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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+b sinh(e z)+c cosh(e z))-n





http://functions.wolfram.com/01.07.21.2668.01









  


  








Input Form





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








Standard Form





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<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> <plus /> <ci> e </ci> <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