Question

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

Answer 1

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

Let $1+x^2=t$

$2xdx=dt$

Therefore,

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

$I=\log t+C$

$I=\log (1+x^2)+C$