Integrate....... x^2 * exp(-x^2 / 2)...?

Question

i need urgent help in integrating this function. Please provide some explanation too.

Thnx...

need more time to analyze ur answer, z_o_r_r_o....But thnx a million anywayz....

Answer 1

Hmmm, that's a tricky one....

Try by parts:

u=x

dv = x * exp((-x^2)/2)

du = dx

v= -2exp((-x^2)/2)

-2x exp((-x^2)/2) + 2 Integral (exp(-x^2)/2))

If this were a probability question, the integral from -infinity to +infinity of exp((-x^2)/2) is the integral under the bell curve which turns out to be one.

Other than that, I am not sure how to approach this problem.

Answer 2

This integral is not elementary. It's solution involves
the error function. Zorro's work is essentially correct.