Hyperbolic secant: Integration (formula 01.24.21.0217)

Sech

$Mathematica Notation$

Elementary Functions

Sech[z]

Integration

Indefinite integration

Involving one direct function and elementary functions

Involving hyperbolic and trigonometric functions

Involving cos and coth

Involving cos(a z)coth(c z) sech( c z)

http://functions.wolfram.com/01.24.21.0217.01

Input Form

Integrate[Cos[a z] Coth[c z] Sech[c z], z] == ((a - I c) E^(c z) Hypergeometric2F1[((-I) a + c)/(2 c), 1, 3/2 - (I a)/(2 c), E^(2 c z)] - (a + I c) E^((2 I a + c) z) Hypergeometric2F1[(I a + c)/(2 c), 1, 3/2 + (I a)/(2 c), E^(2 c z)])/ E^(I a z)/((a + I c) (I a + c))

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