Tricky Improper Integral.

Hi, I'm trying to work through perhaps someone could advise me on this...

I'm trying to show that $\displaystyle \displaystyle \int_{0}^{1}(ln(1/s))^{x-1}ds$ is the same function as $\displaystyle \displaystyle \int_{0}^{inf}x^3e^{-x}dx$ and explain why this i

I am told that $\displaystyle \displaystyle \int_{0}^{inf}x^3e^{-x}dx $converges to (n-1)!

This is a little out of my league.

Here's what I'm thinking that I do a u substitution with the ln(1/s). Because I don't have an x on the bottom I don't have to use $\displaystyle \displaystyle \int_{a}^{1}(ln(1/s))^{x-1}ds$ right?

For the second function I use integration by parts?

Any clue as to why it's well defined at 2?

What steps would you advise me to take?