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 Cos

 http://functions.wolfram.com/01.07.21.2693.01

 Input Form

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

 Standard Form

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 MathML Form

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