How do you solve #intx/(x-4)# #dx#?

1 Answer
Oct 23, 2017

# I = x + 4ln|x-4| + C #

Explanation:

We seek:

# I = int \ x/(x-4) \ dx #

We can write as:

# I = int \ ((x-4)+4)/(x-4) \ dx #
# \ \ = int \ (x-4)/(x-4) + 4/(x-4) \ dx #
# \ \ = int \ 1 + 4/(x-4) \ dx #
# \ \ = x + 4ln|x-4| + C #