Hyperbolic sine: Integration (formula 01.19.21.1073)

Sinh

$Mathematica Notation$

Elementary Functions

Sinh[z]

Integration

Indefinite integration

Involving one direct function and elementary functions

Involving trigonometric and a power functions

Involving cos and power

Involving z^alpha-1 cos(b z^r+e) sinh(c z^r+g)

http://functions.wolfram.com/01.19.21.1073.01

Input Form

Integrate[z^n Cos[b z^2 + e] Sinh[c z^2 + g], z] == (-(1/8)) z^(1 + n) (E^(I e + g) (((-I) b - c) z^2)^((1/2) (-1 - n)) Gamma[(1 + n)/2, ((-I) b - c) z^2] + E^((-I) e + g) ((I b - c) z^2)^((1/2) (-1 - n)) Gamma[(1 + n)/2, (I b - c) z^2] - E^(I e - g) (((-I) b + c) z^2)^((1/2) (-1 - n)) Gamma[(1 + n)/2, ((-I) b + c) z^2] - E^((-I) e - g) ((I b + c) z^2)^((1/2) (-1 - n)) Gamma[(1 + n)/2, (I b + c) z^2]) /; Element[n, Integers] && n >= 0

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