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 Cosh

 http://functions.wolfram.com/01.20.21.1323.01

 Input Form

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

 Standard Form

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 MathML Form

 p z ( a + b cos ( d z ) ) β cosh ( c z ) z 1 2 ( c + p - d β ) ( c - p + d β ) ( ( d z b a - a 2 - b 2 + 1 ) - β ( d z b a + a 2 - b 2 + 1 ) - β ( a + 1 2 b - d z ( 1 + 2 d z ) ) β ( ( c + p ) z ( c - p + d β ) F 1 AppellF1 ( - ( c + p - d β ) d ; - β , - β ; - ( c + d + p - d β ) d ; - b d z a + a 2 - b 2 , b d z a 2 - b 2 - a ) - ( p - c ) z ( c + p - d β ) F 1 AppellF1 ( ( c - p + d β ) d ; - β , - β ; - ( - c + d + p - d β ) d ; - b d z a + a 2 - b 2 , b d z a 2 - b 2 - a ) ) ) z p z a b d z β c z 1 2 c p -1 d β c -1 p d β -1 d z b a -1 a 2 -1 b 2 1 2 -1 1 -1 β d z b a a 2 -1 b 2 1 2 -1 1 -1 β a 1 2 b -1 d z 1 2 d z β c p z c -1 p d β AppellF1 -1 c p -1 d β d -1 -1 β -1 β -1 c d p -1 d β d -1 -1 b d z a a 2 -1 b 2 1 2 -1 b d z a 2 -1 b 2 1 2 -1 a -1 -1 p -1 c z c p -1 d β AppellF1 c -1 p d β d -1 -1 β -1 β -1 -1 c d p -1 d β d -1 -1 b d z a a 2 -1 b 2 1 2 -1 b d 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