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 Cos

 http://functions.wolfram.com/01.07.21.2705.01

 Input Form

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

 Standard Form

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 MathML Form

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

 Rule Form

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

 2002-12-18