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 Cos

 http://functions.wolfram.com/01.07.21.2692.01

 Input Form

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

 Standard Form

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 MathML Form

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

 Rule Form

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

 2002-12-18