Question

интеграл от 0 до 1 xdx/(x^2 +1)^2

Answer 1

$\int\limits^1_0 { \frac{xdx}{(x^2 +1)^2} } = \frac{1}{2} \int\limits^1_0 { \frac{d(x^2+1)}{(x^2 +1)^2} } = -\frac{1}{2}(x^2+1)^{-1}|\limits^1_0 = - \frac{1}{2}(1/2-1)=$
$=\frac{1}{2}*(- \frac{1}{2})= \frac{1}{4}$