I had to examine every pixel on Desmos looking for clues

[@artemetra3262]

desmos tip: you can hold shift and stretch individual axes, and from that you'll be able to stretch the y axis and see the area between 2 and 3 more easily

[@owlsmath]

nice tip! I never knew that before. thanks!

[@MikeMagTech]

Bringing the dilogarithm in was a nice move ; )

[@owlsmath]

thanks Mike! I think it was necessary in this case :)

[@calculusmethods]

Very Nice solution

[@owlsmath]

Thank you! 🙏👍

[@r1ckthe]

what’s Li_2?

[@owlsmath]

It's the Dilogarithm. I have a playlist if you want to know more: th-cam.com/play/PLOvxeHw2nLayk5tB1Lav9RDddMDOZIDBM.html
Or wikipedia is helpful: en.wikipedia.org/wiki/Dilogarithm

[@maxvangulik1988]

t=e^-5x
-dt/5t=dx
I=1/5•int[e^-10,e^-15](-ln(1-t)/t)dt
I=(Li_2(e^-15)-Li_2(e^-10))/5

[@owlsmath]

thanks!

[@erezsolomon3838]

Can you generalize this integral for any s and not just 5?

[@owlsmath]

Hi Erez. Yes you definitely can. Also you can generalize the bounds too to get a formula with 3 constants. Basically it’s the same steps I did in the video I think 👍

[@doronezri1043]

Excellent catch with the dilogarithm 👏👏👏

[@owlsmath]

@@doronezri1043 thanks! :)

[@reaperskyfall6691]

New type hard one for me

[@owlsmath]

makes sense. It's a strange looking solution!