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Tan






Mathematica Notation

Traditional Notation









Elementary Functions > Tan[z] > Integration > Indefinite integration > Involving functions of the direct function > Involving algebraic functions of the direct function > Involving (a+b tan1/2(c z))beta





http://functions.wolfram.com/01.08.21.0130.01









  


  










Input Form





Integrate[Tan[c z] (a + b Sqrt[Tan[c z]])^\[Beta], z] == -(((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







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





2002-12-18





© 1998- Wolfram Research, Inc.