Exponential function: Integration (formula 01.03.21.0748)

Exp

$Mathematica Notation$

Elementary Functions

Exp[z]

Integration

Indefinite integration

Involving functions of the direct function and a power function

Involving products of powers of the direct function and a power function

Involving product of powers of two direct functions and a power function

Involving z^alpha-1(e^{b z^r+e})^mu (e^{c z^r+g})^nu

http://functions.wolfram.com/01.03.21.0748.01

Input Form

Integrate[z^n (E^(b Sqrt[z] + e))^\[Mu] (E^(c Sqrt[z] + g))^\[Nu], z] == (-2 (E^(e + b Sqrt[z]))^\[Mu] (E^(g + c Sqrt[z]))^\[Nu] (-(ExpIntegralEi[Sqrt[z] (b \[Mu] + c \[Nu])]/(-2 (1 + n))!) + E^(Sqrt[z] (b \[Mu] + c \[Nu])) Sum[((-Sqrt[z]) (b \[Mu] + c \[Nu]))^j/ Pochhammer[2 (1 + n), j - 2 n - 1], {j, 0, 2 n + 1}] - E^(Sqrt[z] (b \[Mu] + c \[Nu])) Sum[((-Sqrt[z]) (b \[Mu] + c \[Nu]))^j/ Pochhammer[2 (1 + n), j - 2 n - 1], {j, 2 (1 + n), -1}]))/ (E^(Sqrt[z] (b \[Mu] + c \[Nu])) (b \[Mu] + c \[Nu])^(2 (1 + n))) /; 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