If $u=x^3+36$ is substituted into ${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}{x}^2\sqrt[\phantom{2}]{x^3+36}dx,$ then we have ${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}{x}^2(u{)}^{\frac{1}{2}}dx={\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}{u}^{\frac{1}{2}}{x}^{2}dx.$

We must also convert $x^{2}dx$ into an expression involving $u.$

We know that $du=3x^{2}dx,$ and so $x^{2}dx=du.$