Hyperbolic sine: Integration (formula 01.19.21.1827)

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

http://functions.wolfram.com/01.19.21.1827.01

Input Form

Integrate[(a + b Sinh[c z]^2)^\[Nu] (d + e Sinh[c z]^2)^\[Beta] Sinh[c z], z] == ((1/c) AppellF1[1/2, -\[Nu], -\[Beta], 3/2, -((b Cosh[c z]^2)/(a - b)), -((e Cosh[c z]^2)/(d - e))] Cosh[c z] (a + b Sinh[c z]^2)^\[Nu] (d + e Sinh[c z]^2)^\[Beta])/ (((a + b Sinh[c z]^2)/(a - b))^\[Nu] ((d + e Sinh[c z]^2)/(d - e))^\[Beta])

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