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$\displaystyle\int_0^\infty x^3 e^{-x}\, dx = ?$

A$3!$
B$3$
C$e^{-3}$
D$\infty$
Answer & Solution
Correct answer: A. $3!$
**Gamma:** $\Gamma(n+1) = \int_0^\infty x^n e^{-x}\, dx = n!$. Here $n = 3$: result $= 3! = 6$.
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