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Sinh






Mathematica Notation

Traditional Notation









Elementary Functions > Sinh[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))-nsinh(c z)





http://functions.wolfram.com/01.19.21.1246.01









  


  










Input Form





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










Standard Form





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MathML Form







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





2002-12-18