I've got two improper integrals, and need to determine whether or not they are convergent.

1) 1/(x*sqrt(x+3)) integrated from 1 to infinity

I said that this function was =< 1/x, and was hoping to say that the integral from 1 to infinity of 1/x converged, therefore my given function would... but that's not the case

Can someone point me in the right direction? I know that it's supposed to converge, but is there an easy way to see this?

2) (x^2)e^(-x^2) from 0 to infinity

No idea where to go with this one, any hints? Something I should look for?

Thanks!!