Question

Solve : $\int \frac{2x}{x^2+5}dx$

Answer 1

Consider $I=\int \frac{2x}{x^2+5}dx$

Let $x^2+5=t$

$2xdx=dt$

Therefore,

$I=\int \frac{dt}{t}=\log t+C$

$I=\log |x^2+5|+C$