A trickier example

(Wednesday, August 25, 2021)

6)

$\int x^{3}e^{-x^{2}}~{}dx$

For this one, there are two options: first is to write $x^{3}=x^{2}\cdot x$ , and to set $u=x^{2}$ . (Why is this a good idea?) The other is to let $w=x^{2}$ and do a substitution first; you should recognize the resulting integral.