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Cos






Mathematica Notation

Traditional Notation









Elementary Functions > Cos[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving trigonometric and exponential functions > Involving rational functions of sin and exp > Involving ep z(a+b sin2(d z))-ncos(c z)





http://functions.wolfram.com/01.07.21.0965.01









  


  










Input Form





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










Standard Form





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MathML Form







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





2002-12-18