# WHat is the integral of this function?

• July 10th 2008, 09:45 AM
chopet
WHat is the integral of this function?
$\int x^{-3} e^{-2 \over x} dx$

Couldn't figure out what substitution to use for this one.
Thanks.
• July 10th 2008, 10:28 AM
invite_moon
Ok!
• July 10th 2008, 10:30 AM
Moo
Hello !

Quote:

Originally Posted by chopet
$\int x^{-3} e^{-2 \over x} dx$

Couldn't figure out what substitution to use for this one.
Thanks.

Use the substitution $t=-\frac 2x$

$\dots \implies dx=\frac 12 \cdot x^2 \ dt$

And you will see that the integral is $-\frac 14 \ \int t e^t \ dt$

And here, use integration by parts
(Wink)
• July 10th 2008, 10:35 AM
nikhil
use ILATE method that will give solution very easily
• July 10th 2008, 05:43 PM
chopet
Thanks guys. Sometimes when we subst, we get the whole exp term, seomtimes just the power. Substitution is really an art.