Hyperbolic sine: Integration (formula 01.19.21.1795)

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/01.19.21.1795.01

Input Form

Integrate[(a + b Sinh[c z]^2)^(3/2) Sinh[c z]^2, z] == (-16 I a (3 a^2 - 13 a b + 8 b^2) Sqrt[(2 a - b + b Cosh[2 c z])/a] EllipticE[I c z, b/a] + 16 I a (3 a^2 - 7 a b + 4 b^2) Sqrt[(2 a - b + b Cosh[2 c z])/a] EllipticF[I c z, b/a] + Sqrt[2] b (48 a^2 - 68 a b + 25 b^2 + 4 (9 a - 7 b) b Cosh[2 c z] + 3 b^2 Cosh[4 c z]) Sinh[2 c z])/(240 b 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