Highschool tricks

Calculus Level 3

\[ \large \int_0^\infty x^2 e^{-\left( x^2 + \left(\frac{3}{2x}\right)^2 \right)} \ dx = \ \frac {\sqrt[a]\pi}{e^b} \]

The equation above holds true for positive integers \(a\) and \(b\). Find the value of \(a+b\).

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