Question

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

Answer 1

Let $x^2$=t

$2x$ $dx$=dt

$=\frac{1}{2}{\int }_0^1\frac{2x}{1+x^2}dx$

$={\int }_0^1\frac{dt}{1+t}$

$=\frac{1}{2}\ln {(1+t)]}_0^1$

$=\frac{1}{2}\ln \left(2\right)$