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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 sin(e z)+c cos(e z))beta





http://functions.wolfram.com/01.07.21.2390.01









  


  








Input Form





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