Answer
$x^2 e^x+ e^x+c$
Work Step by Step
Integration by parts formula suggests that $\int p'(x) q(x)=p(x) q(x)-\int p(x) q'(x)dx$
$\int (x+1)^2 e^x dx=\int (x^2+2x+1) e^x dx$
or, $\int (x^2+2x+1) e^x dx=\int x^2 e^x dx+\int 2x e^x dx+\int e^x dx=x^2 e^x-\int 2x e^x dx+\int 2x e^x dx+e^x +c$
Thus, we have
$x^2 e^x-\int 2x e^x dx+\int 2x e^x dx+e^x +c=x^2 e^x+ e^x+c$
