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; }

 Cos

 http://functions.wolfram.com/01.07.21.2695.01

 Input Form

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

 Standard Form

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 MathML Form

 p z sin ( d z ) cos ( e z ) ( a + b cos 2 ( c z ) ) β z - 1 4 ( 2 c z b 2 a + b - 2 a ( a + b ) + 1 ) - β ( 2 c z b 2 a + b + 2 a ( a + b ) + 1 ) - β ( 1 4 b - 2 c z ( 1 + 2 c z ) 2 + a ) β ( ( d + e + p ) z d + e - p - 2 c β F 1 AppellF1 ( d + e - p - 2 c β 2 c ; - β , - β ; - 2 β c + 2 c + d + e - p 2 c ; - b 2 c z 2 a + b + 2 a ( a + b ) , - b 2 c z 2 a + b - 2 a ( a + b ) ) + ( - d + e + p ) z d - e + p + 2 c β F 1 AppellF1 ( - d - e + p + 2 c β 2 c ; - β , - β ; - d - e + p + 2 c ( β - 1 ) 2 c ; - b 2 c z 2 a + b + 2 a ( a + b ) , - b 2 c z 2 a + b - 2 a ( a + b ) ) + ( d - e + p ) z d - e - p - 2 c β F 1 AppellF1 ( - - d + e + p + 2 c β 2 c ; - β , - β ; - - d + e + p + 2 c ( β - 1 ) 2 c ; - b 2 c z 2 a + b + 2 a ( a + b ) , - b 2 c z 2 a + b - 2 a ( a + b ) ) + - ( d + e + p ) z d + e + p + 2 c β F 1 AppellF1 ( - d + e + p + 2 c β 2 c ; - β , - β ; - d + e + p + 2 c ( β - 1 ) 2 c ; - b 2 c z 2 a + b + 2 a ( a + b ) , - b 2 c z 2 a + b - 2 a ( a + b ) ) ) z p z d z e z a b c z 2 β -1 1 4 2 c z b 2 a b -1 2 a a b 1 2 -1 1 -1 β 2 c z b 2 a b 2 a a b 1 2 -1 1 -1 β 1 4 b -2 c z 1 2 c z 2 a β d e p z d e -1 p -1 2 c β -1 AppellF1 d e -1 p -1 2 c β 2 c -1 -1 β -1 β -2 β c 2 c d e -1 p 2 c -1 -1 b 2 c z 2 a b 2 a a b 1 2 -1 -1 b 2 c z 2 a b -1 2 a a b 1 2 -1 -1 d e p z d -1 e p 2 c β -1 AppellF1 -1 d -1 e p 2 c β 2 c -1 -1 β -1 β -1 d -1 e p 2 c β -1 2 c -1 -1 b 2 c z 2 a b 2 a a b 1 2 -1 -1 b 2 c z 2 a b -1 2 a a b 1 2 -1 d -1 e p z d -1 e -1 p -1 2 c β -1 AppellF1 -1 -1 d e p 2 c β 2 c -1 -1 β -1 β -1 -1 d e p 2 c β -1 2 c -1 -1 b 2 c z 2 a b 2 a a b 1 2 -1 -1 b 2 c z 2 a b -1 2 a a b 1 2 -1 -1 d e p z d e p 2 c β -1 AppellF1 -1 d e p 2 c β 2 c -1 -1 β -1 β -1 d e p 2 c β -1 2 c -1 -1 b 2 c z 2 a b 2 a a b 1 2 -1 -1 b 2 c 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