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 Cos

 http://functions.wolfram.com/01.07.21.2406.01

 Input Form

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

 Standard Form

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 MathML Form

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

 Rule Form

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

 2002-12-18