1. ## nasty integral

which is the integral for exp( -a/x ) dx ?

i have tried every method

thanks

2. Originally Posted by v71
which is the integral for exp( -a/x ) dx ?

i have tried every method

thanks
That's because the indefinite form is...ugly. I don't think it has a closed form. If this is supposed to be a definite integral, though, you may be able to calculate an exact value.

-Dan

3. Topsquark is correct.
---
It is a famous case that,
$\displaystyle \int \frac{e^x}{x}dx$ is non-elementary.
We shall convert this integral into this form.
For simplicity sake we shall use $\displaystyle a=1$, thus,
$\displaystyle \int e^{-1/x}dx$
Manipulate it as,
$\displaystyle \int \frac{x^2e^{1/x}}{x^2}dx$
Let, (going to apply the substitution rule)
$\displaystyle u=-1/x$ then, $\displaystyle u'=1/x^2$
Thus,
$\displaystyle \int \frac{e^u}{u^2}du$
If you use integration by parts with,
$\displaystyle v=e^u$ and $\displaystyle w'=1/u^2$
Then,
$\displaystyle -\frac{e^u}{u}+\int \frac{e^u}{u}du$
We have converted this integral into an integral which has no elementary anti-derivative. This confirms topsquarks guess.

4. Originally Posted by ThePerfectHacker
Topsquark is correct.
---
It is a famous case that,
$\displaystyle \int \frac{e^x}{x}dx$ is non-elementary.
We shall convert this integral into this form.
For simplicity sake we shall use $\displaystyle a=1$, thus,
$\displaystyle \int e^{-1/x}dx$
Manipulate it as,
$\displaystyle \int \frac{x^2e^{1/x}}{x^2}dx$
Let, (going to apply the substitution rule)
$\displaystyle u=-1/x$ then, $\displaystyle u'=1/x^2$
Thus,
$\displaystyle \int \frac{e^u}{u^2}du$
If you use integration by parts with,
$\displaystyle v=e^u$ and $\displaystyle w'=1/u^2$
Then,
$\displaystyle -\frac{e^u}{u}+\int \frac{e^u}{u}du$
We have converted this integral into an integral which has no elementary anti-derivative. This confirms topsquarks guess.
Yeah, what he said.

-Dan