[tex] \it \int^1_0 \dfrac{x}{x^2+1} dx = \dfrac{1}{2}\int^1_0 \dfrac{2x}{x^2+1} dx = \dfrac{1}{2} \int^1_0 \dfrac{(x^2+1)'}{x^2+1} dx = \dfrac{1}{2} ln(x^2+1)\Big{|}^1 _0 =
\\ \\ \\
= \dfrac{1}{2}(ln2-ln1) = \dfrac{1}{2}(ln2- 0) = \dfrac{1}{2}ln2 [/tex]
