I have an integral
$\int\frac{\frac{2x-1}{\sqrt3}}{(\frac{2x-1}{\sqrt3})^2+1} \,\text{d}x$
I am replacing $\frac{2x-1}{\sqrt3}$ with $t$ so I have
$\int\frac{t}{t^2+1}\,\text{d}t$ is it wrong if I replace now $t^2+1$ with $u$ and then have
$\frac{1}{2}\int\frac{du}{u}$ so this is $\ln(u)=\ln|t^2+1|=\ln|\frac{2x-1}{\sqrt3}|$ all the result $\frac{1}{2}\ln|\frac{2x-1}{\sqrt3}|$ if wrong can someone explain why ?