How to Evaluate the Integral of x^2 * e^(-2*a*x^2) from 0 to Infinity?

[eku_girl83]

Evaluate the integral of x^2 * e^(-2*a*x^2) with respect to x as x ranges from 0 to infinity.

I can't find anything in the integral tables that match this exactly...Can someone help me out?

 

[NateTG]

Evaluate the integral of x^2 * e^(-2*a*x^2) with respect to x as x ranges from 0 to infinity.

I can't find anything in the integral tables that match this exactly...Can someone help me out?

That looks like a straightforward substitution to me.

Sorry. misread the integral.. thougt it was 2xe^...

Try using integration by parts - x^2 e ^{-2ax^2}=x \times xe^{-2ax^2}

 

[Dr Transport]

integrate by parts or chage variables and let 2a = b, I'm sure there is a listing for
\int^{\infty} _{0} x^{p} e^{-bx^{2}} dx.