Hey guys, after differentiating $\displaystyle y=x^{2}e^{-x^{2}}$by the product rule to get $\displaystyle y=2xe^{-x^{2}}-2x^{3}e^{-x^{2}}

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how do I use this result when integrating $\displaystyle \displaystyle\int x^{3}e^{-x^{2}}\,dx$

thanks a lot