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/01.20.21.0191.01

 Input Form

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

 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["c", " ", "z"]], "]"]], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", FractionBox[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["b", " ", SqrtBox["z"]]], "-", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "c"]], "-", "d"]], ")"]], " ", "z"]]]]], RowBox[List[RowBox[List["-", "c"]], "-", "d"]]]]], "-", FractionBox[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["b", " ", SqrtBox["z"]]], "-", RowBox[List[RowBox[List["(", RowBox[List["c", "-", "d"]], ")"]], " ", "z"]]]]], RowBox[List["c", "-", "d"]]], "+", FractionBox[RowBox[List["b", SqrtBox["\[Pi]"], " ", SuperscriptBox["\[ExponentialE]", FractionBox[SuperscriptBox["b", "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "c"]], "-", "d"]], ")"]]]]]], " ", RowBox[List["Erf", "[", FractionBox[RowBox[List[RowBox[List["-", "b"]], "-", RowBox[List["2", " ", "c", " ", SqrtBox["z"]]], "-", RowBox[List["2", " ", "d", " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox[RowBox[List[RowBox[List["-", "c"]], "-", "d"]]]]]], "]"]]]], RowBox[List["2", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "c"]], "-", "d"]], ")"]], RowBox[List["3", "/", "2"]]]]]], "+", FractionBox[RowBox[List["b", SqrtBox["\[Pi]"], " ", SuperscriptBox["\[ExponentialE]", FractionBox[SuperscriptBox["b", "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["c", "-", "d"]], ")"]]]]]], " ", RowBox[List["Erf", "[", FractionBox[RowBox[List[RowBox[List["-", "b"]], "+", RowBox[List["2", " ", "c", " ", SqrtBox["z"]]], "-", RowBox[List["2", " ", "d", " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox[RowBox[List["c", "-", "d"]]]]]], "]"]]]], RowBox[List["2", " ", SuperscriptBox[RowBox[List["(", RowBox[List["c", "-", "d"]], ")"]], RowBox[List["3", "/", "2"]]]]]]]], ")"]]]]]]]]

 MathML Form

 z b + d z cosh ( c z ) z 1 2 ( b b 2 4 ( - c - d ) π erf ( - b - 2 c z - 2 d z 2 - c - d ) 2 ( - c - d ) 3 / 2 + b b 2 4 ( c - d ) π erf ( - b + 2 c z - 2 d z 2 c - d ) 2 ( c - d ) 3 / 2 - b z - ( - c - d ) z - c - d - b z - ( c - d ) z c - d ) z z 1 2 b d z c z 1 2 b b 2 4 -1 c -1 d -1 1 2 Erf -1 b -1 2 c z 1 2 -1 2 d z 1 2 2 -1 c -1 d 1 2 -1 2 -1 c -1 d 3 2 -1 b b 2 4 c -1 d -1 1 2 Erf -1 b 2 c z 1 2 -1 2 d z 1 2 2 c -1 d 1 2 -1 2 c -1 d 3 2 -1 -1 b z 1 2 -1 -1 c -1 d z -1 c -1 d -1 -1 b z 1 2 -1 c -1 d z c -1 d -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["c_", " ", "z_"]], "]"]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", FractionBox[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["b", " ", SqrtBox["z"]]], "-", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "c"]], "-", "d"]], ")"]], " ", "z"]]]]], RowBox[List[RowBox[List["-", "c"]], "-", "d"]]]]], "-", FractionBox[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["b", " ", SqrtBox["z"]]], "-", RowBox[List[RowBox[List["(", RowBox[List["c", "-", "d"]], ")"]], " ", "z"]]]]], RowBox[List["c", "-", "d"]]], "+", FractionBox[RowBox[List["b", " ", SqrtBox["\[Pi]"], " ", SuperscriptBox["\[ExponentialE]", FractionBox[SuperscriptBox["b", "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "c"]], "-", "d"]], ")"]]]]]], " ", RowBox[List["Erf", "[", FractionBox[RowBox[List[RowBox[List["-", "b"]], "-", RowBox[List["2", " ", "c", " ", SqrtBox["z"]]], "-", RowBox[List["2", " ", "d", " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox[RowBox[List[RowBox[List["-", "c"]], "-", "d"]]]]]], "]"]]]], RowBox[List["2", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "c"]], "-", "d"]], ")"]], RowBox[List["3", "/", "2"]]]]]], "+", FractionBox[RowBox[List["b", " ", SqrtBox["\[Pi]"], " ", SuperscriptBox["\[ExponentialE]", FractionBox[SuperscriptBox["b", "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["c", "-", "d"]], ")"]]]]]], " ", RowBox[List["Erf", "[", FractionBox[RowBox[List[RowBox[List["-", "b"]], "+", RowBox[List["2", " ", "c", " ", SqrtBox["z"]]], "-", RowBox[List["2", " ", "d", " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox[RowBox[List["c", "-", "d"]]]]]], "]"]]]], RowBox[List["2", " ", SuperscriptBox[RowBox[List["(", RowBox[List["c", "-", "d"]], ")"]], RowBox[List["3", "/", "2"]]]]]]]], ")"]]]]]]]]

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

 2002-12-18