Question: The Problem
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[![enter image description here](https://i.stack.imgur.com/8xWjD.jpg)](https://i.stack.imgur.com/8xWjD.jpg)

My Work
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We know that:

$\frac{Q'(z)}{Q(z)}=\sum\limits\_{k=1}^{n}\frac{1}{(z-\alpha\_k)}$

Thus

$\frac{P(z)}{Q(z)}=\sum\limits\_{k=1}^{n}\frac{P(z)}{Q'(z)(z-\alpha\_k)}$

This is about as far as I have traveled any ideas?

Possible Ideas
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I get the feeling that I should use : 

[![enter image description here](https://i.stack.imgur.com/0KH6d.jpg)](https://i.stack.imgur.com/0KH6d.jpg)

But I am not sure of it's relevancy.

Answer: 
When you put $u=x\ln (x) $ you forgot to change the limits they should become $e,2e^2$ thus answer should be $\ln (u)|\_{e} ^{2e^2}=ln (2e^2)-ln (e)=\ln (2e ) $
**hint**: Let $u = \ln x$. Can you finish it?