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 Cos

 http://functions.wolfram.com/01.07.21.2700.01

 Input Form

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

 Standard Form

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 MathML Form

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

 Rule Form

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

 2002-12-18