令 u = √x，则 x = u^2，dx = 2udu，原式 = ∫(u^3-1) / (u+1) * 2udu=∫(2u^3-2u^2+2u-4+4/(u+1))du= 1/2*u^4 - 2/3*u^3 + u^2 - 4u + 4ln|u+1|+C= 1/2*x^2 - 2/3*x^(3/2) + x - 4√x + 4ln(√x+1) + C
