为自己加油

∫(√x+1-1/√x+1-1)dx

令x+1=t²，则=t²-1，dx=2tdt ∫[(√x+1-1)/(√x+1+1)]dx=∫[(t-1)/(t+1)]2tdt =2∫[(t²-t)/(t+1)]dt=2∫[t-2+2/(t+1)]dt =2∫tdt+4∫dt+4∫[1/(t+1)]dt =t²-4t+4ln|t+1|+C =(x+1)-4√x+1+41n(√x+1)+C.