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 Cos

 http://functions.wolfram.com/01.07.21.2707.01

 Input Form

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

 Standard Form

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 MathML Form

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

 Rule Form

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

 2002-12-18