From Mystery Recapped recap of part1 of South Korean series I'm Not a Robot (video is Man Is Allergic To Human Touch, So Spends $1M On Female Robot; Turns Out She's Human In Disguise)
It looks like
$$p(r)=\frac{4}{a_0^3}r^2e^{\frac{-2r}{a_0}}, r \ge 0$$
and has some antiderivative
$$P(r) = \int_0^r \frac{4}{a_0^3}s^2e^{\frac{-2}{a_0}}, r \ge 0$$
- Is the integrand missing an $s$? I think it's supposed to be
$$P(r) = \int_0^r \frac{4}{a_0^3}s^2e^{\frac{-2s}{a_0}}, r \ge 0$$
- Btw the way to integrate $\int x^2 e^{-x} dx$ is like double integration by parts with $u=x$ and $dv = xe^{-x} dx$?
Yes, it's a typo.
No need. It's just $u=x^2$. https://www.wolframalpha.com/input?i=integrate+x%5E2+e%5E%28-x%29+dx
I was thinking of something else namely $\int(2x^2+1)e^{x^2}dx$