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 Cos

 http://functions.wolfram.com/01.07.21.2390.01

 Input Form

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

 Standard Form

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 MathML Form

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

 Rule Form

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

 2002-12-18