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Tanh






Mathematica Notation

Traditional Notation









Elementary Functions > Tanh[z] > Integration > Indefinite integration > Involving functions of the direct function and hyperbolic functions > Involving algebraic functions of the direct function and hyperbolic functions > Involving sinh > Involving sinh(c z)(a+b tanh(c z))beta





http://functions.wolfram.com/01.21.21.0356.01









  


  










Input Form





Integrate[Sinh[c z]/Sqrt[a + b Tanh[c z]], z] == (1/((a - b) c)) (Sqrt[-(1/(a + b))] Cosh[c z] (I (-a + b) EllipticE[I ArcSinh[Sqrt[-(1/(a + b))] Sqrt[a + b Tanh[c z]]], (a + b)/(a - b)] Sqrt[(b (1 + Tanh[c z]))/(-a + b)] Sqrt[(b - b Tanh[c z])/(a + b)] - I (-a + b) EllipticF[I ArcSinh[Sqrt[-(1/(a + b))] Sqrt[a + b Tanh[c z]]], (a + b)/(a - b)] Sqrt[(b (1 + Tanh[c z]))/(-a + b)] Sqrt[(b - b Tanh[c z])/(a + b)] + Sqrt[-(1/(a + b))] (-a + b Tanh[c z]) Sqrt[a + b Tanh[c z]]))










Standard Form





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MathML Form







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Rule Form





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





2002-12-18





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