Exponential function: Integration (formula 01.03.21.0589)

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 z^alpha-1a^{b z^r+e}h^{c z^r+g}

http://functions.wolfram.com/01.03.21.0589.01

Input Form

Integrate[z^(2 n) a^(b z^2 + e) h^(c z^2 + g), z] == (-(1/2)) a^e h^g z^(1 + 2 n) ((-z^2) (b Log[a] + c Log[h]))^(-(1/2) - n) (Erfc[Sqrt[(-z^2) (b Log[a] + c Log[h])]] Gamma[1/2 + n] + a^(b z^2) h^(c z^2) Sum[((-z^2) (b Log[a] + c Log[h]))^(1/2 + j)/ Pochhammer[1/2 + n, 1 + j - n], {j, 0, -1 + n}] - a^(b z^2) h^(c z^2) Sum[((-z^2) (b Log[a] + c Log[h]))^(1/2 + j)/ Pochhammer[1/2 + n, 1 + j - n], {j, n, -1}]) /; Element[n, Integers]

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