how to find the right integral for comparison test?

Question

I should determine whether this is a convergent or divergent integral. i need to use the comparison test but i don't know where to start.

$$ \int_{1}^{\infty} e^{-\sqrt{x}}dx $$

Answer 1

Let $u = \sqrt{x}$ then $x = u^2 \to dx = 2udu \to I = \int_{1}^\infty 2ue^{-u}du$. I am sure you can continue with integration by part to finish.