# $u$-substitution for integrating $\int\frac{\log|x|}{x\sqrt{1+\log|x|}}\,dx\;\;?$

How can I integrate $$\int\frac{\log|x|}{x\sqrt{1+\log|x|}}\,dx\;\;?$$

I'm not sure what I should put equal to $\,u.$

Can someone give me a hint on how to solve this question? I don't need a full solution, I want to try it on my own.

Thanks!

• Substitute $u = \log \lvert x\rvert$. Be careful with the sign of $x$. – Daniel Fischer Jul 5 '13 at 18:52

Hint: Let $u = \log|x|$. Then $\;du = \dfrac {1}{x}\,dx$.