Hyperbolic sine: Integration (formula 01.19.21.1287)

Sinh

$Mathematica Notation$

Elementary Functions

Sinh[z]

Integration

Indefinite integration

Involving one direct function and elementary functions

Involving trigonometric and exponential functions

Involving powers of cos and exp

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

http://functions.wolfram.com/01.19.21.1287.01

Input Form

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