Question

Evaluate $\underset{0}{\overset{1}{\int }}\frac{2x}{5x^2+1}dx$

Answer 1

${\int }_0^1\frac{2x}{5x^2+1}dx$
$x^2=t$ $2xdx=dt$

${\int }_0^1\frac{dt}{st+1}$

${[\frac{1}{5}\log |5t+1|]}_0^1$

${[\frac{1}{5}\log |5x^2+1|]}_0^1$

$\frac{1}{5}\log 6$