WHat is the integral of this function?

**chopet** · July 10th 2008, 09:45 AM

$\int x^{-3} e^{-2 \over x} dx$

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

**invite_moon** · July 10th 2008, 10:28 AM

Ok!

**Moo** · July 10th 2008, 10:30 AM

Hello !

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

**nikhil** · July 10th 2008, 10:35 AM

use ILATE method that will give solution very easily

**chopet** · July 10th 2008, 05:43 PM

Thanks guys. Sometimes when we subst, we get the whole exp term, seomtimes just the power. Substitution is really an art.

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