Prove that: `I_n=int_0^oox^(2n+1) e^ (-x^2) dx=(n !)/2,n in N`.

Explanation

To prove that

\[ I_n = \int_0^\infty x^{2n+1} e^{-x^2} \, dx = \frac{n!}{2}, \quad n \in \mathbb{N}, \]

we will follow these steps:

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