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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 rational functions of the direct function, trigonometric and exponential functions > Involving rational functions of sin and exp > Involving ep zsin(d z)(a sin2(e z)+b cos2(e z))-n





http://functions.wolfram.com/01.07.21.2677.01









  


  








Input Form





Integrate[(E^(p z) Sin[d z])/(a Sin[e z]^2 + b Cos[e z]^2)^2, z] == ((1/((-I) d + 2 I e + p)) (E^(((-I) d + 2 I e + p) z) ((-(Sqrt[-a] + I Sqrt[b])^2) (a + b) Hypergeometric2F1[ 1 - (d + I p)/(2 e), 1, 2 - (d + I p)/(2 e), ((-a + b) E^(2 I e z))/ (Sqrt[-a] - I Sqrt[b])^2] + (Sqrt[-a] - I Sqrt[b])^2 (a + b) Hypergeometric2F1[1 - (d + I p)/(2 e), 1, 2 - (d + I p)/(2 e), ((-a + b) E^(2 I e z))/(Sqrt[-a] + I Sqrt[b])^2] - 2 I Sqrt[-a] Sqrt[b] ((Sqrt[-a] + I Sqrt[b])^2 Hypergeometric2F1[ 1 - (d + I p)/(2 e), 2, 2 - (d + I p)/(2 e), ((-a + b) E^(2 I e z))/ (Sqrt[-a] - I Sqrt[b])^2] + (Sqrt[-a] - I Sqrt[b])^2 Hypergeometric2F1[1 - (d + I p)/(2 e), 2, 2 - (d + I p)/(2 e), ((-a + b) E^(2 I e z))/(Sqrt[-a] + I Sqrt[b])^2]))) - (1/(I d + 2 I e + p)) (E^((I d + 2 I e + p) z) ((-(Sqrt[-a] + I Sqrt[b])^2) (a + b) Hypergeometric2F1[ (d + 2 e - I p)/(2 e), 1, (d + 4 e - I p)/(2 e), ((-a + b) E^(2 I e z))/(Sqrt[-a] - I Sqrt[b])^2] + (Sqrt[-a] - I Sqrt[b])^2 (a + b) Hypergeometric2F1[ (d + 2 e - I p)/(2 e), 1, (d + 4 e - I p)/(2 e), ((-a + b) E^(2 I e z))/(Sqrt[-a] + I Sqrt[b])^2] - 2 I Sqrt[-a] Sqrt[b] ((Sqrt[-a] + I Sqrt[b])^2 Hypergeometric2F1[ (d + 2 e - I p)/(2 e), 2, (d + 4 e - I p)/(2 e), ((-a + b) E^(2 I e z))/(Sqrt[-a] - I Sqrt[b])^2] + (Sqrt[-a] - I Sqrt[b])^2 Hypergeometric2F1[(d + 2 e - I p)/(2 e), 2, (d + 4 e - I p)/(2 e), ((-a + b) E^(2 I e z))/ (Sqrt[-a] + I Sqrt[b])^2]))))/(4 (-a)^(3/2) b^(3/2) (-a + b))








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