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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 cos(c z)





http://functions.wolfram.com/01.07.21.1251.01









  


  








Input Form





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