Hyperbolic sine: Integration (formula 01.19.21.1824)

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/01.19.21.1824.01

Input Form

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