Question

how do I solve this improper integral?

\[\int^{\infty}_{-\infty}\lambda x^2 e^{-2\lambda |x|}dx\]

Answer 1

I have already broken it into two integrals and used integration by parts twice. but I cannot "plug" the infinities in the end to get the definite integral...

Answer 2

like how do I figure out what \[\left. \frac{e^{2 \lambda x} \left(2 \lambda ^2 x^2-2 \lambda x+1\right)}{4 \lambda ^3}\right|^0_{-\infty}\]