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





http://functions.wolfram.com/01.07.21.2702.01









  


  










Input Form





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










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