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 Tanh

 http://functions.wolfram.com/01.21.21.0057.01

 Input Form

 Integrate[E^(p z) Cos[b z]^m Tanh[c z], z] == (Binomial[m, m/2] (-((E^(p z) Hypergeometric2F1[p/(2 c), 1, (2 c + p)/(2 c), -E^(2 c z)])/p) + (E^((2 c + p) z) Hypergeometric2F1[(2 c + p)/(2 c), 1, (4 c + p)/(2 c), -E^(2 c z)])/(2 c + p)) (1 - Mod[m, 2]))/2^m + Sum[Binomial[m, k] (-(E^((p - I b (-2 k + m)) z) Hypergeometric2F1[ (p - I b (-2 k + m))/(2 c), 1, (2 c + p - I b (-2 k + m))/(2 c), -E^(2 c z)])/(p - I b (-2 k + m)) + (E^((2 c + p - I b (-2 k + m)) z) Hypergeometric2F1[ (2 c + p - I b (-2 k + m))/(2 c), 1, (4 c + p - I b (-2 k + m))/ (2 c), -E^(2 c z)])/(2 c + p - I b (-2 k + m)) - (E^((p + I b (-2 k + m)) z) Hypergeometric2F1[(p + I b (-2 k + m))/ (2 c), 1, (2 c + p + I b (-2 k + m))/(2 c), -E^(2 c z)])/ (p + I b (-2 k + m)) + (E^((2 c + p + I b (-2 k + m)) z) Hypergeometric2F1[(2 c + p + I b (-2 k + m))/(2 c), 1, (4 c + p + I b (-2 k + m))/(2 c), -E^(2 c z)])/ (2 c + p + I b (-2 k + m))), {k, 0, Floor[(1/2) (-1 + m)]}]/2^m /; Element[m, Integers] && m > 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