Hyperbolic tangent: Integration (formula 01.21.21.0355)

Tanh

$Mathematica Notation$

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/01.21.21.0355.01

Input Form

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