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 Tan

 http://functions.wolfram.com/01.08.21.0127.01

 Input Form

 Integrate[(a + b Sqrt[Tan[c z]])^\[Beta], z] == (I ((a^3 + (-1)^(1/4) a^2 b + I a b^2 + (-1)^(3/4) b^3) Hypergeometric2F1[1 + \[Beta], 1, 2 + \[Beta], (a + b Sqrt[Tan[c z]])/ (a - (-1)^(1/4) b)] + (a^3 - (-1)^(1/4) a^2 b + I a b^2 - (-1)^(3/4) b^3) Hypergeometric2F1[1 + \[Beta], 1, 2 + \[Beta], (a + b Sqrt[Tan[c z]])/(a + (-1)^(1/4) b)] - a^3 Hypergeometric2F1[1 + \[Beta], 1, 2 + \[Beta], (a + b Sqrt[Tan[c z]])/(a - (-1)^(3/4) b)] - (-1)^(3/4) a^2 b Hypergeometric2F1[1 + \[Beta], 1, 2 + \[Beta], (a + b Sqrt[Tan[c z]])/(a - (-1)^(3/4) b)] + I a b^2 Hypergeometric2F1[1 + \[Beta], 1, 2 + \[Beta], (a + b Sqrt[Tan[c z]])/(a - (-1)^(3/4) b)] - (-1)^(1/4) b^3 Hypergeometric2F1[1 + \[Beta], 1, 2 + \[Beta], (a + b Sqrt[Tan[c z]])/(a - (-1)^(3/4) b)] - a^3 Hypergeometric2F1[1 + \[Beta], 1, 2 + \[Beta], (a + b Sqrt[Tan[c z]])/(a + (-1)^(3/4) b)] + (-1)^(3/4) a^2 b Hypergeometric2F1[1 + \[Beta], 1, 2 + \[Beta], (a + b Sqrt[Tan[c z]])/(a + (-1)^(3/4) b)] + I a b^2 Hypergeometric2F1[1 + \[Beta], 1, 2 + \[Beta], (a + b Sqrt[Tan[c z]])/(a + (-1)^(3/4) b)] + (-1)^(1/4) b^3 Hypergeometric2F1[1 + \[Beta], 1, 2 + \[Beta], (a + b Sqrt[Tan[c z]])/(a + (-1)^(3/4) b)]) (a + b Sqrt[Tan[c z]])^(1 + \[Beta]))/(2 (a^4 + b^4) c (1 + \[Beta]))

 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