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/01.20.21.0860.01

 Input Form

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

 Standard Form

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RowBox[List["(", RowBox[List["c", "+", RowBox[List["\[ImaginaryI]", " ", "e"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "d", " ", "\[Beta]"]]]], ")"]]]], RowBox[List["2", " ", "d"]]], ",", RowBox[List["-", "\[Beta]"]], ",", RowBox[List["-", "\[Beta]"]], ",", FractionBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["c", "+", RowBox[List["\[ImaginaryI]", " ", "e"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "d", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "\[Beta]"]], ")"]]]]]], ")"]]]], RowBox[List["2", " ", "d"]]], ",", RowBox[List["-", FractionBox[RowBox[List["b", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "\[ImaginaryI]", " ", "d", " ", "z"]]]]], RowBox[List[RowBox[List["2", " ", "a"]], "+", "b", "+", RowBox[List["2", " ", SqrtBox[RowBox[List["a", " ", RowBox[List["(", RowBox[List["a", "+", "b"]], ")"]]]]]]]]]]]], ",", RowBox[List["-", FractionBox[RowBox[List["b", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "\[ImaginaryI]", " ", "d", " ", "z"]]]]], RowBox[List[RowBox[List["2", " ", "a"]], "+", "b", "-", RowBox[List["2", " ", SqrtBox[RowBox[List["a", " ", RowBox[List["(", RowBox[List["a", "+", "b"]], ")"]]]]]]]]]]]]]], "]"]]]], ")"]], "/", RowBox[List["(", RowBox[List["c", "+", RowBox[List["\[ImaginaryI]", " ", "e"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "d", " ", "\[Beta]"]]]], ")"]]]]]], ")"]]]]]]]]

 MathML Form

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

 Rule Form

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

 2002-12-18