How do you find the integral of xln(x) dxxln(x)dx from 0 to 1?
3 Answers
Solution
Integrating by parts
Because
This is an improper integral, so we use:
Use integration by parts (with
Recalling that
But,
Rewriting as:
Applying l'Hopital's Rule gives us:
So, we conclude:
The integration by parts of x ln(x) would be as follows:
ln(x)
ln(x)
ln(x)
On taking limits from 0 to 1, the final answer would be