Exponential function: Integration (formula 01.03.21.0567)

Exp

$Mathematica Notation$

Elementary Functions

Exp[z]

Integration

Indefinite integration

Involving functions of the direct function and a power function

Involving products of the direct function and a power function

Involving products of two direct functions and a power function

Involving zⁿa^{b z} h^{c z^r}

http://functions.wolfram.com/01.03.21.0567.01

Input Form

Integrate[z^n a^(b z) h^(c z^2), z] == ((-(1/2)) (c Log[h])^(-1 - n) Sum[2^(j - n) Binomial[n, j] Gamma[(1 + j)/2, -((b Log[a] + 2 c z Log[h])^2/(4 c Log[h]))] ((-b) Log[a])^(-j + n) (b Log[a] + 2 c z Log[h])^(1 + j) (-((b Log[a] + 2 c z Log[h])^2/(c Log[h])))^((1/2) (-1 - j)), {j, 0, n}])/E^((b^2 Log[a]^2)/(4 c Log[h])) /; 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