I'm learning integrals and I have one question.
I have this integral:
$\int\frac{2x}{1+x^2}$
I thought the solution was using $f'/(1+f^2)$ letting $f'=2x$ and $f^2 = x^2$ so the solution would be $\arcsin(x) + C$.
Searching for the right answer on the internet, everyone uses $\frac{f'}{f}$ so the solution is $\log|1+x^2| + C$
Can someone explain me why my solution is wrong?