Need help understanding proof of natural log integrals

[annoying]

[PLAIN]http://img31.imageshack.us/img31/9004/screenshot20111117at720.png

Proofs always get to me for some reason. It's like other problems I can do, but when it comes to proofs I don't know what to put. Can anyone show me steps?

Thank you

 

[Pablo Antuna]

Here you need to prove an identity. So, start with one side of the equation and arrive at something. Then start messing with the other side and try to reach that same something.

If you have already proved the product rule, this little trick may come in handy:

[tex]\frac{1}{x}=\frac{1}{x}^2x[\tex]

 

[HallsofIvy]

You want to look at
$$\int_1^{1/x} \frac{1}{t}dt$$

Try the substitution u= xt.