Hyperbolic sine: Integration (formula 01.19.21.1807)

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/01.19.21.1807.01

Input Form

Integrate[Sinh[c z]^6/Sqrt[a + b Sinh[c z]^2], z] == (-16 I a (8 a^2 + 7 a b + 8 b^2) Sqrt[(2 a - b + b Cosh[2 c z])/a] EllipticE[I c z, b/a] + 16 I a (8 a^2 + 3 a b + 4 b^2) Sqrt[(2 a - b + b Cosh[2 c z])/a] EllipticF[I c z, b/a] + Sqrt[2] b (-32 a^2 - 28 a b + 25 b^2 - 4 b (a + 7 b) Cosh[2 c z] + 3 b^2 Cosh[4 c z]) Sinh[2 c z])/(240 b^3 c Sqrt[2 a - b + b Cosh[2 c z]])

Standard Form

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MathML Form

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type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> -16 </cn> <apply> <power /> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> <apply> <times /> <ci> b </ci> <apply> <cosh /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <power /> <ci> a </ci> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <ci> a </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 8 </cn> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 7 </cn> <ci> b </ci> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> 8 </cn> <apply> 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Rule Form

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Date Added to functions.wolfram.com (modification date)

2002-12-18