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Sinh




Mathematica Notation

Traditional Notation









Elementary Functions > Sinh[z] > Integration > Indefinite integration > Involving functions of the direct function > Involving rational functions of the direct function > Involving sinh(e z)sinh(d z)/a+b sinh(c z)





http://functions.wolfram.com/01.19.21.1704.01









  


  








Input Form





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








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