Hyperbolic sine: Integration (formula 01.19.21.1800)

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))^beta sinh^nu(c z)

http://functions.wolfram.com/01.19.21.1800.01

Input Form

Integrate[Sqrt[a + b Sinh[c z]^2] Sinh[c z]^4, z] == (16 I a (2 a^2 + 3 a b - 8 b^2) Sqrt[(2 a - b + b Cosh[2 c z])/a] EllipticE[I c z, b/a] - 32 I a (a^2 + a b - 2 b^2) Sqrt[(2 a - b + b Cosh[2 c z])/a] EllipticF[I c z, b/a] + Sqrt[2] b (8 a^2 - 48 a b + 25 b^2 + 4 (4 a - 7 b) b Cosh[2 c z] + 3 b^2 Cosh[4 c z]) Sinh[2 c z])/(240 b^2 c 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