Hyperbolic sine: Integration (formula 01.19.21.1074)

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/01.19.21.1074.01

Input Form

Integrate[z^n Cos[b Sqrt[z] + e] Sinh[c Sqrt[z] + g], z] == (1/2) ((-((-I) b - c)^(-2 (1 + n))) E^(I e + g) Gamma[2 (1 + n), ((-I) b - c) Sqrt[z]] - (E^((-I) e + g) Gamma[2 (1 + n), (I b - c) Sqrt[z]])/ (I b - c)^(2 (1 + n)) + (E^(I e - g) Gamma[2 (1 + n), ((-I) b + c) Sqrt[z]])/ ((-I) b + c)^(2 (1 + n)) + (E^((-I) e - g) Gamma[2 (1 + n), (I b + c) Sqrt[z]])/ (I b + c)^(2 (1 + n))) /; 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