解：∵y^4/(y^3-y^2+y-1)=(y^4-1+1)/[(y-1)(y^2+1)]=y+1+1/[(y-1)(y^2+1)]，设1/[(y-1)(y^2+1)]=a/(y-1)+(by+c)/(y^2+1)，解得a=b=c=1/2。 ∴原式=∫[2y+2+1/(y-1)-(y+1)/(y^2+1)]dy=y^2+2y+ln丨y-1丨-(1/2)ln(1+y^2)-arctany+C。 供参考。
