Question

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

Answer 1

$\int \frac{2x}{1+x^2}dx$

Let, $1+x^2=t$

Differentiating, we get

$\Rightarrow$ $2x.dx=dt$

Substituting values,

$\Rightarrow$ $\int \frac{1}{t}.dt$

$\Rightarrow$ $\ln |t|+C$

$\Rightarrow$ $\ln |1+x^2|+C$