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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 zsin(e z)cos(c z)/a+b sin(d z)





http://functions.wolfram.com/01.07.21.0966.01









  


  










Input Form





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










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