<s>[INST] 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?
 [/INST] Take the differential form ($dx$) out from underneath the squareroot sign. It reads $\int x^2\cdot (x^3+3)^{1/3} dx = 1/3 \int (3x^2 dx)\cdot (x^3+3)^{1/3} = 1/3\cdot (x^3+3)^{4/3} / (4/3) + c = \frac{(x^3+3)^{4/3}}{4} + c$.
</s>