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Cos




Mathematica Notation

Traditional Notation









Elementary Functions > Cos[z] > Integration > Indefinite integration > Involving functions of the direct function > Involving rational functions of the direct function > Involving cos(d z)(a+b cos2(c z))-n





http://functions.wolfram.com/01.07.21.1272.01









  


  








Input Form





Integrate[Cos[d z]/(a + b Cos[c z]^2)^2, z] == (-((1/(2 I c - I d)) (E^((2 I c - I d) z) ((-2 a - b) (2 a + b + 2 Sqrt[a] Sqrt[a + b]) Hypergeometric2F1[ 1 - d/(2 c), 1, 2 - d/(2 c), -((b E^(2 I c z))/ (2 a + b - 2 Sqrt[a] Sqrt[a + b]))] - (2 a + b) (-2 a - b + 2 Sqrt[a] Sqrt[a + b]) Hypergeometric2F1[ 1 - d/(2 c), 1, 2 - d/(2 c), -((b E^(2 I c z))/ (2 a + b + 2 Sqrt[a] Sqrt[a + b]))] + 2 Sqrt[a] ((2 a^(3/2) + 2 Sqrt[a] b + 2 a Sqrt[a + b] + b Sqrt[a + b]) Hypergeometric2F1[1 - d/(2 c), 2, 2 - d/(2 c), -((b E^(2 I c z))/(2 a + b - 2 Sqrt[a] Sqrt[a + b]))] + (-2 a^(3/2) - 2 Sqrt[a] b + 2 a Sqrt[a + b] + b Sqrt[a + b]) Hypergeometric2F1[1 - d/(2 c), 2, 2 - d/(2 c), -((b E^(2 I c z))/(2 a + b + 2 Sqrt[a] Sqrt[a + b]))])))) - (1/(2 I c + I d)) (E^((2 I c + I d) z) ((-2 a - b) (2 a + b + 2 Sqrt[a] Sqrt[a + b]) Hypergeometric2F1[ 1 + d/(2 c), 1, 2 + d/(2 c), -((b E^(2 I c z))/ (2 a + b - 2 Sqrt[a] Sqrt[a + b]))] - (2 a + b) (-2 a - b + 2 Sqrt[a] Sqrt[a + b]) Hypergeometric2F1[ 1 + d/(2 c), 1, 2 + d/(2 c), -((b E^(2 I c z))/ (2 a + b + 2 Sqrt[a] Sqrt[a + b]))] + 2 Sqrt[a] ((2 a^(3/2) + 2 Sqrt[a] b + 2 a Sqrt[a + b] + b Sqrt[a + b]) Hypergeometric2F1[1 + d/(2 c), 2, 2 + d/(2 c), -((b E^(2 I c z))/(2 a + b - 2 Sqrt[a] Sqrt[a + b]))] + (-2 a^(3/2) - 2 Sqrt[a] b + 2 a Sqrt[a + b] + b Sqrt[a + b]) Hypergeometric2F1[1 + d/(2 c), 2, 2 + d/(2 c), -((b E^(2 I c z))/(2 a + b + 2 Sqrt[a] Sqrt[a + b]))]))))/ (4 a^(3/2) b (a + b)^(3/2))








Standard Form





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MathML Form







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Rule Form





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





2002-12-18