Integral using integral tables

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
Homework Helper
eku_girl83 said:
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 - $x^2 e ^{-2ax^2}=x \times xe^{-2ax^2}$

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