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 Tanh

 http://functions.wolfram.com/01.21.21.0170.01

 Input Form

 Integrate[Cos[a z]^m Cosh[c z]^\[Mu] Tanh[c z], z] == (Binomial[m, m/2] Cosh[c z]^\[Mu] ((E^(2 c z) Hypergeometric2F1[(2 - \[Mu])/2, 1 - \[Mu], (4 - \[Mu])/2, -E^(2 c z)])/(c (2 - \[Mu])) + Hypergeometric2F1[-(\[Mu]/2), 1 - \[Mu], (2 - \[Mu])/2, -E^(2 c z)]/(c \[Mu])) (1 - Mod[m, 2]))/ (2^m (1 + E^(2 c z))^\[Mu]) + (Cosh[c z]^\[Mu] Sum[Binomial[m, k] ((E^((2 c - I a (-2 k + m)) z) Hypergeometric2F1[ ((-I) a (-2 k + m) + c (2 - \[Mu]))/(2 c), 1 - \[Mu], (1/2) (4 - (I a (-2 k + m))/c - \[Mu]), -E^(2 c z)])/ ((-I) a (-2 k + m) + c (2 - \[Mu])) + (E^((2 c + I a (-2 k + m)) z) Hypergeometric2F1[ (I a (-2 k + m) + c (2 - \[Mu]))/(2 c), 1 - \[Mu], (1/2) (4 + (I a (-2 k + m))/c - \[Mu]), -E^(2 c z)])/ (I a (-2 k + m) + c (2 - \[Mu])) - Hypergeometric2F1[((-I) a (-2 k + m) - c \[Mu])/(2 c), 1 - \[Mu], (1/2) (2 - (I a (-2 k + m))/c - \[Mu]), -E^(2 c z)]/ E^(I a (-2 k + m) z)/((-I) a (-2 k + m) - c \[Mu]) - (E^(I a (-2 k + m) z) Hypergeometric2F1[(I a (-2 k + m) - c \[Mu])/ (2 c), 1 - \[Mu], (1/2) (2 + (I a (-2 k + m))/c - \[Mu]), -E^(2 c z)])/(I a (-2 k + m) - c \[Mu])), {k, 0, Floor[(1/2) (-1 + m)]}])/(2^m (1 + E^(2 c z))^\[Mu]) /; 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