How to solve an integration problem involving exponential functions?

[stunner5000pt]

How do i solve
$$\int_{0}^{\infty} \lambda^2 r e^{-\lambda r} dr$$

if i were to integrate it i get
$$\left[-e^{-lambda r} (1 + r \lambda)\right]_{0}^{\infty}$$

what is $$\lim_{r \rightarrow \infty} \frac{r}{e^r}$$

is it zero?? by virtue of e increasing faster than r ??

 

[dextercioby]

The exponential increases faster than any polynomial.

Daniel.