How do you find the integral of x ln x from (1,0)?
You can integrat by Parts to get:
You can do this slightly differently as well.
From the Fundamental Theorem of Calculus and basic properties of Integrals, where
Using Integration by Parts, let:
Let's do the limit instead, on the right term, due to an indeterminate form, and then L'Hopital's Rule.
Thus, the answer is