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/01.20.21.0599.01

 Input Form

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

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[RowBox[List["Sin", "[", RowBox[List[RowBox[List["b", " ", SqrtBox["z"]]], "+", RowBox[List["d", " ", "z"]], "+", "e"]], "]"]], RowBox[List["Cosh", "[", RowBox[List[RowBox[List["c", " ", SqrtBox["z"]]], "+", RowBox[List["f", " ", "z"]], "+", "g"]], "]"]], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[FractionBox["\[ImaginaryI]", "8"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "e"]], "-", "g"]]]]], " ", RowBox[List["(", RowBox[List[FractionBox[RowBox[List["4", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "e"]], "+", "g"]]], " ", RowBox[List["Cos", "[", RowBox[List["e", "+", RowBox[List["\[ImaginaryI]", " ", "g"]], "+", RowBox[List[RowBox[List["(", RowBox[List["b", "+", RowBox[List["\[ImaginaryI]", " ", "c"]]]], ")"]], " ", SqrtBox["z"]]], "+", 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"f"]], ")"]], " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox[RowBox[List[RowBox[List["\[ImaginaryI]", " ", "d"]], "+", "f"]]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "d"]], "+", "f"]], ")"]], RowBox[List["3", "/", "2"]]]]]], ")"]]]]]], ")"]]]]]]]]

 MathML Form

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

 Rule Form

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

 2002-12-18