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 Cosh

 http://functions.wolfram.com/01.20.21.0858.01

 Input Form

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

 Standard Form

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 MathML Form

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

 Rule Form

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

 2002-12-18