Today, we use complex analysis to evaluate the improper integral from 0 to infinity of ln(x)/(x^n+1) where our n is a real number greater than 2. We also come across some other familiar results which you can check out in more detail through these links to other videos I have created:
Solutions to z^n+1=0:
https://www.youtube.com/watch?v=LqS5hoHSnCQ
Integral of 1/(x^n+1):
https://www.youtube.com/watch?v=iWt_XL3JvXE&t=377s
Logarithm of complex numbers:
https://www.youtube.com/watch?v=mFyfpkVjVMk
Complex exponential definition of sine:
https://www.youtube.com/watch?v=bun_ucJVWr8
Outtakes for integral over Gamma and gamma:
https://www.youtube.com/watch?v=FvG629wTEbo