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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 zcos(d z)(a+b sin(e z)+c cos(e z))-n





http://functions.wolfram.com/01.07.21.2672.01









  


  








Input Form





Integrate[(E^(p z) Cos[d z])/(a + b Sin[e z] + c Cos[e z]), z] == -(-((1/(d - e + I p)) (I E^(((-I) d + I e + p) z) ((a + Sqrt[a^2 - b^2 - c^2]) Hypergeometric2F1[(-d + e - I p)/e, 1, -((d - 2 e + I p)/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 - I p)/e, 1, -((d - 2 e + I p)/e), (I (b + I c) E^(I e z))/(a + Sqrt[a^2 - b^2 - c^2])]))) + (1/(d + e - I p)) (I E^((I d + I e + p) z) ((a + Sqrt[a^2 - b^2 - c^2]) Hypergeometric2F1[(d + e - I p)/e, 1, (d + 2 e - I p)/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 - I p)/e, 1, (d + 2 e - I p)/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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<apply> <plus /> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> c </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </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