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 Cos

 http://functions.wolfram.com/01.07.21.2419.01

 Input Form

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

 Standard Form

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 MathML Form

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

 Rule Form

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

 2002-12-18