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Cos






Mathematica Notation

Traditional Notation









Elementary Functions > Cos[z] > Integration > Indefinite integration > Involving functions of the direct function and trigonometric functions > Involving algebraic functions of the direct function and trigonometric functions > Involving algebraic functions of sin > Involving cos(d z) (a+b sin2(e z)+c cos2(e z))beta





http://functions.wolfram.com/01.07.21.2417.01









  


  










Input Form





Integrate[Cos[d z] (a + b Sin[e z]^2 + c Cos[e z]^2)^\[Beta], z] == (-(1/(d^2 - 4 e^2 \[Beta]^2))) ((I 2^(-1 - 2 \[Beta]) ((4 a E^(2 I e z) - b (-1 + E^(2 I e z))^2 + c (1 + E^(2 I e z))^2)/E^(2 I e z))^\[Beta] (E^(2 I d z) (d + 2 e \[Beta]) AppellF1[d/(2 e) - \[Beta], -\[Beta], -\[Beta], 1 + d/(2 e) - \[Beta], ((b - c) E^(2 I e z))/ (2 a + b + c + 2 Sqrt[(a + b) (a + c)]), ((b - c) E^(2 I e z))/ (2 a + b + c - 2 Sqrt[(a + b) (a + c)])] - (d - 2 e \[Beta]) AppellF1[-((d + 2 e \[Beta])/(2 e)), -\[Beta], -\[Beta], 1 - d/(2 e) - \[Beta], ((b - c) E^(2 I e z))/ (2 a + b + c + 2 Sqrt[(a + b) (a + c)]), ((b - c) E^(2 I e z))/ (2 a + b + c - 2 Sqrt[(a + b) (a + c)])]))/ (E^(I d z) (1 + ((-b + c) E^(2 I e z))/(2 a + b + c - 2 Sqrt[(a + b) (a + c)]))^\[Beta] (1 + ((-b + c) E^(2 I e z))/(2 a + b + c + 2 Sqrt[(a + b) (a + c)]))^ \[Beta]))










Standard Form





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MathML Form







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Rule Form





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





2002-12-18