原式=∫ln(x+1)d(x+1)
=(x+1)ln(x+1)-∫(x+1)dln(x+1)
=(x+1)ln(x+1)-∫(x+1)*1/(x+1) dx
=(x+1)ln(x+1)-∫dx
=(x+1)ln(x+1)-x+C