You may use the formula
∫udvdx dx=uv−∫vdudx dx\displaystyle\int u\frac{dv}{dx}\,dx = uv - \int v\frac{du}{dx}\,dx∫udxdvdx=uv−∫vdxdudx
Use integration by parts, twice, to find
∫x2ex dx\displaystyle\int x^2 e^x\,dx∫x2exdx