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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 sin and exp > Involving ep zsin(d z)(a+b cos2(c z))-n





http://functions.wolfram.com/01.07.21.2656.01









  


  










Input Form





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