∫(x^2-1)/(x^2) dx
=∫[1-1/(x^2)] dx
=∫ 1dx-∫1/(x^2) dx
=x+1/x+C朋友反了∫(x^2)/[(x^2)-1] dx=∫[(x^2)-1+1]/[(x^2)-1] dx=∫ 1+1/[(x^2)-1] dx=∫1 dx+∫1/[(x^2)-1] dx=∫1 dx+1/2·∫[1/(x-1)-1/(x+1)] dx=x+1/2·[ln|x-1|-ln|x+1|]+C=x+1/2·ln|(x-1)/(x+1)|+C