Hyperbolic sine: Integration (formula 01.19.21.1719)

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/01.19.21.1719.01

Input Form

Integrate[1/Sqrt[(a + b Sinh[c z])^5], z] == 2 (a + b Sinh[c z]) (((1/(a + I b)^2) ((4 I a EllipticE[(1/4) (Pi - 2 I c z), -((2 I b)/(a - I b))] + ((-I) a + b) EllipticF[(1/4) (Pi - 2 I c z), -((2 I b)/(a - I b))]) ((a + b Sinh[c z])/(a - I b))^(3/2)) - (b Cosh[c z] (5 a^2 + b^2 + 4 a b Sinh[c z]))/(a^2 + b^2)^2)/ (3 c Sqrt[(a + b Sinh[c z])^5]))

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