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 Tanh

 http://functions.wolfram.com/01.21.21.0248.01

 Input Form

 Integrate[Sqrt[(a + b Tanh[c z]^2)^3], z] == -(Sqrt[(a + b Tanh[c z]^2)^3] (Sqrt[b] (3 a + 2 b) Log[2 (Sqrt[b] Tanh[c z] + Sqrt[a + b Tanh[c z]^2])] + (a + b)^(3/2) (Log[(4 (a - b Tanh[c z] + Sqrt[a + b] Sqrt[a + b Tanh[c z]^2]))/((a + b)^(5/2) (1 + Tanh[c z]))] - Log[-((4 (a + b Tanh[c z] + Sqrt[a + b] Sqrt[a + b Tanh[c z]^2]))/ ((a + b)^(5/2) (-1 + Tanh[c z])))]) + b Tanh[c z] Sqrt[a + b Tanh[c z]^2]))/(2 c (a + b Tanh[c z]^2)^(3/2))

 Standard Form

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 MathML Form

 ( a + b tanh 2 ( c z ) ) 3 z - 1 2 c ( b tanh 2 ( c z ) + a ) 3 / 2 ( ( b tanh 2 ( c z ) + a ) 3 ( ( log ( 4 ( a - b tanh ( c z ) + a + b b tanh 2 ( c z ) + a ) ( a + b ) 5 / 2 ( tanh ( c z ) + 1 ) ) - log ( - 4 ( a + b tanh ( c z ) + a + b b tanh 2 ( c z ) + a ) ( a + b ) 5 / 2 ( tanh ( c z ) - 1 ) ) ) ( a + b ) 3 / 2 + b ( 3 a + 2 b ) log ( 2 ( b tanh ( c z ) + b tanh 2 ( c z ) + a ) ) + b tanh ( c z ) b tanh 2 ( c z ) + a ) ) z a b c z 2 3 1 2 -1 1 2 c b c z 2 a 3 2 -1 b c z 2 a 3 1 2 4 a -1 b c z a b 1 2 b c z 2 a 1 2 a b 5 2 c z 1 -1 -1 -1 4 a b c z a b 1 2 b c z 2 a 1 2 a b 5 2 c z -1 -1 a b 3 2 b 1 2 3 a 2 b 2 b 1 2 c z b c z 2 a 1 2 b c z b c z 2 a 1 2 [/itex]

 Rule Form

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

 2002-12-18