I was calculating basic rational integrals and came up with this kind of problem. I have this expression:


I can re-write it down like that:


and thus cancel the modulus.

The question is, what about $\frac{1}{2}\ln|x|$?

Should I write it down like this:

$$\ln{\sqrt{x}}$$ or like this: $$\ln{|\sqrt{x}|}\,?$$

  • 1
    $\begingroup$ You should write $\ln{\sqrt{|x|}}$ $\endgroup$ – Gabriele Cassese Mar 22 at 18:59

As $\ln\sqrt{\lvert x\rvert}$. Otherwise, think about what would happen if $x$ was equal to, say, $-1$.


There is no reason to remove the absolute value.


which doesn't fit with your proposals.

This works with the square, because



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.