It's better to generalize this

Calculus Level 5

0ex3dx \large \int_0^\infty e^{-x^3} \, dx

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

Bonus: Generalize this for 0exAdx\displaystyle \large \int_0^\infty e^{-x^A} \, dx with positive number AA.

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