∫dx/(x(1+x^2)) = 0.5 ∫1/(x^2(1+x^2) dx^2 =0.5 ∫1/x^2 -1/(1+x^2) dx^2=0.5 ln(x^2)-0.5 ln(1+x^2)|1,无穷大=0.5 ln (x^2/(1+x^2) |1,无穷大=0.5 (0-ln(1/2)) = 0.5 ln2