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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 sin(d z)(a sin2(e z)+b cos2(e z))-n





http://functions.wolfram.com/01.07.21.2259.01









  


  








Input Form





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