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 Cosh

 http://functions.wolfram.com/01.20.21.3896.01

 Input Form

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

 Standard Form

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 MathML Form

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

 Rule Form

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

 2002-12-18