Hyperbolic sine: Integration (formula 01.19.21.1717)

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 sinh(c z))^nu)^beta

http://functions.wolfram.com/01.19.21.1717.01

Input Form

Integrate[Sqrt[(a + b Sinh[c z])^3], z] == Sqrt[(a + b Sinh[c z])^3] ((2 b Cosh[c z] (a + b Sinh[c z]) + 8 a (I a + b) EllipticE[(1/4) (Pi - 2 I c z), -((2 I b)/(a - I b))] Sqrt[(a + b Sinh[c z])/(a - I b)] - 2 I (a^2 + b^2) EllipticF[(1/4) (Pi - 2 I c z), -((2 I b)/(a - I b))] Sqrt[(a + b Sinh[c z])/(a - I b)])/(3 c (a + b Sinh[c z])^2))

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