# It's better to generalize this

Calculus Level 5

$\large \int_0^\infty e^{-x^3} \, dx$

If the integral above equals to $\Gamma \left( \frac ab \right)$ for coprime positive integers $a,b$, find the value of $a+b$.

Bonus: Generalize this for $\displaystyle \large \int_0^\infty e^{-x^A} \, dx$ with positive number $A$.

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