Answer
$$\int x^2e^{x^3}dx=\frac{e^{x^3}}{3}+C$$
Work Step by Step
$$A=\int x^2e^{x^3}dx$$
Let $u=x^3$
Then $du=(x^3)'dx=3x^2dx$. So $x^2dx=\frac{1}{3}du$
Substitute into $A$, we have $$A=\int e^u(\frac{1}{3})du$$ $$A=\frac{1}{3}\int e^udu$$ $$A=\frac{1}{3}e^u+C$$ $$A=\frac{e^{x^3}}{3}+C$$
