∫(x^2e^x)/(x+2)^2dx
=∫e^x(x^2+4x+4-4x-8+4)/(x+2)^2dx
=∫e^x(x+2)^2-4(x+2)+4)/(x+2)^2dx
=∫e^x[(x+2)^2-4(x+2)+4]/(x+2)^2dx
=∫e^x[1-4/(x+2)+4/(x+2)^2]dx
=∫e^x-4e^x/(x+2)+4e^x/(x+2)^2dx
=e^x-4∫e^x/(x+2)dx+4∫e^x/(x+2)^2dx
=e^x-4∫e^x/(x+2)dx-4∫e^xd[1/(x+2)]
=e^x-4∫e^x/(x+2)dx-4e^x/(x+2)-4∫1/(x+2)de^x
=e^x-4∫e^x/(x+2)dx-4e^x/(x+2)+4∫1/(x+2)de^x
=e^x-4e^x/(x+2)+C
