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 Sech

 http://functions.wolfram.com/01.24.21.0460.01

 Input Form

 Integrate[1/(a Csch[z] + b Sech[z])^2, z] == (Csch[z] Sech[z]^2 (a Cosh[z] + b Sinh[z]) (-(1/a) + Csch[z] (a Cosh[z] + b Sinh[z]) (-((4 (a^4 + 6 a^2 b^2 + b^4) z)/((a - b)^3 (a + b)^3)) - (4 a b Cosh[2 z])/((a - b)^2 (a + b)^2) + (16 a b (a^2 + b^2) Log[a Cosh[z] + b Sinh[z]])/(a^2 - b^2)^3 + ((a^4 + 6 a^2 b^2 + b^4) Sinh[z])/(a (a - b)^2 (a + b)^2 (a Cosh[z] + b Sinh[z])) + (2 (a^2 + b^2) Sinh[2 z])/ ((a - b)^2 (a + b)^2))))/(8 (a Csch[z] + b Sech[z])^2)

 Standard Form

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 MathML Form

 1 ( a csch ( z ) + b sech ( z ) ) 2 z 1 8 ( a csch ( z ) + b sech ( z ) ) 2 ( csch ( z ) sech 2 ( z ) ( a cosh ( z ) + b sinh ( z ) ) ( csch ( z ) ( a cosh ( z ) + b sinh ( z ) ) ( - 4 ( a 4 + 6 b 2 a 2 + b 4 ) z ( a - b ) 3 ( a + b ) 3 + 16 a b ( a 2 + b 2 ) log ( a cosh ( z ) + b sinh ( z ) ) ( a 2 - b 2 ) 3 + 2 ( a 2 + b 2 ) sinh ( 2 z ) ( a - b ) 2 ( a + b ) 2 - 4 a b cosh ( 2 z ) ( a - b ) 2 ( a + b ) 2 + ( a 4 + 6 b 2 a 2 + b 4 ) sinh ( z ) a ( a - b ) 2 ( a + b ) 2 ( a cosh ( z ) + b sinh ( z ) ) ) - 1 a ) ) z 1 a z b z 2 -1 1 8 a z b z 2 -1 z z 2 a z b z z a z b z -1 4 a 4 6 b 2 a 2 b 4 z a -1 b 3 a b 3 -1 16 a b a 2 b 2 a z b z a 2 -1 b 2 3 -1 2 a 2 b 2 2 z a -1 b 2 a b 2 -1 -1 4 a b 2 z a -1 b 2 a b 2 -1 a 4 6 b 2 a 2 b 4 z a a -1 b 2 a b 2 a z b z -1 -1 1 a -1 [/itex]

 Rule Form

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

 2002-12-18