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Cos




Mathematica Notation

Traditional Notation









Elementary Functions > Cos[z] > Integration > Indefinite integration > Involving functions of the direct function, trigonometric and exponential functions > Involving rational functions of the direct function, trigonometric and exponential functions > Involving rational functions of sin and exp > Involving ep z(a sin2(e z)+b sin(2 e z)+c cos2(e z))-n





http://functions.wolfram.com/01.07.21.2687.01









  


  








Input Form





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








Standard Form





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MathML Form







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/> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <ci> a </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <ci> a </ci> <ci> c </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <ci> c </ci> <apply> <power /> <apply> <plus /> <apply> <times /> <ci> a </ci> <ci> c </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <ci> Hypergeometric2F1 </ci> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> p </ci> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> e </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <cn type='integer'> 2 </cn> <apply> <plus /> <cn type='integer'> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> p </ci> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> e </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> b </ci> </apply> </apply> <ci> c </ci> </apply> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> e </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <plus /> <ci> a </ci> <ci> c </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <plus /> <apply> <times /> <ci> a </ci> <ci> c </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <plus /> <apply> <times /> <ci> a </ci> <ci> c </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='rational'> 3 <sep /> 2 </cn> </apply> <apply> <plus /> <ci> a </ci> <ci> c </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <plus /> <apply> <times /> <ci> a </ci> <ci> c </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> <apply> <plus /> <ci> a </ci> <ci> c </ci> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <plus /> <apply> <times /> <ci> a </ci> <ci> c </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> e </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> p </ci> </apply> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2002-12-18