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 Tanh

 http://functions.wolfram.com/01.21.21.0053.01

 Input Form

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