Need help with single variable integral I need help with the following integral. I used integration by parts to get started but I have no idea where to go from there. If someone could please show me step by step how to solve this, I would be most appreciative!
$$
\int_0^\infty 4y^{2}e^{-2y}dy\,.
$$

Hint: 
Use integration by parts, twice.
Start with $$u = 4y^2\implies du = 8y\,dy\\dv = e^{-2y} dy\implies v = -\frac 12e^{-2y}$$ Where the integral evaluates to $$uv - \int v\,du$$ That gives us, to start, $$4y^2\cdot -\frac 12e^{-2y} - \int -\frac 12 e^{-2y}(8y\,dy)\\ = -2y^2 e^{-2y} + 4\int ye^{-2y}\,dy$$
Now, one more application of integration by parts, and you're there.
