Probability - u substitution to find gamma function.

[sirhc1]

Homework Statement

\int_0^∞ x^2exp(-x/2) dx

Homework Equations

The Attempt at a Solution

Using u substitution:

u = x/2
du = 1/2 dx

\int_0^∞ 4u^2exp(-u) du*2
= 8 \Gamma(3)
= 8*3!
= 48

But the correct answer is 16 when I plug it in Wolfram's definite integral calculator. I don't see where's my mistake?

Thank you very much!

 

[sirhc1]

Wow, Gamma(3) = 2!, not 3!. Silly me! Thanks anyways.