Help for integration

1. The problem statement, all variables and given/known data
[tex]\int_{0}^{∞} x^{2n+1}.e^{-x^2}dx[/tex]
is equal to (n ε N)
a)n!
b)2(n!)
c)n!/2
d)(n+1)!/2

2. Relevant equations



3. The attempt at a solution
I can go on solving this by using n=1 or n=2. But i want to do it by a correct method. Is there a proper way to do it? I am having no idea, how should i begin?

 

Hello uart!

I have already tried that substitution and i end up with this:
[tex]\frac{1}{2} \int_{0}^{∞} u^n \cdot e^{-u}du[/tex]
Gamma function? I guess i have never heard of it.
Any other way to solve it? If there's no way, i would try to see what this "gamma function" is.

 

Thanks a lot uart!