Hyperbolic sine: Integration (formula 01.19.21.1733)

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))^betaand rational function of sinh(c z)

http://functions.wolfram.com/01.19.21.1733.01

Input Form

Integrate[Sqrt[a + b Sinh[c z]]/(d + e Sinh[c z]), z] == -(2 (b (d - I e) EllipticF[(1/4) (Pi - 2 I c z), -((2 I b)/(a - I b))] + ((-b) d + a e) EllipticPi[-((2 I e)/(d - I e)), (1/4) (Pi - 2 I c z), -((2 I b)/(a - I b))]) Sqrt[(a + b Sinh[c z])/(a - I b)])/ (c e (I d + e) Sqrt[a + b Sinh[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