https://mindyourdecisions.com/blog/2023/07/06/bottle-burger-beer-hot-dog-viral-puzzle/
"As viral puzzles became popular, mathematicians joined the game too. Here’s a fun puzzle that has been widely shared."
The first 3 lines are trivial, but it's been a while since I did any calculus. Would you use integration by parts for it?
Wolfram gives me:
::: spoiler spoiler 5/2 🥧 :::
I don’t think that would work. You just use the fact that the integral from negative to positive infinity of sin(x)/x is pi, so from 0 to infinity it is pi/2, which you can derive from using Feynman’s trick for computing weird integrals like these.
:::