Hyperbolic sine: Integration (formula 01.19.21.1821)

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/01.19.21.1821.01

Input Form

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