Question

Integrate w.r.t $x$
$\frac{2x}{1+x^2}$

Answer 1

$I=\int \frac{2xdx}{1+x^2}$

Let $t=1+x^2\Rightarrow dt=2xdx$

$I=\int \frac{dt}{t}$

$I=\ln \left|t\right|+c$ where $c$ is the constant of integration.

$I=\ln |1+x^2|+c$