The integral of $\int \frac{\ln{x}}{x}\, dx$ is right that is $\frac{1}{2}\ln^2{|x|}+c$?
I am in doubt if I have to consider or not the absolute value since I know that $\int \frac{1}{x}\, dx=\ln{|x|}+c$, but now I have to consider that if I derive $\frac{1}{2}\ln^2{|x|}+c$ I obtain $\frac{\ln{|x|}}{x}$...
What do you think about it?
As a general rule , you can also remember that :
$\int(f(x)^n)(f'(x))dx$=$\frac{f(x)^{n+1}}{n+1}$ +$C$