Hyperbolic cosecant: Integration (formula 01.23.21.0181)

Csch

$Mathematica Notation$

Elementary Functions

Csch[z]

Integration

Indefinite integration

Involving one direct function and elementary functions

Involving hyperbolic and exponential functions

Involving sinh and exp

Involving e^{p z} sinh(b z) csch( c z)

http://functions.wolfram.com/01.23.21.0181.01

Input Form

Integrate[E^(p z) Sinh[b z] Csch[c z], z] == (-E^(c z)) ((1/(b - p - c)) (E^((-b + p) z) HypergeometricPFQ[ {(p + c - b)/(2 c), 1}, {1 + (p + c - b)/(2 c)}, E^(2 c z)]) + (1/(b + p + c)) (E^((b + p) z) HypergeometricPFQ[{(p + c + b)/(2 c), 1}, {1 + (p + c + b)/(2 c)}, E^(2 c z)]))

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