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/01.20.21.0194.01

 Input Form

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

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[SuperscriptBox["a", RowBox[List[RowBox[List["b", " ", SqrtBox["z"]]], "+", RowBox[List["d", " ", "z"]], "+", "e"]]], RowBox[List["Cosh", "[", RowBox[List["c", " ", "z"]], "]"]], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[FractionBox[SuperscriptBox["a", "e"], "2"], " ", RowBox[List["(", " ", RowBox[List[RowBox[List["b", " ", SqrtBox["\[Pi]"], RowBox[List["Log", "[", "a", "]"]], RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", FractionBox[RowBox[List[SuperscriptBox["b", "2"], " ", SuperscriptBox[RowBox[List["Log", "[", "a", "]"]], "2"]]], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "c"]], "-", RowBox[List["d", " ", RowBox[List["Log", "[", "a", "]"]]]]]], ")"]]]]]], " ", RowBox[List[RowBox[List["Erf", "[", FractionBox[RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "c", " ", SqrtBox["z"]]], "-", RowBox[List["b", " ", RowBox[List["Log", "[", "a", "]"]]]], "-", RowBox[List["2", " ", "d", " ", SqrtBox["z"], " ", RowBox[List["Log", "[", "a", "]"]]]]]], RowBox[List["2", " ", SqrtBox[RowBox[List[RowBox[List["-", "c"]], "-", RowBox[List["d", " ", RowBox[List["Log", "[", "a", "]"]]]]]]]]]], "]"]], " ", "/", RowBox[List["(", RowBox[List["2", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "c"]], "-", RowBox[List["d", " ", RowBox[List["Log", "[", "a", "]"]]]]]], ")"]], RowBox[List["3", "/", "2"]]]]], ")"]]]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", FractionBox[RowBox[List[SuperscriptBox["b", "2"], " ", SuperscriptBox[RowBox[List["Log", "[", "a", "]"]], "2"]]], RowBox[List["4", " ", RowBox[List["(", RowBox[List["c", "-", RowBox[List["d", " ", RowBox[List["Log", "[", "a", "]"]]]]]], ")"]]]]]], " ", RowBox[List[RowBox[List["Erf", "[", FractionBox[RowBox[List[RowBox[List["2", " ", "c", " ", SqrtBox["z"]]], "-", RowBox[List["b", " ", RowBox[List["Log", "[", "a", "]"]]]], "-", RowBox[List["2", " ", "d", " ", SqrtBox["z"], " ", RowBox[List["Log", "[", "a", "]"]]]]]], RowBox[List["2", " ", SqrtBox[RowBox[List["c", "-", RowBox[List["d", " ", RowBox[List["Log", "[", "a", "]"]]]]]]]]]], "]"]], " ", "/", RowBox[List["(", RowBox[List["2", " ", SuperscriptBox[RowBox[List["(", RowBox[List["c", "-", RowBox[List["d", " ", RowBox[List["Log", "[", "a", "]"]]]]]], ")"]], RowBox[List["3", "/", "2"]]]]], ")"]]]]]]]], ")"]]]], "-", FractionBox[RowBox[List[SuperscriptBox["a", RowBox[List[RowBox[List["b", " ", SqrtBox["z"]]], "+", RowBox[List["d", " ", "z"]]]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["c", " ", "z"]]]]], RowBox[List[RowBox[List["-", "c"]], "-", RowBox[List["d", " ", RowBox[List["Log", "[", "a", "]"]]]]]]], "-", FractionBox[RowBox[List[SuperscriptBox["a", RowBox[List[RowBox[List["b", " ", SqrtBox["z"]]], "+", RowBox[List["d", " ", "z"]]]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", "c"]], " ", "z"]]]]], RowBox[List["c", "-", RowBox[List["d", " ", RowBox[List["Log", "[", "a", "]"]]]]]]]]], ")"]]]]]]]]

 MathML Form

 a z b + e + d z cosh ( c z ) z 1 2 a e ( - c z a z b + d z - c - d log ( a ) - - c z a z b + d z c - d log ( a ) + b π log ( a ) ( b 2 log 2 ( a ) 4 ( - c - d log ( a ) ) erf ( - 2 z c - b log ( a ) - 2 d z log ( a ) 2 - c - d log ( a ) ) 2 ( - c - d log ( a ) ) 3 / 2 + b 2 log 2 ( a ) 4 ( c - d log ( a ) ) erf ( 2 z c - b log ( a ) - 2 d z log ( a ) 2 c - d log ( a ) ) 2 ( c - d log ( a ) ) 3 / 2 ) ) z a z 1 2 b e d z c z 1 2 a e -1 c z a z 1 2 b d z -1 c -1 d a -1 -1 -1 c z a z 1 2 b d z c -1 d a -1 b 1 2 a b 2 a 2 4 -1 c -1 d a -1 Erf -2 z 1 2 c -1 b a -1 2 d z 1 2 a 2 -1 c -1 d a 1 2 -1 2 -1 c -1 d a 3 2 -1 b 2 a 2 4 c -1 d a -1 Erf 2 z 1 2 c -1 b a -1 2 d z 1 2 a 2 c -1 d a 1 2 -1 2 c -1 d a 3 2 -1 [/itex]

 Rule Form

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

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

 2002-12-18