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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(d z)(a+b sinh2(c z))-n





http://functions.wolfram.com/01.19.21.1701.01









  


  








Input Form





Integrate[Sinh[d z]/(a + b Sinh[c z]^2)^2, z] == (-((1/(2 c - d)) (E^((2 c - d) z) ((2 a - b) (-2 a + 2 Sqrt[a] Sqrt[a - b] + b) Hypergeometric2F1[1 - d/(2 c), 1, 2 - d/(2 c), (b E^(2 c z))/(-2 a - 2 Sqrt[a] Sqrt[a - b] + b)] + (2 a - b) (2 a + 2 Sqrt[a] Sqrt[a - b] - b) Hypergeometric2F1[ 1 - d/(2 c), 1, 2 - d/(2 c), (b E^(2 c z))/ (-2 a + 2 Sqrt[a] Sqrt[a - b] + b)] + 2 Sqrt[a] ((2 a^(3/2) - 2 a Sqrt[a - b] - 2 Sqrt[a] b + Sqrt[a - b] b) Hypergeometric2F1[1 - d/(2 c), 2, 2 - d/(2 c), (b E^(2 c z))/ (-2 a - 2 Sqrt[a] Sqrt[a - b] + b)] + (-2 a^(3/2) - 2 a Sqrt[a - b] + 2 Sqrt[a] b + Sqrt[a - b] b) Hypergeometric2F1[1 - d/(2 c), 2, 2 - d/(2 c), (b E^(2 c z))/ (-2 a + 2 Sqrt[a] Sqrt[a - b] + b)])))) + (1/(2 c + d)) (E^((2 c + d) z) ((2 a - b) (-2 a + 2 Sqrt[a] Sqrt[a - b] + b) Hypergeometric2F1[1 + d/(2 c), 1, 2 + d/(2 c), (b E^(2 c z))/(-2 a - 2 Sqrt[a] Sqrt[a - b] + b)] + (2 a - b) (2 a + 2 Sqrt[a] Sqrt[a - b] - b) Hypergeometric2F1[ 1 + d/(2 c), 1, 2 + d/(2 c), (b E^(2 c z))/ (-2 a + 2 Sqrt[a] Sqrt[a - b] + b)] + 2 Sqrt[a] ((2 a^(3/2) - 2 a Sqrt[a - b] - 2 Sqrt[a] b + Sqrt[a - b] b) Hypergeometric2F1[1 + d/(2 c), 2, 2 + d/(2 c), (b E^(2 c z))/(-2 a - 2 Sqrt[a] Sqrt[a - b] + b)] + (-2 a^(3/2) - 2 a Sqrt[a - b] + 2 Sqrt[a] b + Sqrt[a - b] b) Hypergeometric2F1[1 + d/(2 c), 2, 2 + d/(2 c), (b E^(2 c z))/(-2 a + 2 Sqrt[a] Sqrt[a - b] + b)]))))/ (4 a^(3/2) (a - b)^(3/2) 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