The value of \( \int_{0}^{\infty} x^{2 n+1} e^{-x^{2}} d x, n \in N \) (a) \( n ! \) (b) \( (n+1...

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The value of \( \int_{0}^{\infty} x^{2 n+1} e^{-x^{2}} d x, n \in N \)
(a) \( n ! \)
(b) \( (n+1) \) !
(c) \( \left(\frac{n !}{2}\right) \)
(d) \( \left(\frac{n+1 !}{2}\right) \)
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