html, body, form { margin: 0; padding: 0; width: 100%; } #calculate { position: relative; width: 177px; height: 110px; background: transparent url(/images/alphabox/embed_functions_inside.gif) no-repeat scroll 0 0; } #i { position: relative; left: 18px; top: 44px; width: 133px; border: 0 none; outline: 0; font-size: 11px; } #eq { width: 9px; height: 10px; background: transparent; position: absolute; top: 47px; right: 18px; cursor: pointer; }

 Sech

 http://functions.wolfram.com/01.24.21.0458.01

 Input Form

 Integrate[1/(a Coth[z] + b Sech[z])^2, z] == (Csch[z]^2 Sech[z]^2 (a + a Cosh[2 z] + 2 b Sinh[z])^2 (-((Sqrt[2] Sqrt[(-b) (b + Sqrt[-4 a^2 + b^2])] (-4 a^4 + a^2 b (7 b - 5 Sqrt[-4 a^2 + b^2]) + b^3 (-b + Sqrt[-4 a^2 + b^2])) ArcTan[(2 a + (-b + Sqrt[-4 a^2 + b^2]) Tanh[z/2])/ (Sqrt[2] Sqrt[b] Sqrt[-b + Sqrt[-4 a^2 + b^2]])] + Sqrt[b] Sqrt[-b + Sqrt[-4 a^2 + b^2]] ((-(-4 a^2 + b^2)^(3/2)) Sqrt[(-b) (b + Sqrt[-4 a^2 + b^2])] z + Sqrt[2] (4 a^4 + b^3 (b + Sqrt[-4 a^2 + b^2]) - a^2 b (7 b + 5 Sqrt[-4 a^2 + b^2])) ArcTan[(2 a - (b + Sqrt[-4 a^2 + b^2]) Tanh[z/2])/ (Sqrt[2] Sqrt[(-b) (b + Sqrt[-4 a^2 + b^2])])]))/ (Sqrt[b] (-4 a^2 + b^2)^(3/2) Sqrt[-b + Sqrt[-4 a^2 + b^2]] Sqrt[(-b) (b + Sqrt[-4 a^2 + b^2])])) - (2 a Cosh[z] ((-a) b + (2 a^2 - b^2) Sinh[z]))/ ((4 a^2 - b^2) (a + a Cosh[2 z] + 2 b Sinh[z]))))/ (4 a^2 (a Coth[z] + b Sech[z])^2)

 Standard Form

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 MathML Form

 1 ( a coth ( z ) + b sech ( z ) ) 2 z 1 4 a 2 ( a coth ( z ) + b sech ( z ) ) 2 ( csch 2 ( z ) sech 2 ( z ) ( cosh ( 2 z ) a + a + 2 b sinh ( z ) ) 2 ( - ( 2 - b ( b + b 2 - 4 a 2 ) ( - 4 a 4 + b ( 7 b - 5 b 2 - 4 a 2 ) a 2 + b 3 ( b 2 - 4 a 2 - b ) ) tan - 1 ( 2 a + ( b 2 - 4 a 2 - b ) tanh ( z 2 ) 2 b b 2 - 4 a 2 - b ) + b b 2 - 4 a 2 - b ( 2 ( 4 a 4 - b ( 7 b + 5 b 2 - 4 a 2 ) a 2 + b 3 ( b + b 2 - 4 a 2 ) ) tan - 1 ( 2 a - ( b + b 2 - 4 a 2 ) tanh ( z 2 ) 2 - b ( b + b 2 - 4 a 2 ) ) - ( b 2 - 4 a 2 ) 3 / 2 - b ( b + b 2 - 4 a 2 ) z ) ) / ( b ( b 2 - 4 a 2 ) 3 / 2 b 2 - 4 a 2 - b - b ( b + b 2 - 4 a 2 ) ) - 2 a cosh ( z ) ( ( 2 a 2 - b 2 ) sinh ( z ) - a b ) ( 4 a 2 - b 2 ) ( cosh ( 2 z ) a + a + 2 b sinh ( z ) ) ) ) z 1 a z b z 2 -1 1 4 a 2 a z b z 2 -1 z 2 z 2 2 z a a 2 b z 2 -1 2 1 2 -1 b b b 2 -1 4 a 2 1 2 1 2 -4 a 4 b 7 b -1 5 b 2 -1 4 a 2 1 2 a 2 b 3 b 2 -1 4 a 2 1 2 -1 b 2 a b 2 -1 4 a 2 1 2 -1 b z 2 -1 2 1 2 b 1 2 b 2 -1 4 a 2 1 2 -1 b 1 2 -1 b 1 2 b 2 -1 4 a 2 1 2 -1 b 1 2 2 1 2 4 a 4 -1 b 7 b 5 b 2 -1 4 a 2 1 2 a 2 b 3 b b 2 -1 4 a 2 1 2 2 a -1 b b 2 -1 4 a 2 1 2 z 2 -1 2 1 2 -1 b b b 2 -1 4 a 2 1 2 1 2 -1 -1 b 2 -1 4 a 2 3 2 -1 b b b 2 -1 4 a 2 1 2 1 2 z b 1 2 b 2 -1 4 a 2 3 2 b 2 -1 4 a 2 1 2 -1 b 1 2 -1 b b b 2 -1 4 a 2 1 2 1 2 -1 -1 2 a z 2 a 2 -1 b 2 z -1 a b 4 a 2 -1 b 2 2 z a a 2 b z -1 [/itex]

 Rule Form

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

 2002-12-18