Hyperbolic sine integral: Integration (formula 06.39.21.0014)

SinhIntegral

$Mathematica Notation$

Gamma, Beta, Erf

SinhIntegral[z]

Integration

Indefinite integration

Involving one direct function and elementary functions

Involving exponential function and a power function

Involving exp and power

http://functions.wolfram.com/06.39.21.0014.01

Input Form

Integrate[z^n E^(b z) SinhIntegral[a z], z] == (n!/2) (-b)^(-n - 1) (-2 SinhIntegral[a z] E^(b z) Sum[((-b) z)^k/k!, {k, 0, n}] - ExpIntegralEi[(-a + b) z] + ExpIntegralEi[(a + b) z] - E^((a + b) z) Sum[(1/m) (b/(a + b))^m Sum[((-a - b)^k z^k)/k!, {k, 0, -1 + m}], {m, 1, n}] + E^((-a + b) z) Sum[(1/m) (b/(b - a))^m Sum[((a - b)^k z^k)/k!, {k, 0, -1 + m}], {m, 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)

2001-10-29