Hyperbolic sine: Integration (formula 01.19.21.1030)

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-1cos(c z)sinh(a z)

http://functions.wolfram.com/01.19.21.1030.01

Input Form

Integrate[z^n Cos[c z] Sinh[a z], z] == (1/4) n! ((-(-a + I c)^(-1 - n)) E^((a - I c) z) Sum[((-(a - I c)) z)^k/k!, {k, 0, n}] + (a - I c)^(-1 - n) E^((-a) z + I c z) Sum[((a - I c) z)^k/k!, {k, 0, n}] - (-a - I c)^(-1 - n) E^((a + I c) z) Sum[((-(a + I c)) z)^k/k!, {k, 0, n}] + ((a + I c)^(-1 - n) Sum[((a + I c) z)^k/k!, {k, 0, n}])/ E^((a + I c) z)) /; 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