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Sinh




Mathematica Notation

Traditional Notation









Elementary Functions > Sinh[z] > Integration > Indefinite integration > Involving functions of the direct function and exponential function > Involving rational functions of the direct function and exponential function > Involving exp > Involving ep z(a+b sinh(c z))-nsinh(d z)





http://functions.wolfram.com/01.19.21.2270.01









  


  








Input Form





Integrate[(E^(p z) Sinh[d z])/(a + b Sinh[c z])^2, z] == (1/(2 b (a^2 + b^2)^(3/2))) (-((1/(c - d + p)) (E^((c - d + p) z) ((-a) (a + Sqrt[a^2 + b^2]) Hypergeometric2F1[(c - d + p)/c, 1, 2 + (-d + p)/c, (b E^(c z))/(-a + Sqrt[a^2 + b^2])] + a (a - Sqrt[a^2 + b^2]) Hypergeometric2F1[(c - d + p)/c, 1, 2 + (-d + p)/c, -((b E^(c z))/(a + Sqrt[a^2 + b^2]))] + (a^2 + b^2 + a Sqrt[a^2 + b^2]) Hypergeometric2F1[(c - d + p)/c, 2, 2 + (-d + p)/c, (b E^(c z))/(-a + Sqrt[a^2 + b^2])] + (-a^2 - b^2 + a Sqrt[a^2 + b^2]) Hypergeometric2F1[(c - d + p)/c, 2, 2 + (-d + p)/c, -((b E^(c z))/(a + Sqrt[a^2 + b^2]))]))) + (1/(c + d + p)) (E^((c + d + p) z) ((-a) (a + Sqrt[a^2 + b^2]) Hypergeometric2F1[(c + d + p)/c, 1, 2 + (d + p)/c, (b E^(c z))/(-a + Sqrt[a^2 + b^2])] + a (a - Sqrt[a^2 + b^2]) Hypergeometric2F1[(c + d + p)/c, 1, 2 + (d + p)/c, -((b E^(c z))/(a + Sqrt[a^2 + b^2]))] + (a^2 + b^2 + a Sqrt[a^2 + b^2]) Hypergeometric2F1[(c + d + p)/c, 2, 2 + (d + p)/c, (b E^(c z))/(-a + Sqrt[a^2 + b^2])] + (-a^2 - b^2 + a Sqrt[a^2 + b^2]) Hypergeometric2F1[(c + d + p)/c, 2, 2 + (d + p)/c, -((b E^(c z))/(a + Sqrt[a^2 + b^2]))])))








Standard Form





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Rule Form





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





2002-12-18