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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 algebraic functions of the direct function, trigonometric and exponential functions > Involving algebraic functions of sin and exp > Involving ep zcos(d z)(a sin(e z)+b cos(e z))beta





http://functions.wolfram.com/01.07.21.2698.01









  


  








Input Form





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








Standard Form





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MathML Form







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</ci> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <apply> <power /> <cn type='integer'> 2 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#946; </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> e </ci> <ci> z </ci> </apply> </apply> <apply> <plus /> <ci> b </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> a </ci> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <ci> b </ci> <apply> <times /> <imaginaryi /> <ci> a </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#946; </ci> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <imaginaryi /> </apply> <ci> e </ci> <ci> z </ci> </apply> </apply> <apply> <plus /> <apply> <times /> <ci> b </ci> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> e </ci> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> a </ci> <apply> <plus /> <cn type='integer'> -1 </cn> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> e </ci> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <ci> &#946; 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Rule Form





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





2002-12-18