Question

Integrate 1/x(x-1) dx

Answer 1

Decompose the integrand into partial fractions:

1 / (x (x - 1)) = 1/(x - 1) - 1/x

Then

∫ 1 / (x (x - 1)) dx = ln|x - 1| - ln|x| + C = ln|1 - 1/x| + C