Question

Integrate the function $\frac{2x}{1+x^2}$

Answer 1

$\int \frac{2x}{1+x^2}dx$
Put $1+x^2=t\Rightarrow 2xdx=dt$
$\Rightarrow \int \frac{2x}{1+x^2}dx=\int \frac{1}{t}dt$
$=\log |t|+C$
$=\log (1+x^2)+C$