Hyperbolic secant: Integration (formula 01.24.21.0324)

Sech

$Mathematica Notation$

Elementary Functions

Sech[z]

Integration

Indefinite integration

Involving functions of the direct function

Involving algebraic functions of the direct function

Involving ((a+b sech²(c z))ⁿ)^beta

http://functions.wolfram.com/01.24.21.0324.01

Input Form

Integrate[((a + b Sech[c z]^2)^n)^\[Beta], z] == (-(1/(c (-1 + 2 n \[Beta])))) ((AppellF1[1/2 - n \[Beta], 1/2, (-n) \[Beta], 3/2 - n \[Beta], Cosh[c z]^2, -((a Cosh[c z]^2)/b)] Coth[c z] ((a + b Sech[c z]^2)^n)^ \[Beta] Sqrt[-Sinh[c z]^2])/(1 + (a Cosh[c z]^2)/b)^(n \[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