Hyperbolic sine: Integration (formula 01.19.21.1817)

Sinh

$Mathematica Notation$

Elementary Functions

Sinh[z]

Integration

Indefinite integration

Involving functions of the direct function

Involving algebraic functions of the direct function

Involving (a+b sinh²(c z))^betaand rational function of sinh(c z)

http://functions.wolfram.com/01.19.21.1817.01

Input Form

Integrate[Sinh[c z]/((d + e Sinh[c z]) Sqrt[a + b Sinh[c z]^2]), z] == Sqrt[(2 a - b + b Cosh[2 c z])/a] (((d ArcTanh[(Sqrt[2 + (2 b d^2)/(a e^2)] Cosh[c z])/ (Sqrt[1 + d^2/e^2] Sqrt[(2 a - b + b Cosh[2 c z])/a])])/ (Sqrt[1 + d^2/e^2] Sqrt[1 + (b d^2)/(a e^2)]) - I e EllipticF[I c z, b/a] + I e EllipticPi[-(e^2/d^2), I c z, b/a])/ (c e^2 Sqrt[2 a - b + b Cosh[2 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