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 Cos

 http://functions.wolfram.com/01.07.21.2391.01

 Input Form

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

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

 Rule Form

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

 2002-12-18