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Calculus Level 4

If \[ \displaystyle \int_0^\infty e^{ -x^{\frac {5}{2}} } \ \mathrm{d} x \] can be expressed in the form of \[ \dfrac {a}{b} \Gamma \left ( \dfrac {2}{5} \right ) \] for positive coprime integers \(a\) and \(b\). Find \(a + b \).

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