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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 z sin(d z) (a sin2(e z)+b cos2(e z))beta





http://functions.wolfram.com/01.07.21.2703.01









  


  








Input Form





Integrate[E^(p z) Sin[d z] (a Sin[e z]^2 + b Cos[e z]^2)^\[Beta], z] == -((2^(-1 - 2 \[Beta]) (((-a) (-1 + E^(2 I e z))^2 + b (1 + E^(2 I e z))^2)/ E^(2 I e z))^\[Beta] (E^((I d + p) z) (d + I p + 2 e \[Beta]) AppellF1[(d - I p - 2 e \[Beta])/(2 e), -\[Beta], -\[Beta], (d + 2 e - I p - 2 e \[Beta])/(2 e), ((a - b) E^(2 I e z))/ (a + b + 2 Sqrt[a b]), ((a - b) E^(2 I e z))/ (a + b - 2 Sqrt[a b])] + E^(((-I) d + p) z) (d - I p - 2 e \[Beta]) AppellF1[-((d + I p + 2 e \[Beta])/(2 e)), -\[Beta], -\[Beta], -((d + I p + 2 e (-1 + \[Beta]))/(2 e)), ((a - b) E^(2 I e z))/ (a + b + 2 Sqrt[a b]), ((a - b) E^(2 I e z))/ (a + b - 2 Sqrt[a b])]))/ ((1 + ((-a + b) E^(2 I e z))/(a + b - 2 Sqrt[a b]))^\[Beta] (1 + ((-a + b) E^(2 I e z))/(a + b + 2 Sqrt[a b]))^\[Beta]))/ (d^2 + (p - 2 I e \[Beta])^2)








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





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





2002-12-18