Hyperbolic cotangent: Integration (formula 01.22.21.0172)

Coth

$Mathematica Notation$

Elementary Functions

Coth[z]

Integration

Indefinite integration

Involving one direct function and elementary functions

Involving hyperbolic and exponential functions

Involving powers of cosh and exp

Involving e^{p z} cosh^u(b z) coth(c z)

http://functions.wolfram.com/01.22.21.0172.01

Input Form

Integrate[E^(p z) Cosh[c z]^\[Mu] Coth[c z], z] == (Cosh[c z]^\[Mu] ((E^(p z) AppellF1[-((p + c \[Mu])/(2 c)), -\[Mu], 1, (-c - p + c (3 - \[Mu]))/(2 c), -E^(-2 c z), E^(-2 c z)])/ (c + p + c (-1 + \[Mu])) + (E^((-2 c + p) z) AppellF1[-((-2 c + p + c \[Mu])/(2 c)), -\[Mu], 1, (c - p + c (3 - \[Mu]))/(2 c), -E^(-2 c z), E^(-2 c z)])/ (-c + p + c (-1 + \[Mu]))))/(1 + E^(-2 c z))^\[Mu]

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