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Sech






Mathematica Notation

Traditional Notation









Elementary Functions > Sech[z] > Integration > Indefinite integration > Involving functions of the direct function > Involving algebraic functions of the direct function > Involving ((a+b sech(c z))n)beta





http://functions.wolfram.com/01.24.21.0316.01









  


  










Input Form





Integrate[Sech[c z] Sqrt[(a + b Sech[c z])^3], z] == -(16 Cosh[(c z)/2]^2 Cosh[c z]^2 Coth[(c z)/2] Sqrt[1 - Sech[c z]] Sqrt[(a + b Sech[c z])^3] (b (-1 + Sech[c z]) (a + b Sech[c z]) + (Sqrt[1 - Sech[c z]] ((4 a ((a + b) EllipticE[ArcSin[Sqrt[(a + b Sech[c z])/(a - b)]], (a - b)/(a + b)] - b EllipticF[ArcSin[Sqrt[(a + b Sech[c z])/ (a - b)]], (a - b)/(a + b)]) (1 + Sech[c z]) Sqrt[(b - b Sech[c z])/(a + b)] Sqrt[(a + b Sech[c z])/(a - b)])/ Sqrt[(b (1 + Sech[c z]))/(-a + b)] - 3 a^2 EllipticF[ArcSin[Sqrt[1 - Sech[c z]]/Sqrt[2]], (2 b)/(a + b)] Sqrt[(a + b Sech[c z])/(a + b)] Sqrt[Tanh[c z]^2] - b^2 EllipticF[ArcSin[Sqrt[1 - Sech[c z]]/Sqrt[2]], (2 b)/(a + b)] Sqrt[(a + b Sech[c z])/(a + b)] Sqrt[Tanh[c z]^2]))/ (Sqrt[1 + Sech[c z]] Sqrt[Tanh[c z]^2])))/ (c (4 Cosh[(c z)/2]^2 (4 a b Cosh[c z] + 3 (a^2 + 2 b^2 + a^2 Cosh[2 c z])) Sqrt[1 - Sech[c z]] + 16 a b Cosh[c z]^2 Sqrt[1 + Sech[c z]] Sqrt[Tanh[c z]^2]))










Standard Form





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MathML Form







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





2002-12-18





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