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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 cos and exp > Involving ep zsinh(c z)/a+b cos2(d z)





http://functions.wolfram.com/01.19.21.1318.01









  


  








Input Form





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








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