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/01.20.21.0691.01

 Input Form

 Integrate[Sin[e z] Cosh[c z] (a + b Sin[d z])^\[Beta], z] == ((-(1/4)) I (-((E^((c - I e) z) AppellF1[(I (c - I e))/d - \[Beta], -\[Beta], -\[Beta], 1 + (I (c - I e))/d - \[Beta], -((I b)/(E^(I d z) (a + Sqrt[a^2 - b^2]))), -((I b)/(E^(I d z) (a - Sqrt[a^2 - b^2])))])/ (c - I e + I d \[Beta])) + (E^((-c + I e) z) AppellF1[(I (-c + I e))/d - \[Beta], -\[Beta], -\[Beta], 1 + (I (-c + I e))/d - \[Beta], -((I b)/(E^(I d z) (a + Sqrt[a^2 - b^2]))), -((I b)/(E^(I d z) (a - Sqrt[a^2 - b^2])))])/ (-c + I e + I d \[Beta]) + (E^((c + I e) z) AppellF1[(I (c + I e))/d - \[Beta], -\[Beta], -\[Beta], 1 + (I (c + I e))/d - \[Beta], -((I b)/(E^(I d z) (a + Sqrt[a^2 - b^2]))), -((I b)/(E^(I d z) (a - Sqrt[a^2 - b^2])))])/(c + I e + I d \[Beta]) + (E^((-c - I e) z) AppellF1[-((I (c + I e - I d \[Beta]))/d), -\[Beta], -\[Beta], -((-d + I (c + I e) + d \[Beta])/d), -((I b)/(E^(I d z) (a + Sqrt[a^2 - b^2]))), -((I b)/(E^(I d z) (a - Sqrt[a^2 - b^2])))])/(c + I e - I d \[Beta])) (a + b Sin[d z])^\[Beta])/((1 - (I b)/(E^(I d z) (-a + Sqrt[a^2 - b^2])))^ \[Beta] (1 + (I b)/(E^(I d z) (a + Sqrt[a^2 - b^2])))^\[Beta])

 Standard Form

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"\[ImaginaryI]"]], " ", "d", " ", "z"]]]]], RowBox[List["a", "-", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "-", SuperscriptBox["b", "2"]]]]]]]]]]], "]"]]]], ")"]], "/", RowBox[List["(", RowBox[List["c", "+", RowBox[List["\[ImaginaryI]", " ", "e"]], "-", RowBox[List["\[ImaginaryI]", " ", "d", " ", "\[Beta]"]]]], ")"]]]]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["a", "+", RowBox[List["b", " ", RowBox[List["Sin", "[", RowBox[List["d", " ", "z"]], "]"]]]]]], ")"]], "\[Beta]"]]]]]]]

 MathML Form

 ( a + b sin ( d z ) ) β sin ( e z ) cosh ( c z ) z - 1 4 ( 1 - b - d z a 2 - b 2 - a ) - β ( 1 + b - d z a + a 2 - b 2 ) - β ( a + b sin ( d z ) ) β ( ( - c - e ) z c + e - d β F 1 AppellF1 ( - ( c + e - d β ) d ; - β , - β ; - β d - d + ( c + e ) d ; - b - d z a + a 2 - b 2 , - b - d z a - a 2 - b 2 ) + ( e - c ) z - c + e + d β F 1 AppellF1 ( ( e - c ) d - β ; - β , - β ; 1 + ( e - c ) d - β ; - b - d z a + a 2 - b 2 , - b - d z a - a 2 - b 2 ) + ( c + e ) z c + e + d β F 1 AppellF1 ( ( c + e ) d - β ; - β , - β ; 1 + ( c + e ) d - β ; - b - d z a + a 2 - b 2 , - b - d z a - a 2 - b 2 ) - ( c - e ) z c - e + d β F 1 AppellF1 ( ( c - e ) d - β ; - β , - β ; 1 + ( c - e ) d - β ; - b - d z a + a 2 - b 2 , - b - d z a - a 2 - b 2 ) ) z a b d z β e z c z -1 1 4 1 -1 b -1 d z a 2 -1 b 2 1 2 -1 a -1 -1 β 1 b -1 d z a a 2 -1 b 2 1 2 -1 -1 β a b d z β -1 c -1 e z c e -1 d β -1 AppellF1 -1 c e -1 d β d -1 -1 β -1 β -1 β d -1 d c e d -1 -1 b -1 d z a a 2 -1 b 2 1 2 -1 -1 b -1 d z a -1 a 2 -1 b 2 1 2 -1 e -1 c z -1 c e d β -1 AppellF1 e -1 c d -1 -1 β -1 β -1 β 1 e -1 c d -1 -1 β -1 b -1 d z a a 2 -1 b 2 1 2 -1 -1 b -1 d z a -1 a 2 -1 b 2 1 2 -1 c e z c e d β -1 AppellF1 c e d -1 -1 β -1 β -1 β 1 c e d -1 -1 β -1 b -1 d z a a 2 -1 b 2 1 2 -1 -1 b -1 d z a -1 a 2 -1 b 2 1 2 -1 -1 c -1 e z c -1 e d β -1 AppellF1 c -1 e d -1 -1 β -1 β -1 β 1 c -1 e d -1 -1 β -1 b -1 d z a a 2 -1 b 2 1 2 -1 -1 b -1 d z a -1 a 2 -1 b 2 1 2 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[RowBox[List[RowBox[List["Sin", "[", RowBox[List["e_", " ", "z_"]], "]"]], " ", RowBox[List["Cosh", "[", RowBox[List["c_", " ", "z_"]], "]"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["a_", "+", RowBox[List["b_", " ", RowBox[List["Sin", "[", RowBox[List["d_", " ", "z_"]], "]"]]]]]], ")"]], "\[Beta]_"]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["-", FractionBox["1", "4"]]], " ", "\[ImaginaryI]", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", FractionBox[RowBox[List["\[ImaginaryI]", " ", "b", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "d", " ", "z"]]]]], RowBox[List[RowBox[List["-", "a"]], "+", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "-", SuperscriptBox["b", "2"]]]]]]]]], ")"]], RowBox[List["-", "\[Beta]"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", 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 Date Added to functions.wolfram.com (modification date)

 2002-12-18