Hyperbolic tangent: Integration (formula 01.21.21.0158)

Tanh

$Mathematica Notation$

Elementary Functions

Tanh[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) tanh(c z)

http://functions.wolfram.com/01.21.21.0158.01

Input Form

Integrate[E^(p z) Cosh[c z]^\[Mu] Tanh[c z], z] == (Cosh[c z]^\[Mu] ((-(1/(p - c \[Mu]))) E^(p z) Hypergeometric2F1[ (p - c \[Mu])/(2 c), 1 - \[Mu], 1 + (p - c \[Mu])/(2 c), -E^(2 c z)] + (1/(2 c + p - c \[Mu])) E^((2 c + p) z) Hypergeometric2F1[ 1 + (p - c \[Mu])/(2 c), 1 - \[Mu], 2 + (p - c \[Mu])/(2 c), -E^(2 c z)]))/(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