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 Tanh

 http://functions.wolfram.com/01.21.21.0151.01

 Input Form

 Integrate[E^(p z) Sinh[b z]^u Tanh[c z], z] == (I^u Binomial[u, u/2] ((-(1/p)) (E^(p z) Hypergeometric2F1[p/(2 c), 1, (2 c + p)/(2 c), -E^(2 c z)]) + (1/(2 c + p)) (E^((2 c + p) z) Hypergeometric2F1[(2 c + p)/(2 c), 1, (4 c + p)/(2 c), -E^(2 c z)])) (1 - Mod[u, 2]))/2^u + Sum[(-1)^k Binomial[u, k] (-((-1)^u E^((p - b (-2 k + u)) z) Hypergeometric2F1[(p - b (-2 k + u))/(2 c), 1, (2 c + p - b (-2 k + u))/(2 c), -E^(2 c z)])/(p - b (-2 k + u)) + ((-1)^u E^((2 c + p - b (-2 k + u)) z) Hypergeometric2F1[ (2 c + p - b (-2 k + u))/(2 c), 1, (4 c + p - b (-2 k + u))/(2 c), -E^(2 c z)])/(2 c + p - b (-2 k + u)) - (E^((p + b (-2 k + u)) z) Hypergeometric2F1[(p + b (-2 k + u))/(2 c), 1, (2 c + p + b (-2 k + u))/(2 c), -E^(2 c z)])/ (p + b (-2 k + u)) + (E^((2 c + p + b (-2 k + u)) z) Hypergeometric2F1[(2 c + p + b (-2 k + u))/(2 c), 1, (4 c + p + b (-2 k + u))/(2 c), -E^(2 c z)])/ (2 c + p + b (-2 k + u))), {k, 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