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 Cosh

 http://functions.wolfram.com/01.20.21.1324.01

 Input Form

 Integrate[E^(p z) (a + b Cos[d z]^2)^\[Beta] Cosh[c z], z] == ((a + ((1/4) b (1 + E^(2 I d z))^2)/E^(2 I d z))^\[Beta] (E^((c + p) z) (c - p + 2 I d \[Beta]) AppellF1[-((I (c + p - 2 I d \[Beta]))/(2 d)), -\[Beta], -\[Beta], 1 - (I (c + p))/(2 d) - \[Beta], -((b E^(2 I d z))/(2 a + b + 2 Sqrt[a (a + b)])), -((b E^(2 I d z))/(2 a + b - 2 Sqrt[a (a + b)]))] - E^((-c + p) z) (c + p - 2 I d \[Beta]) AppellF1[(I (c - p + 2 I d \[Beta]))/(2 d), -\[Beta], -\[Beta], 1 - (I (-c + p))/(2 d) - \[Beta], -((b E^(2 I d z))/(2 a + b + 2 Sqrt[a (a + b)])), -((b E^(2 I d z))/(2 a + b - 2 Sqrt[a (a + b)]))]))/ ((1 + (b E^(2 I d z))/(2 a + b - 2 Sqrt[a (a + b)]))^\[Beta] (1 + (b E^(2 I d z))/(2 a + b + 2 Sqrt[a (a + b)]))^\[Beta])/ (2 (c + p - 2 I d \[Beta]) (c - p + 2 I d \[Beta]))

 Standard Form

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 MathML Form

 p z ( a + b cos 2 ( d z ) ) β cosh ( c z ) z ( ( 2 d z b 2 a + b - 2 a ( a + b ) + 1 ) - β ( 2 d z b 2 a + b + 2 a ( a + b ) + 1 ) - β ( 1 4 b - 2 d z ( 1 + 2 d z ) 2 + a ) β ( ( c + p ) z ( c - p + 2 d β ) F 1 AppellF1 ( - ( c + p - 2 d β ) 2 d ; - β , - β ; - ( c + p ) 2 d - β + 1 ; - b 2 d z 2 a + b + 2 a ( a + b ) , - b 2 d z 2 a + b - 2 a ( a + b ) ) - ( p - c ) z ( c + p - 2 d β ) F 1 AppellF1 ( ( c - p + 2 d β ) 2 d ; - β , - β ; - ( p - c ) 2 d - β + 1 ; - b 2 d z 2 a + b + 2 a ( a + b ) , - b 2 d z 2 a + b - 2 a ( a + b ) ) ) ) / ( 2 ( c + p - 2 d β ) ( c - p + 2 d β ) ) z p z a b d z 2 β c z 2 d z b 2 a b -1 2 a a b 1 2 -1 1 -1 β 2 d z b 2 a b 2 a a b 1 2 -1 1 -1 β 1 4 b -2 d z 1 2 d z 2 a β c p z c -1 p 2 d β AppellF1 -1 c p -1 2 d β 2 d -1 -1 β -1 β -1 c p 2 d -1 -1 β 1 -1 b 2 d z 2 a b 2 a a b 1 2 -1 -1 b 2 d z 2 a b -1 2 a a b 1 2 -1 -1 p -1 c z c p -1 2 d β AppellF1 c -1 p 2 d β 2 d -1 -1 β -1 β -1 p -1 c 2 d -1 -1 β 1 -1 b 2 d z 2 a b 2 a a b 1 2 -1 -1 b 2 d z 2 a b -1 2 a a b 1 2 -1 2 c p -1 2 d β c -1 p 2 d β -1 [/itex]

 Rule Form

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

 2002-12-18