∫dx/x+x^3=?,初学,求详解,凑微分?

∫ 1/(x+x^3) dx=∫ (1+x^2-x^2)/[x(1+x^2)] dx=∫ (1+x^2)/[x(1+x^2)] dx-∫ x^2/[x(1+x^2)] dx=∫ 1/x dx-∫ x/(1+x^2) dx=ln|x|-1/2∫ 1/(1+x^2) d(x^2)=ln|x|-1/2ln(1+x^2)+C