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 Coth

 http://functions.wolfram.com/01.22.21.0165.01

 Input Form

 Integrate[E^(p z) Sinh[b z]^u Coth[c z], z] == -((1/(p (2 c + p))) ((I/2)^u E^(p z) Binomial[u, u/2] ((2 c + p) Hypergeometric2F1[p/(2 c), 1, 1 + p/(2 c), E^(2 c z)] + E^(2 c z) p Hypergeometric2F1[1 + p/(2 c), 1, 2 + p/(2 c), E^(2 c z)]) (1 - Mod[u, 2]))) - Sum[(-1)^s Binomial[u, s] (((-1)^u E^((p - b (-2 s + u)) z) ((2 c + p - b (-2 s + u)) Hypergeometric2F1[(p - b (-2 s + u))/ (2 c), 1, 1 + (p - b (-2 s + u))/(2 c), E^(2 c z)] + E^(2 c z) (p - b (-2 s + u)) Hypergeometric2F1[ 1 + (p - b (-2 s + u))/(2 c), 1, 2 + (p - b (-2 s + u))/(2 c), E^(2 c z)]))/((p - b (-2 s + u)) (2 c + p - b (-2 s + u))) + (E^((p + b (-2 s + u)) z) ((2 c + p + b (-2 s + u)) Hypergeometric2F1[(p + b (-2 s + u))/(2 c), 1, 1 + (p + b (-2 s + u))/(2 c), E^(2 c z)] + E^(2 c z) (p + b (-2 s + u)) Hypergeometric2F1[ 1 + (p + b (-2 s + u))/(2 c), 1, 2 + (p + b (-2 s + u))/(2 c), E^(2 c z)]))/((p + b (-2 s + u)) (2 c + p + b (-2 s + u)))), {s, 0, Floor[(1/2) (-1 + u)]}]/2^u /; Element[u, Integers] && u > 0

 Standard Form

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 MathML Form

 Rule Form

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

 2002-12-18