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 Cos

 http://functions.wolfram.com/01.07.21.2708.01

 Input Form

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

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