\displaystyle \int t^2e^{\frac{-t^2}{2}}dt=\left{t=u, du=1, v'=te^{\frac{-t^2}{2}}, v=-e^{\frac{-t^2}{2}} \riht}=-te^{\frac{-t^2}{2}}+\int e^{\frac{-t^2}{2}}dt