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.


  • 4
    $\begingroup$ Substitute $u = \log \lvert x\rvert$. Be careful with the sign of $x$. $\endgroup$ – Daniel Fischer Jul 5 '13 at 18:52

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

  • $\begingroup$ @amWhy: Looks spot on to me ;-) +1 $\endgroup$ – Amzoti Jul 5 '13 at 19:54

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.