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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