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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 sin2(e z)+b sin(2 e z)+c cos2(e z))beta





http://functions.wolfram.com/01.07.21.2420.01









  


  










Input Form





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










Standard Form





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MathML Form







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





2002-12-18