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

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SUMMARY

The integral of x^2 * e^(-2*a*x^2) from 0 to infinity can be evaluated using integration by parts or variable substitution. Specifically, substituting 2a with b simplifies the integral to a known form: ∫ from 0 to ∞ x^p * e^(-bx^2) dx. This approach allows for the application of established integral tables to find the solution effectively.

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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?
 
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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 - [itex]x^2 e ^{-2ax^2}=x \times xe^{-2ax^2}[/itex]
 
Last edited:
integrate by parts or chage variables and let [tex]2a = b[/tex], I'm sure there is a listing for
[tex]\int^{\infty} _{0} x^{p} e^{-bx^{2}} dx[/tex].
 

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