html, body, form { margin: 0; padding: 0; width: 100%; } #calculate { position: relative; width: 177px; height: 110px; background: transparent url(/images/alphabox/embed_functions_inside.gif) no-repeat scroll 0 0; } #i { position: relative; left: 18px; top: 44px; width: 133px; border: 0 none; outline: 0; font-size: 11px; } #eq { width: 9px; height: 10px; background: transparent; position: absolute; top: 47px; right: 18px; cursor: pointer; }

 Cosh

 http://functions.wolfram.com/01.20.21.0868.01

 Input Form

 Integrate[Cosh[d z]/(a + b Sin[e z]^2 + c Cos[e z]^2)^2, z] == (1/2) (-(((-b + c) E^((d + 2 I e) z) (((2 a + b + c) Hypergeometric2F1[1 - (I d)/(2 e), 1, 2 - (I d)/(2 e), ((-b + c) E^(2 I e z))/(-2 a - b - c - 2 Sqrt[(a + b) (a + c)])])/ (2 a + b + c + 2 Sqrt[(a + b) (a + c)]) - ((2 a + b + c) Hypergeometric2F1[1 - (I d)/(2 e), 1, 2 - (I d)/(2 e), ((-b + c) E^(2 I e z))/(-2 a - b - c + 2 Sqrt[(a + b) (a + c)])])/ (2 a + b + c - 2 Sqrt[(a + b) (a + c)]) + 2 Sqrt[(a + b) (a + c)] (Hypergeometric2F1[1 - (I d)/(2 e), 2, 2 - (I d)/(2 e), ((-b + c) E^(2 I e z))/(-2 a - b - c - 2 Sqrt[(a + b) (a + c)])]/ (2 a + b + c + 2 Sqrt[(a + b) (a + c)]) - Hypergeometric2F1[1 - (I d)/(2 e), 2, 2 - (I d)/(2 e), ((-b + c) E^(2 I e z))/(-2 a - b - c + 2 Sqrt[(a + b) (a + c)])]/ (-2 a - b - c + 2 Sqrt[(a + b) (a + c)]))))/ (2 ((a + b) (a + c))^(3/2) (d + 2 I e))) - ((-b + c) E^((-d + 2 I e) z) (((2 a + b + c) Hypergeometric2F1[1 + (I d)/(2 e), 1, 2 + (I d)/(2 e), ((-b + c) E^(2 I e z))/(-2 a - b - c - 2 Sqrt[(a + b) (a + c)])])/ (2 a + b + c + 2 Sqrt[(a + b) (a + c)]) - ((2 a + b + c) Hypergeometric2F1[1 + (I d)/(2 e), 1, 2 + (I d)/(2 e), ((-b + c) E^(2 I e z))/(-2 a - b - c + 2 Sqrt[(a + b) (a + c)])])/ (2 a + b + c - 2 Sqrt[(a + b) (a + c)]) + 2 Sqrt[(a + b) (a + c)] (Hypergeometric2F1[1 + (I d)/(2 e), 2, 2 + (I d)/(2 e), ((-b + c) E^(2 I e z))/(-2 a - b - c - 2 Sqrt[(a + b) (a + c)])]/ (2 a + b + c + 2 Sqrt[(a + b) (a + c)]) - Hypergeometric2F1[1 + (I d)/(2 e), 2, 2 + (I d)/(2 e), ((-b + c) E^(2 I e z))/(-2 a - b - c + 2 Sqrt[(a + b) (a + c)])]/ (-2 a - b - c + 2 Sqrt[(a + b) (a + c)]))))/ (2 ((a + b) (a + c))^(3/2) (-d + 2 I e)))

 Standard Form

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 MathML Form

 Rule Form

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

 2002-12-18