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Cos




Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/01.07.21.2252.01









  


  








Input Form





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