设t=x^2+1 ∫x^3/(x^2+1) dx = ∫(x^2)/2(x^2+1) d(x^2+1) = ∫(t-1)/(2t) dt = ∫(1/2)dt - ∫(1/2t)dt = t/2 - (1/2)·lnt + C . = (x^2+1)/2 - (1/2)·ln(x^2+1) + C.