Помогите, пожалуйста, найти интеграл
int (1 2) (1 + 2 * x^2)/(x^2 * (1 + x^2)) dx
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int (1 2) (1 + 2 * x^2)/(x^2 * (1 + x^2)) dx =
= int (1 2) ((1 + x^2) + x^2)/(x^2 * (1 + x^2)) dx =
= int (1 2) (1 + x^2)/(x^2 * (1 + x^2)) dx + int (1 2) x^2/(x^2 * (1 + x^2)) dx =
= int (1 2) dx/x^2 + int (1 2) 1/(1 + x^2) dx =
= (-1/x)_{1}^{2} + (arctg x)_{1}^{2} = (-1/2 + 1/1) + (arctg 2 - arctg 1) =
= -1/2 + 1 + arctg 2 - pi/4 = 1/2 + arctg 2 - pi/4