The Logarithmic Integral li(x)

Here we have the Logarithmic Integral.
We integrate from 2 to x for the reciprocal of ln(t). We choose 2 to x as it is key in showing the Prime Number Theorem.
Hence this is video number 3 in the Prime Number Theorem series.
Integration by Parts is the way shown and we can see even after integration by parts thrice we are in a never ending spiral.
Hence li(x) is a Non-Elementary Integral and has no solution by traditional methods.
The Prime Counting Function part 2
#primenumbers
#primes
#primenumber
#logarithm
#logarithmicfunction
#logarithmic
#integrationbyparts
#logarithmic_differentiation
#logarithmicfunctions

[@MikeT10101]

I recently subscribed to your channel and am glad I did. I really appreciate your clear, thorough, and direct teaching style.

[@omargaber3122]

You are one of the shadow geniuses. Idiots are busy with trivial matters now. I hope you add an introduction of yourself on KZbin. Thank you very much.

[@PunmasterSTP]

This video was great, no li!