Question

se considera functia :

Answer 1

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