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 Cos

 http://functions.wolfram.com/01.07.21.2702.01

 Input Form

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

 p z ( a sin 2 ( e z ) + b cos 2 ( e z ) ) β z 1 p - 2 e β ( 4 - β p 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 F 1 AppellF1 ( - p 2 e - β ; - β , - β ; - p 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 p z a e z 2 b e z 2 β 1 p -1 2 e β -1 4 -1 β p 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 AppellF1 -1 p 2 e -1 -1 β -1 β -1 β -1 p 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