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 Cos

 http://functions.wolfram.com/01.07.21.2651.01

 Input Form

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

 Standard Form

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 MathML Form

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

 Rule Form

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

 2002-12-18