Using the method $of$ substitution,

where

$u=$

$du=,dx$

$f(u)=$

$.$

Using the above information:

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}{x}^2(1+3x^3{)}^{3}dx$

$={\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}f(u)du$

$=|,u=+,x$