Integral of exp(a/x)

Question

I know the integral of exp(ax) but couldn't find a solution for integral exp(a/x). I very appreciate if somebody help me.

Thanks Reza

I believe it isn't expressible in terms of functions you know — ruler501, Sep 11 '14 at 21:56

score 2 · Answer 1 · answered Sep 11 '14 at 22:02

2

$\int e^{\frac{a}x}\mathrm{d}x$ does not resolve to any elementary form.

The closest thing I could give would be $\int e^{\frac{a}x}\mathrm{d}x=xe^{a/x}-aEi(a/x)$ where $Ei(x) =\sum\limits_{n=1}^\infty \frac{x^n}{n\cdot n!}+ \ln(x) + \gamma$

answered Sep 11 '14 at 22:02

Hippalectryon

7,730

Can you please provide some links for further reference to this? – Barun Sep 13 '14 at 06:17
1

The solution to the above can be found in Wolfram Mathematica – Barun Sep 13 '14 at 09:45

Integral of exp(a/x)

1 Answers1