原式=∫ln(x+2)dx²
=x²ln(x+2)-∫x²dln(x+2)
=x²ln(x+2)-∫(x²-4+4)/(x+2) dx
=x²ln(x+2)-∫[x+2+4/(x+2)] dx
=x²ln(x+2)-x²/2-2x-4ln|x+2|+C