Understanding substitution to compute primitive To compute the primitive
$$\int x^2 \sqrt[3]{x^3+3}\ dx$$
I am trying this:
$t = x^3+3$
$dt = 3x^2dx$
but
$\int x^2 \sqrt[3]{x^3+3}\ dx=\ ?$
How to continue from here?

Make the substitution $t=x^3+3$. Then $dt=3x^2dx$, and we have
$$
\frac{1}{3}\int t^{1/3}dt = \frac{1}{3}\left(\frac{3}{4}t^{4/3}\right) + C=\frac{1}{4}\left( x^3+3\right)^{4/3} +C.
$$
