Hyperbolic sine: Integration (formula 01.19.21.1755)

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(2c z))^beta sinh^v(c z)

http://functions.wolfram.com/01.19.21.1755.01

Input Form

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