Antiderivatives practice question 8

Compare the factor $x^{2}$ in front with the exponent $x^{3}$. How are they related, and which rule, run backwards, does that suggest?

Try $e^{x^{3}}$: $\dfrac{d}{dx}e^{x^{3}} = 3x^{2}e^{x^{3}}$, so $F(x) = 2e^{x^{3}} + C$.

Now use $F(0) = 0$ to find $C$. What is $2e^{x^{3}}$ at $x = 0$?