Time for easier problems 2

Let the integral be $I$ , then we have:

$\begin{aligned} I & = \int_0^\infty x^2 e^{-\sqrt{x}} dx \quad \quad \small \color{#3D99F6}{\text{Let }t^2 = x, \space 2t \space dt = dx} \\ & = 2 \int_0^\infty t^{\color{#3D99F6}{6}-1} e^{-t} dt \\ & = 2\Gamma (6) \quad \quad \quad \quad \quad \quad \small \color{#3D99F6}{\Gamma (n) \text{ is Gamma function}} \\ & = 2(5!) = \boxed{240} \end{aligned}$