原式=∫[2/x-2/(x+1)-2/(x+1)²+1/(x+1)³]dx
=2ln│x│-2ln│x+1│+2/(x+1)-(1/2)/(x+1)²+C(C是积分常数)
=2ln│x/(x+1)│+2/(x+1)-(1/2)/(x+1)²+C.