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## Main Question or Discussion Point

I ran into an integral while working on response of a signal processing filter, it looks like:

[tex]\int_{-\infty}^{\infty} x^{2} e^{-x^{2}} dx [/tex]

While trying integration by parts u = [tex]x^{2}[/tex] we get du = 2xdx but can't proceed with dv = [tex]e^{-x^{2}}[/tex] because then

v = [tex]\int e^{-x^{2}}[/tex]

can't be integrated unless we use the limits.

Can anyone suggest an approach for this?

Thanks,

Niks

[tex]\int_{-\infty}^{\infty} x^{2} e^{-x^{2}} dx [/tex]

While trying integration by parts u = [tex]x^{2}[/tex] we get du = 2xdx but can't proceed with dv = [tex]e^{-x^{2}}[/tex] because then

v = [tex]\int e^{-x^{2}}[/tex]

can't be integrated unless we use the limits.

Can anyone suggest an approach for this?

Thanks,

Niks