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

i have tried every method

thanks

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- Sep 7th 2006, 02:04 PMv71nasty integral
which is the integral for exp( -a/x ) dx ?

i have tried every method

thanks - Sep 7th 2006, 03:11 PMtopsquarkQuote:

Originally Posted by**v71**

-Dan - Sep 7th 2006, 04:34 PMThePerfectHacker
Topsquark is correct.

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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. - Sep 7th 2006, 04:44 PMtopsquarkQuote:

Originally Posted by**ThePerfectHacker**

-Dan