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Cos






Mathematica Notation

Traditional Notation









Elementary Functions > Cos[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving trigonometric functions > Involving rational functions of sin > Involving (a+b sin(d z))-ncos(c z)





http://functions.wolfram.com/01.07.21.0739.01









  


  










Input Form





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










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