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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 functions > Involving rational functions of sin and cos > Involving sinh(d z)(a sin2(e z)+b cos2(e z))-n





http://functions.wolfram.com/01.19.21.0864.01









  


  








Input Form





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