Question

Это интеграл
{xdx/(x^2+1)^2=

Answer 1

$int frac{xdx}{( {x}^{2} + 1)^{2} } = int frac{x}{ {t}^{2} } times frac{1}{2x} dt = \ {x}^{2} + 1 = t, : dt = 2xdx, : dx = frac{1}{2x} dt \ = frac{1}{2} int {t}^{ - 2} dt = - frac{1}{2t} = - frac{1}{2( {x}^{2} + 1) } + C$