Hyperbolic cosine integral: Integration (formula 01.20.21.1844)

Cosh

$Mathematica Notation$

Elementary Functions

Cosh[z]

Integration

Indefinite integration

Involving one direct function and elementary functions

Involving hyperbolic and exponential functions

Involving powers of sinh and exp

Involving e^{p z}sinh^mu(c z)cosh(a z+b)

http://functions.wolfram.com/01.20.21.1844.01

Input Form

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