AQA Core 3 7.04b Integration by Parts TWICE: an indefinite integral example

[husseinjusab]

I understand how the LATE rule works but what if there is a product of two functions where both are algebra then how do you determine what "u" should be?

[Nick-uxzt]

Could you not take e^x out at the end and write it as e^x(x^2-2x+2)+c ?