]]]]]

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

 2002-12-18