Step $2$

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 ${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}{x}^2(u{)}^{\frac{1}{2}}dx=$ We must also convert $x^{2}dx$ into an expression involving $u.$

We know that $du=3x^{2}dx,$ so $x^{2}dx=,\frac{1}{3}du.$

Step $3$

INow, if $u=x^3+36,$ then ${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}{x}^2\sqrt[\phantom{2}]{x^3+36}dx={\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}{u}^{\frac{1}{2}}(\frac{1}{3}du)=\frac{1}{3}{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}{u}^{\frac{1}{2}}du.$

This evaluates as follows. $($Enter your answer in terms of u$.)$

$\frac{1}{3}{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}{u}^{\frac{1}{2}}du=,+C$

SKIP $($YOU CANNOT COME BACK$)$

$[1/1$ Points$]$

Evaluate the integral by making the given substitution. $($Use C for the constant of integration.$)$

$4(2)(2)(2)(2)$