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 Cosh

 http://functions.wolfram.com/01.20.21.0690.01

 Input Form

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

 Standard Form

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 MathML Form

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

 Rule Form

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

 2002-12-18