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 Tanh

 http://functions.wolfram.com/01.21.21.0225.01

 Input Form

 Integrate[(A + B Tanh[z])/(a + b Tanh[z])^3, z] == ((Sech[z]^2 (a Cosh[z] + b Sinh[z]) (A + B Tanh[z]))/ (2 (A Cosh[z] + B Sinh[z]) (a + b Tanh[z])^3)) ((b^2 ((-A) b + a B))/((a - b)^2 (a + b)^2) + (2 b (-3 a A b + 2 a^2 B + b^2 B) Sinh[z] (a Cosh[z] + b Sinh[z]))/ (a (a - b)^2 (a + b)^2) + (2 (a^3 A + 3 a A b^2 - 3 a^2 b B - b^3 B) z (a Cosh[z] + b Sinh[z])^2)/((a - b)^3 (a + b)^3) + (1/(a^2 - b^2)^3) (2 (-3 a^2 A b - A b^3 + a^3 B + 3 a b^2 B) Log[a Cosh[z] + b Sinh[z]] (a Cosh[z] + b Sinh[z])^2))

 Standard Form

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 MathML Form

 A + B tanh ( z ) ( a + b tanh ( z ) ) 3 z sech 2 ( z ) ( a cosh ( z ) + b sinh ( z ) ) ( A + B tanh ( z ) ) 2 ( A cosh ( z ) + B sinh ( z ) ) ( a + b tanh ( z ) ) 3 ( ( a B - A b ) b 2 ( a - b ) 2 ( a + b ) 2 + 2 ( 2 B a 2 - 3 A b a + b 2 B ) sinh ( z ) ( a cosh ( z ) + b sinh ( z ) ) b a ( a - b ) 2 ( a + b ) 2 + 2 ( A a 3 - 3 b B a 2 + 3 A b 2 a - b 3 B ) z ( a cosh ( z ) + b sinh ( z ) ) 2 ( a - b ) 3 ( a + b ) 3 + 2 ( B a 3 - 3 A b a 2 + 3 b 2 B a - A b 3 ) log ( a cosh ( z ) + b sinh ( z ) ) ( a cosh ( z ) + b sinh ( z ) ) 2 ( a 2 - b 2 ) 3 ) z A B z a b z 3 -1 z 2 a z b z A B z 2 A z B z a b z 3 -1 a B -1 A b b 2 a -1 b 2 a b 2 -1 2 2 B a 2 -1 3 A b a b 2 B z a z b z b a a -1 b 2 a b 2 -1 2 A a 3 -1 3 b B a 2 3 A b 2 a -1 b 3 B z a z b z 2 a -1 b 3 a b 3 -1 2 B a 3 -1 3 A b a 2 3 b 2 B a -1 A b 3 a z b z a z b z 2 a 2 -1 b 2 3 -1 [/itex]

 Rule Form

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

 2002-12-18