Hyperbolic cotangent: Integration (formula 01.22.21.0403)

Coth

$Mathematica Notation$

Elementary Functions

Coth[z]

Integration

Indefinite integration

Involving functions of the direct function and hyperbolic functions

Involving algebraic functions of the direct function and hyperbolic functions

Involving cosh

Involving cosh(c z)(a+b coth(c z))^beta

http://functions.wolfram.com/01.22.21.0403.01

Input Form

Integrate[Cosh[c z]/Sqrt[a + b Coth[c z]], z] == (Cosh[c z] Sqrt[a + b Coth[c z]] Sinh[c z] (Cosh[c z] + Sinh[c z]) (I b Sqrt[-1 + Coth[c z]] Sqrt[(a + b Coth[c z])/(-b + b Coth[c z])] EllipticE[I ArcSinh[Sqrt[(a + b)/b]/Sqrt[-1 + Coth[c z]]], (2 b)/(a + b)] Sqrt[Cosh[2 c z] + Sinh[2 c z]] (-1 + Tanh[c z]) - Sqrt[(a + b)/b] (b + a Tanh[c z])))/(b (-a + b) Sqrt[(a + b)/b] c Sqrt[1 + (a + b)/(-b + b Coth[c z])] Sqrt[((Cosh[c z] + Sinh[c z]) (b Cosh[c z] + a Sinh[c z]))/b])

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