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Cos




Mathematica Notation

Traditional Notation









Elementary Functions > Cos[z] > Integration > Indefinite integration > Involving functions of the direct function > Involving rational functions of the direct function > Involving cos(e z)cos(d z)/a+b cos2(c z)





http://functions.wolfram.com/01.07.21.1277.01









  


  








Input Form





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