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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 sin2(e z)+c cos2(e z))-n





http://functions.wolfram.com/01.07.21.2276.01









  


  








Input Form





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








Standard Form





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MathML Form







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type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> </apply> <ci> b </ci> <ci> c </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <times /> <apply> <plus /> <ci> a </ci> <ci> b </ci> </apply> <apply> <plus /> <ci> a </ci> <ci> c </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> </apply> <ci> b </ci> <ci> c </ci> </apply> <apply> <ci> Hypergeometric2F1 </ci> <apply> <plus /> <apply> <times /> <ci> d </ci> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> e </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 1 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Rule Form





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





2002-12-18