SF2

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$\int_0^\infty x^6 e^{-2x}dx\,$

Let $y = 2x, dx=dy/2\,$ .

$\int_0^\infty \left(\frac{y}{2}\right)^6e^{-y}\frac{dy}{2}\,$

$=\frac{1}{2^7}\int_0^\infty y^6e^{-y}dy = \frac{\Gamma(7)}{2^7} = \frac{6!}{2^7} = \frac{720}{128} = \frac{45}{8}\,$

Special Functions

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