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

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2002-12-18